1. Principal × percent interest = interest earned
Principle× (0.075)× 1/(12 x 4) = $68. Solve to find the principal (68 × 12 x 4)/0.075=
$43,520. The correct answer is D.
2. Use the factors of 120 are: 1x120, 2x60, 3x40, 10x12, 4x30, 5x24, 6x20 and 8x15.
We are looking for combinations of (row x column) that are all between 8 and 30.
The possibilities are: 8x15, 15x8, 4x30, 30x4, 5x24, 24x5, 6x20, 20x6, 10x12 and
12x10. That is 10 possibilities total. The correct answer is E.
3. The total estimated amount that will be spent on type A product next year:
5625$
1001254500$=×.
The total estimated amount that will be spent on type B product next year:
9130$
1001108300$=×.
Giving a total spending of $14,755. The correct answer is A.
4. The side of a cube equals the cubic root of its volume; in this question it is 4. The
lateral area of a cube equals the sum of four faces; in this question each face is 16, and
the lateral area is four times that, giving 64. The correct answer is B.
5. The fact that X is divisible by 7 does not help figure out whether it is odd or even,
both even and odd numbers could be divisible by 7. The same applies for 11; both
even and odd numbers could be divisible by 11. Both statements taken together do not
shed a new light on the matter, there could be even and odd numbers that are divisible
by 7 and 11. The correct answer is E.
6. The prime factors of 22 are 2 and 11. Hence, if X is divisible by 4, it is divisible by
2 and if Y is divisible by 11, surely XY is divisible by 22. The correct answer is C.
7. Since three digits are zero, only 4 digits are left for consideration (of which, none is
zero). Since 1 does not appear in the numbers, there are 4 even numbers (without 0),
and 4 odd numbers (without 1) to choose from. The probability for every digit to be odd is
21. There are 4 different ways to arrange 3 odd numbers and one even number
in 4 places. Each of these ways has a probability of ()214. And together:
()16416144214=×=×. The correct answer is D.
8. From 8:00 am to 9:00 am, Pipe A, which fills the pool in 4 hours, was open for one
hour, filling one quarter of the pool. From 9:00 am, the two Pipes worked together at
the rate of:
1216141=-, one pool in 12 hours. Since the pool was already one quarter
full at 9:00 am, it will take only 9 hours to fill the remaining three quarters of the
pool. 9 hours from 9:00 am is 18:00. The correct answer is C.
9. Since a2-b2=(a+b)(a-b), 133=(a+b)7, and (a+b)=19.
Both statements are needed to solve the question. The correct answer is C.
10. Each statement alone leaves out one of the terms x or z, so we cannot find their
sum using any statement alone. Moreover, even combining both statements does not
help:
1113xzz13x11z13yx 11y13yz 11yx-=-
-=-
-=-=
=+=+
It is only possible to find z-x. The correct answer is E.
11. Knowing the interest alone is not enough to calculate the profit.
Knowing the total amount invested is not enough to calculate the profit, unless we
have the interest rate.
Since we have no knowledge of the amount invested in each investment, there is no
way to know how much was earned. The correct answer is E.
12. The only two possible sets that have 4 different positive integers and an average of
3 are: [1, 2, 3, 6] and [1, 2, 4, 5]. The sum of the two smallest integers in both sets is
always 3. The correct answer is C.
13. If X is the number of students in the largest class, then the numbers of students in
the other classes are: X-2, X-4, X-6 and X-8. The total number of students is:
958)(X6)(X4)(X2)(XX=-+-+-+-+ and 23X1155X95205X=.=.=-.
The correct answer is D.
14. Take 40 litters as the volume of the large container to ease the calculations. Of this
volume, 20 litters are ice cream. The volume of the second is 20 litters and 15 litters
are ice cream. So, the total volume of both containers is 40+20=60, and the ice cream
is 20+15=35. Now,
1276035=. The correct answer is B.
15. Solve a combined average problem: 8%
X)(480%X10%48=+
×+×. The correct
answer is B.
16. The average age of both groups, x and y was n five years ago. Therefore, it is
possible to treat them as one group with that average. Five years later, each student
added 5 years to his age, adding 5 to the average of the whole class, and making it
n+5. The correct answer is: A.
17. The rate of the “racing magic” is 40 rounds per hour, or 1 round every 1.5
minutes. The rate of the “Charging bull” is 1 round every 120 seconds, or 1 round
every 2 minutes.
The best way to solve such a question is to find the least common denominator
between the two rates. At that point, they will meet for the first time, and when
multiplied by 2, we find the second time they meet:
64631.5121.=.. They will
meet for the first time after 6 minutes and for the second time after 12 minutes. The
correct answer is D.
18. The first statement gives no information of the number of cookies. The volume of
the carton box or the percent of its volume filled, do not help in finding any number.
The second statement gives all the information needed in order to find the number of
cookies packed in each carton box. The number of cookies per jar, and the number of
jars per box are sufficient to calculate real numbers. The correct answer is B.
19. In order to find the value of a term in an equation with two unknowns, two
different equations are needed. Since both equations given in statements 1 and 2 are,
in fact, the same equation in a different shape, it is impossible to find the value of X
or Y. 2X3Y3119Y46X=-.-=. The correct answer is E.
20. After spending one quarter of the budget on rent, 75% is left, of that half = 37.5%
is spent for food and beverages. The correct answer is D.
21. Compare x oranges to y peaches at the price of 24 cents per peach. Divide by 100
to receive the amount in dollar:
x100y24O10024yOxPeachesyOrangesx=.=×.×=×. The correct answer is D.
22. Compare the volumes: 3333331RrRr3Rp34rp343=.=×.=×. The correct
answer is A.
23. Since x=y and both are primes,
yx11+could equal 32 when x=y=3, or equal 1
when x=y=2. Therefore, the first statement is not sufficient to solve.
According to the second statement, x+y=4, the only primes to match are x=y=2. Now
we know that yx11+=1 and the question is solved. The correct answer is B.
24. Statement (1) tells us that the diameter of the ball is the height of cube, so we can
find its volume.
Statement (2) actually tells us that the box is a cube, and the rest is similar to
statement one. The correct answer is D.
25. Statement (1) can provide us the height of the cylinder while statement (2) gives
us data we already can conclude from the question. The correct answer is A.
26. The car travels 160 miles in 160 minutes, that is 1 mile per minute. So, it travels
60 miles in 60 minutes, or 60 miles per hour. The correct answer is B.
27. . And x=5. The correct
answer is: E.
186X7)X42221618X67)X418X67X+=+.=.=++++((
28. First find z: z+5+7=16, therefore, z=4. Now, y+4+5=7 making y=(-2). Now we
can find x: x+(-2)+4=5, so, x=3. Hence, x+y=3+(-2)=1. The correct answer is: C.
29. John spends a sum of m dollars and still has m-800 left. So, m+m-800=1,600, and
m=$1,200. Therefore, John still has $1,600-$1,200=$400. The correct answer is B.
30. Calculate the odds of not winning first, second or third prize by deducting the
chances of winning first, second or third from 1:
200193501100120011=..
.
..
.++-. The
correct answer is: C.
31. The red painted area is 3 half faces and the white painted area is a total of 9 half
faces. The ratio is, therefore, 1 to 3. The correct answer is: E.
32. Statement (1) defines the relationship between X and Y.
Statement (2) defines the relationship between Y and R.
We get the following equations:
10 x X + R x Y = 12 (X+Y), Y=X+5, and Y=R. Now solve and find R. The correct
answer is C.
33. Since we don’t know how many children there are at all, it won’t help us to know
the relationship between the child who left and the shortest child.
Statement (2) defines the connection between the sum of the heights before and after
the departure and using the change in the sum divided by the new number of children
we can find the number of children. The correct answer is B.
34. Since we have no concrete info about the exact heights, or about the value of P
and R, we cannot determine whether the NBA players or the weight lifters are taller.
We need more data. The correct answer is E.
35. Statement (1) can tell us the value of Y, and the value of X, which is enough to
solve this problem.
Statement (2) alone only defines the connection between X and Y. The correct answer
is A.
36. Two out of every 10 damaged light bulbs have a broken glass, so if 20 bulbs have
a broken glass, there are 100 damaged light bulbs. Since one out of every 500 is
damaged, there are light bulbs in the shipment. The correct answer
is D. 00050500100,=×
37. Since the even number a is raised to the power of 3, it is always divisible by 8.
Therefore, the whole expression must be an integer, an even or an odd one. Of course,
the expression cannot be a fraction. The correct answer is E.
Click ere to view the answers
Thursday, August 20, 2009
Answers and Explanations to Test 3
GMAT Quantitative Test 3
75 minutes
Have a good GMAT exam.
1. An investment yields an interest payment of $68 each week. If the simple annual
interest rate is 7.5%, what is the amount of the investment assuming there only 48
weeks are calculated in a year?
(a) $28,600
(b) $30,430
(c) $34,330
(d) $37,860
(e) $43,520
2. The flying acrobatic team is made up of 120 airplanes. The team wants to form a
rectangular formation with X planes in a row and Y planes in a column. If the number
of airplanes in a row is no less than 4 and no more than 30, how many different
combinations of rectangular shapes are possible?
(a) 4.
(b) 5.
(c) 6.
(d) 8.
(e) 10.
3. A storeowner estimates that the average price of type A products will increase by
25% next year and that the price of type B products will increase by 10% next year.
This year, the total amount paid for type A products was $4500 and the total price
paid for type B products was $8300. According to the store owner’s estimate, and
assuming the number of products purchased next year remains the same as that of this
year, how much will be spent for both products next year?
(a) $14,755
(b) $15,325
(c) $16,000
(d) $16,225
(e) $17,155
4. If a cube has a volume of 64 cubic feet, what is its lateral area?
(a) 16
(b) 24
(c) 48
(d) 64
(e) 96
5. Is the integer X even?
(1) X is divisible by 7.
(2) X is divisible by 11.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
6. Is the product XY divisible by 22?
(1) X is divisible by 4.
(2) Y is divisible by 11.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
7. A seven-digit combination lock on a safe has zero exactly three times, does not
have the digit 1 at all. What is the probability that exactly 3 of its digits are odd?
(a) 21
(b) 31
(c) 61
(d) 164
(e) 169
8. Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe
A was opened at 8:00 am and Pipe B at 9:00 am, at what time will the pool be full?
(a) 15:00
(b) 17:00
(c) 18:00
(d) 19:00
(e) 20:00
9. What is the value of (a+b)?
(1) a2-b2=133.
(2) a-b=7.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
10. What is the value of X+Z?
(1) X+Y=11
(2) Z+Y=13
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
11. What was the total amount John earned on his two investments?
(1) John received an annual interest of 5% on one investment and 13% on the other.
(2) John invested a total of $15,000 on both investments.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
12. What is the sum of the two smallest integers in a set of different positive integers?
(1) There are 4 integers in the set.
(2) The average of the integers in the set is 3.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
13. In a school with 5 classes, each class has 2 students less then the previous class.
How many students are there in the largest class if the total number of students at
school is 95?
(a) 17
(b) 19
(c) 21
(d) 23
(e) 25
14. A cylindrical ice cream container is half filled with ice cream. A second ice cream
container, half the size of the first one is filled to three quarters of its volume with ice
cream. What fraction of the total volume of the two containers is filled with ice
cream?
(a) 129
(b) 127
(c) 32
(d) 65
(e) 2415
15. A 48 gallon solution of salt and water is 10% salt. How many gallons of water
must be added to the solution in order to decrease the salt to 8% of the volume?
(a) 8
(b) 12
(c) 13
(d) 14
(e) 16
16. Five years ago, the average age of the X students in the class was n. What is their
average age now, if Y more students whose average age was also n five years ago,
joined the class?
(a) 5n+
(b) 5n-
(c) 52yx++
(d) 52yx-+
(e) None of the above
17. The “Racing magic” takes 120 seconds to circle the racing track once. The
“Charging bull” makes 40 rounds of the track in an hour. If they left the starting point
together, how many minutes will it take for them to meet at the starting point for the
second time?
(a) 3
(b) 6
(c) 9
(d) 12
(e) 15
18. If cookies are put in a jar and the jars of cookies are packed in a carton box, how
many cookies does one carton box contain?
(1) Every carton box is filed to half its volume.
(2) Twenty cookies are put in each jar, and 12 jars are put in each carton box.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
19. If X and Y are integers, what is the value of X?
(1) YX946-=
(2) XY23311=-
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
20. A restaurant spends one quarter of its monthly budget for rent and half of the rest
for food and beverages. What percentage of the budget does the restaurant spend for
food and beverages?
(a) 23.5%
(b) 32.5%
(c) 35%
(d) 37.5%
(e) 75%
21. If x oranges cost as much as y peaches do, and peaches cost 24 cents each, how
many dollars does each orange cost?
(a) xy2400
(b) x24y
(c) 24x100y
(d) 100x24y
(e) 24xy
22. The sum of the volumes of three spheres, each with radius r, equals to the volume
of a single sphere with radius R. What is the ratio between r and R?
(a) 1: 33
(b) 1: 3
(c) 1:2
(d) 1: 32
(e) 1:3
23. If x and y are primes, and x@y=
yx11+, is x@y<1?
(1) x=y
(2) x+y=4
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
24. A ball with a diameter of 10 cm is inscribed inside a rectangular box so that it
touches all internal faces of the box. What is the volume trapped between the box and
the ball?
(1) The box is a cube
(2) The surface area of the box is 600 cm2.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
25. A rectangular box is inscribed inside a cylinder. Both the width and length of the
box is 2 cm. What is the volume of the cylinder?
(1) The volume of the box is 20 cm3.
(2) The radius of the cylinder is 2.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
26. A car travels a distance of 160 miles in 2 hours and 40 minutes, what is the speed
of the car in miles per hour?
(a) 54
(b) 60
(c) 84
(d) 116
(e) 120
27. If , what is x? 21618X67X++=
(a) 9
(b) 8
(c) 7
(d) 6
(e) 5
28. In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum
of the three numbers preceding it. What is x+y?
(a) -5
(b) -1
(c) 1
(d) 5
(e) 6
29. John has $1,600 at the beginning of his trip, after spending money, he still has
exactly $800 less than he spent on the trip. How much money does John still have?
(a) $200
(b) $400
(c) $600
(d) $800
(e) $1,200
30. The odds of winning first prize at the casino are 1 to 200. The odds of winning
second prize are 1 to 100 and of winning third prize are 1 to 50. If no one person can
win more than one of the prizes, what is the probability of not winning the first,
second or third prize?
(a) 20014
(b) 5047
(c) 200193
(d) 2007
(e) 10097
31. A cube has three of its faces painted half red, half white. The other three faces are
completely painted white. What is the ratio between the total red painted and the total
white painted areas of the cube?
(a) 1:6
(b) 3:6
(c) 1:2
(d) 1:4.5
(e) 1:3
32. There are X watermelons of 10 Kg each, and Y Watermelons of R Kg each. The
average weight of a watermelon is 12 Kg. What is the value of R?
(1) There are five heavier watermelons more than lighter watermelons.
(2) The weight of the heavier watermelons in Kg is equal to their number.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
33. The average height of a group of children is 125 cm. If one of the children leaves,
the average height drops by 2 cm. how many kids were there originally?
(1) The height of the child who left is twice greater than the height of the shortest
child.
(2) The height of the child who left is 130 cm.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
34. P is the standard deviation of the heights of NBA basketball players. R is the
standard deviation of the heights of 8 weight lifters. Is the average height of the NBA
players greater than the average height of the weight lifters?
(1) R>P
(2) There are 5 basketball players that are taller than the tallest weight lifter, and 2
players that are shorter than the shortest weight lifter.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
35. The average monthly income of 14 younger workers is X, Together with 60 older
workers, the average monthly income of the workers rose to Y. what is the average
monthly income of the older workers?
(1) The factory’s monthly budget for all salaries is 300,000$, which is 10 times the
salary budget for the younger workers.
(2) The monthly income of all the workers is 10 times the younger workers income.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
36. One out of every 500 light bulbs are defected. If 2 out of every 10 defected light
bulbs have a broken glass and there are 20 broken glass light bulbs in the shipment,
how many light bulbs total are there in the shipment?
(a) 2,000
(b) 5,000
(c) 10,000
(d) 50,000
(e) 52,000
37. If a is an even integer and b is an odd integer, what must the expression
8ba33 be?
(a) Always even
(b) Always odd
(c) Always a fraction
(d) Could be a fraction
(e) Always an integer
Answers and Explanations to Test 2
1. The fastest way to solve this problem is by plugging in some numbers.
Lets say: X = 2, Y = 1.
According to answer e: 1 x 1 = 1 and that must be an odd number.
The correct answer is E.
2. Here, it is enough to calculate the simple interest of 8% per year.
$2,400 x 8/100 x 1 = $192. Since we are calculating as a compounded rate, the
interest should be a bit higher, or C as the correct answer.
3. Statement (1) alone is insufficient since there is infinite number of possibilities.
Statement (2) alone is insufficient since there is an infinite number of primes.
The combination of the statements is sufficient since the only even square of a prime
number is can be 22, which is 4. Both statements, taken together, are sufficient. The
correct answer is C.
4. Statement (1) alone is insufficient since we need the value of A + 2B.
Statement (2) is sufficient. A2B = A(AB) = A(40) = 80 .. A=2 and B=20.
Now, we know that A + 2B = 42 and we can calculate the required expression.
The correct answer is B.
5. Statement (1) is insufficient since the expression given is only one of two needed.
Statement (2) by itself is sufficient since X3Y2 = (X3Y)Y = 24Y = 72 .. Y = 3.
If Y=3 then X3=8 and so X=2.
The expression required is a combination of X and Y and is then calculable.
The correct answer is B.
6. Because X is a prime number bigger than 10, it must be odd. Ignoring the powers
of X in the expression of Y, you’ll see that Y is a sum of 4 odd numbers therefore it
must be even. The correct answer is C.
7. Find the sum of the first 4 primes larger than 20: 23+29+31+37=120. The correct
answer is C.
8. The best way is to take an example: Assume x=2 and y=10, then their average z=6.
The average of x=2 and z=6 is w=4. Therefore:
316210442=
-
-
=
-
-
=
-
-
ywwx. The correct
answer is B.
9. First, calculate the fraction of the 25 managerial workers out of the total number of
workers by subtracting the fractions given from 1.
2012019120104512151411=-=
++
-=---.
The 25 managerial workers are
201of the workers, therefore, 5002025=×, a total
number of 500 workers. The correct answer is D.
10. This statement is equivalent to 0.8sb – sa = 3sa. The income is 0.8sb, the cost is
sa, so the profit is three times the cost.
The correct answer is A.
11. From (1) we have X and Y and therefore we can find A easily, A = 300.
(2) Is identical to (1), simplify it and see that it can be written as X = 3Y.
Either statement by itself is sufficient. The correct answer is D.
12. The easiest way to solve such a problem is to plug in numbers.
Use both statements to see that they are both insufficient even together.
Take X=0: 1/(5 – X) = 1/5 and X/5 = 0, in this case the first expression is larger.
Take X=7: 1/(5 – X) = -1/2 and X/5 = 7/5, in this case the second expression is larger.
We can see that the answer is dependent on which numbers we choose and more data
is required in order to determine the answer. The correct answer is E.
13. There are a limited number of possibilities: 21, 42, 63 and 84.
According to statement (1), the only number that is compatible is 63.
According to statement (2), the only number that is compatible is also 63.
Either statement alone is sufficient. The correct answer is D.
14. The total income is 16x200. The cost is 24X, and the total profit is 3200 – 24X =
48X. The correct answer is C.
15. X is Kenny’s age. X/3 is Bob’s age. Answer C is equivalent to (X+P) =
2(X/3+P+Q), which means that in P years, X+P is 2 times (X/3+P) plus Q years. The
correct answer is C.
16. Sign the French cigar as X. The Cuban cigar is 1.5(X-0.7) - 1.
The Arabian cigar is 1.5[1.5(X-0.7)-1] + 0.5.
The sum of all the three is 74.7. The correct answer is A.
17. One notebook can cost 1, 2, 3 or 4 dollars. Subtract 15 times each price from 93,
and check if what you get is divisible by 5 minus the price of the notebook. The
number could be 24, 21 or 33. The correct answer is D.
18. Statement (1) can be written as: Y = 2X + 54.
Statement (2) can be written as: X = 3Y – 72.
Combining both statements, we have two different equations containing X and Y and
so we can solve and find the value of X and Y and calculate what is X percent of Y.
The correct answer is C.
19. Statement (1) is all about the windows and therefore it is not sufficient by itself.
Statement (2) tells us that Q + W/2 = 12, this is sufficient because the total price of
windows and shelves is 150Q + 75W.
Multiply the data in statement (2) be 150 to get: 150Q + 75W = 18,000.
Statement (2) is sufficient by itself.
The correct answer is B.
20. The question tells you that the area is 60, the area of a rectangle is equal to length
x width, in order to find the perimeter, one should find the value of the length and the
value of the width.
Statement (1) tells us that both the length and the width are even integers and
therefore we know their exact values because 60 can be factorized to: 1x60, 2x30,
3x20, 4x15, 5x12 and 6x10.
The only even integers smaller than 25 are (6x10) and we know the perimeter.
The correct answer is A.
21. Statement (1) tells us that 9X2 is an even number (it’s divisible by 4) and therefore
X2 must be an even number. An odd number squared is also odd and therefore X must
be even, this statement is sufficient.
Statement (2) tells us that 3X + 2 is an even number (it’s divisible by 8).
If you subtract 2 from (3X+2) the result will still be even. If 3X is even than X must
be even. This statement is also sufficient to answer the question. The correct answer is
D.
22. Changing the equality: 22X + 24Y = 160, we get: X
Since X must be a positive integer, Y must be smaller than 7. The numerator will be
11, 22, 33, 44 etc. Y must be 3 and X=3. X+Y = 7. The correct answer is C.
23. D shows us the difference between the sum of the percentages and 100 percent. If
X+Y>100, this percent must be subtracted from the sum X+Y in order to get 100
percent. Sum of sets minus the total equals the congruence. The correct answer is D.
24. The buying price for one car is 1,105,000 / 13 = 85,000.The wished for a car is
39,000 / 13 = 3,000. So the selling price must be 85,000 + 3,000. The correct answer
is B.
25. 5% of the total price of the cloths is 45.5 dollars, multiply this number to get the
entire 100% of the total selling price: (45.5 x 20 = $910). Now subtract the profit
$45.5 to get the cost: 910-45.5=$864.5. The correct answer is E.
26. Statement (1) tells us that 9X2 is an even number (it’s divisible by 4) and therefore
X2 must be an even number. An odd number squared is also odd and therefore X must
be even, this statement is sufficient.
Statement (2) tells us that 3X + 2 is an even number (it’s divisible by 8).
If you subtract 2 from (3X+2) the result will still be even. If 3X is even than X must
be even. This statement is also sufficient to answer the question.
27. In order to know how many people aren’t officers you need a fix value, in other
words you need to translate percentage into real values.
Statement (1) doesn’t give any real numbers and therefore it’s not sufficient.
111280Y
Statement (2) is the same as one in that matter, if we wanted to know the percentage
of the woman officers, the statements would have been satisfying. More data is
required. The correct answer is E.
28. 65X/100 is the number of people who didn’t win the tender. 30% of that number
is the number of people who weren’t deeply disappointed about the fact that they
didn’t win. 30 x (65X/100) /100 = 19.5/100 = 39/200. The correct answer is A.
29. Since 0.01 and 0.03 each have 2 decimal places, their product must have 4 (2 + 2)
decimal places. Because 1 x 3 x 5 is 15, you need to add 2 zeros to get the correct
number of decimal places, so the product of 0.01, 5 and 0.03 is 0.0015. To change a
decimal to a percentage you multiply by 100 and move the decimal point 2 places to
the right, so 0.0015 is 0.15%. The correct answer is C.
30. Pick numbers: a barrel of beer costs $40 and a barrel of juice costs $30 according
to the given ratio. One liter of beer will cost $0.5 and one liter of juice will cost $1.
Therefore the price ratio is 2:1. The correct answer is B.
31. Statement (1) tells you that X is greater than X2, that is true only if X is between
zero and one and so the answer to the question is no.
Statement two is identical to one, multiply both sides by (-1) and don’t forget to
change the sign of the inequality. Either statement is sufficient by itself. The correct
answer is D.
32. From statement (1) we have only one set of numbers. We have 5, 6, 7, 8, 9, 10
and 11.
Statement (2) provides no additional data because we can see several sets containing
7. The correct answer is A.
33. Statement (1) tells us that 2M3 + 2M is divisible by 8 and so M4 + M is divisible
by 4 and is even. We have two choices: M3 and M are either odd or even. This
statement is insufficient.
Statement (2) is sufficient, if M + 10 is divisible by 10 then M + 10 is an even
number. This statement is sufficient and the answer is B.
34. One is going north and the other is going west. The distance can be calculated
using the Pythagorean theorem. One made a distance of 1.6 x 5 = 8 Km, The second
one did 1.2 x 5 = 6 Km. The distance between them is the square root of (64 + 36) =
10 Km. The best answer is A.
35. George can fill Q/3 cans of paint in one minute .. There are R cans in one gallon,
so R/(Q/3) = 3R/QIs the time it takes George to fill one gallon (in minutes). In 45
minutes George can fill up 45/(3R/Q) = 15Q/R. The correct answer is E.
36. Plug in the answers.
(a) (4 # 2) = 8. The answer should be 14.
(b) (2 # 3) = (2 + 3)3 = 15. The answer should be 6.
(c) (2 # 3) = (22 – 3) = 1. The answer should be 6.
(d) (4 # 2) = (42 – 2) = 14. This is the right answer; check (2 # 3) also.
The correct answer is D.
37. Draw the x and y-axes, then plot the points and connect them.
The area of a trapezoid is (base1 + base2) x (height) / 2.
Base1 = 5, base2 = 4, height = 18 thus the area is 9 x 9 = 81.
The answer to the question is the square root of 81, meaning 9.
The correct answer is B.
GMAT Quantitative Test 2
37 Questions
75 minutes
These questions closely resemble real test questions collected by students from 1999 to 2003.
The answers and explanations were written by leading Test preparation professionals.
Have a good GMAT exam.
1. X is an even number and Y is a positive odd number. Which of the following
expressions cannot be even?
(a) (XY) Y
(b) X3Y3
(c) X3
(d) XY
(e) Y2
2. How much interest will $2,400 earn at an annual rate of 8% in one year if the
interest is compounded every 4 months?
(a) $141
(b) $150
(c) $197
(d) $234
(e) $312
3. What is the value of P?
(1) P is even.
(2) P is a square of a prime number.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
4. If AB = 40, what is the value of AB(A + 2B)?
(1) A – B = -18.
(2) A2B = 80.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
5. If X3Y = 24, what is the value of (X3Y3 – X2Y2)?
(1) X2Y2 = 36.
(2) X3Y2 = 72.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
6. X is a prime number bigger than 10. Also, Y = X+X3+X5+X7.
What is definitely true about Y?
(a) Y is a prime number.
(b) Y is odd.
(c) Y is even.
(d) Y is divisible by 3.
(e) Y is divisible by 7.
7. What is the least integer that is a sum of four different primes each greater than 20?
(a) 79
(b) 83
(c) 120
(d) 133
(e) 169
8. If X>X, the average of X and Y is Z, and the average of Z and X is W, what is the
value of ?=--ywwx
(a) 41
(b) 31
(c) 21
(d) 3
(e) 4
9. One quarter of the workers at the factory are clerical, one fifth are technical, half
are administrative and the other 25 are managerial. How many workers total are there
in the factory?
(a) 250
(b) 366
(c) 400
(d) 500
(e) 2500
10. The price of a product is $a. Bill bought s products and then sold 80 percents of
them $b. which of the following represents the whole deal if Bill’s profit was three
times the cost?
(a) 0.8sb = 4sa.
(b) (1-0.8)s –ab = 3s.
(c) 3(0.8a – sb) = sa.
(d) (s-0.8s)(b-a) = 3.
(e) (s0.8s) / (b-a) = 3.
11. X equals to Y% of what number?
(1) X = 3Y.
(2) 6Y+2X = 56X/14.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
12. Which expression is larger 1/(5 - X) or X/5?
(1) X <> -8.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
13. X is a two-digit number. If the ratio between the units digit and the tens digit is 1
to 2, what is the value of X?
(1) The sum of the digits multiplied by the tens digit is 54.
(2) The product of the digits divided by 2 is 9.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
14. A grocer bought 24Kg of coffee beans at price X. After a while one third of the
stock got spoiled so he sold the rest for 200$ per Kilo and made a total profit of twice
the cost. What must be price X?
(a) 66 2/3$.
(b) 50 1/3$.
(c) 44 4/9$.
(d) 33 1/3$.
(e) 24 1/2$.
15. Kenny is three times older than Bob. In P years he will be twice older than Bob
will be Q years later. Which of the following represents Kenny’s age comparing to
Bob’s? (If X = Kenny’s age)
(a) X + P = 6X(P+Q).
(b) 2(X+P) = 3X + Q.
(c) (X+P)/2 = X/3 + P + Q.
(d) 3(X+P+Q) = 2X.
(e) 3X = 2(P + Q).
16. A Cuban cigar would cost 1 dollar less than 1.5 times a French cigar, had the
French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents
more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What
is the price of the French cigar?
(a) 16.7$.
(b) 23$.
(c) 25.5$.
(d) 35$.
(e) 37.4$.
17. Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were integers,
how many pencils did Ashley buy if she paid 93 dollars for the pencils and for 15
notebooks?
(a) 6.
(b) 16.
(c) 18.
(d) 21.
(e) 26.
18. What percent is X of Y?
(1) Y is bigger than 2X by 54.
(2) X is smaller than 3Y by 72.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
19. A store bought Q windows at $150 per window and W shelves at $75 per shelve.
What is the total price of the windows and the shelves?
(1) The Q windows cost $600.
(2) Q + W/2 = 12.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
20. What is the perimeter of a rectangle having an area of 60?
(1) The length and width of the rectangle are even integers smaller than 25.
(2) The length of the rectangle is larger than three times the width.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
21. X is a positive integer, is X even?
(1) 9X2 is divisible by 4.
(2) 3X + 2 is divisible by 8.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
22. The sum of the ages of 22 boys and 24 girls is 160.What is the sum of ages of one
boy plus one girl, if all the boys are of the same age and all the girls are of the same
age, and only full years are counted?
(a) 5.
(b) 6.
(c) 7.
(d) 8.
(e) 9.
23. X percents of the rooms are suits, and Y Percents of the rooms are painted light
blue?
Which of the following best represents the least Percentage of the light blue painted
suits?
(a) X-Y.
(b) Y-X + 100.
(c) 100X-Y.
(d) X+Y-100.
(e) 100-XY.
24. David bought 13 BMW cars for a total price of 1,105,000 dollars. If he wants to
make a profit of 39,000 dollars in the deal, at what price should he sell one car?
(a) 85,000$.
(b) 88,000$.
(c) 94,000$.
(d) 124,000$.
(e) 139,000$.
25. Loren bought a roll of cloth and sold it for a 5% profit based on the selling price.
If Loren‘s profit was $45.5 total on the cloth, how much did it cost her to buy the
cloth?
(a) $455.
(b) $525.5.
(c) $675.
(d) $810.5.
(e) $864.5.
26. X is a positive integer, is X even?
(1) 9X2 is divisible by 4.
(2) 3X + 2 is divisible by 8.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
27. If 10% of the employees of the state fare are police officers, what is the number of
employees who are not police officers?
(1) 5% of the police officers employed in the fare are woman.
(2) 45% of the employees at the state fare are woman.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
28. In a recent tender, X people participated. 35% of the X people, who made an offer
won the specific tender they participated in. 70% of the rest, were disappointed from
the result of the tender. Which of the following expressions represents the number of
people who weren’t disappointed although they didn’t win the tender?
(a) 39X/200.
(b) 25X/50.
(c) 19.5X/200.
(d) 35X/250.
(e) 90X/200.
29. What is 0.01 x 5 x 0.03 in terms of percent?
(a) 15%
(b) 1.5%
(c) 0.15%
(d) 0.015%
(e) 0.0015%
30. In a barrel of juice there is 30 liters; in a barrel of beer there are 80 liters. If the
price ratio between a barrel of juice to a barrel of beer is 3:4, what is the price ratio
between one liter of juice and one liter of beer?
(a) 3:2.
(b) 2:1.
(c) 3:1.
(d) 4:3.
(e) 3:4.
31. Is X greater than 1?
(1) X > X2.
(2) –X < -X2. (a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. (b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. (c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. (d) Either statement BY ITSELF is sufficient to answer the question. (e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem. 32. What is the sum of 7 consecutive integers? (1) The median of the seven integers is 8. (2) One of the integers is 7. (a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. (b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. (c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. (d) Either statement BY ITSELF is sufficient to answer the question. (e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem. 33. M is a positive integer, is M odd? (1) 2M3 + 2M is divisible by 8. (2) M + 10 is divisible by 10. (a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. (b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. (c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. (d) Either statement BY ITSELF is sufficient to answer the question. (e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem. 34. From the starting point in a boat race, one competitor started to sail north at a speed of 1.6 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours? (a) 10. (b) 12. (c) 12.5. (d) 14. (e) 15.4. 35. George can fill Q cans of paint in 3 minutes. If there are R cans of paint in one gallon, how many gallons can George fill in 45 minutes? (a) 30R/Q. (b) 15R/Q. (c) 30Q/R. (d) 5Q/R. (e) 15Q/R. 36. If (4 # 2 = 14) and (2 # 3 = 6), what can replace (a # b)? (a) ab. (b) (a+3)b (c) a2 – b. (d) ab – 2. (e) ba + 1. 37. In a rectangular coordinate system, what is the square root of the area of a trapezoid whose vertices have the coordinates (2, -2), (2, 3), (20, 2), (20, -2)? (a) 7.5 (b) 9 (c) 10.22 (d) 12.25 (e) 14
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Answers and Explanations to Test 1
1. Translate piece by piece into numbers. R (Roy) = Erik (E) + 4. The second equation: R = I (Iris)+ 2. The third equation: R +7 = 2(E + 7). We have three equations with three variables. Roy is 6, Iris is 4 and Erik is 2. In four years Erik would be 6 and Iris 8, the answer is 48. The correct answer is C.
2. Principal × percent interest × time = interest earned Principle × (0.09)× 1/12 = $228. Solve to find the principal (228 × 12)/0.09= $30,400. The correct answer is B.
3. The first expression is even and the second is odd, the only difference between the expressions is that the first expression has X and the second has W. So, if X is even W must be odd and the correct answer is C.
4. The area of the triangle is XY/2. Statement (1) tells us that X is a prime number, that can be even (2) or odd (3, 5, 7, etc.). Statement (2) tells us that Y is an odd integer. The multiplication of X and Y can be an odd number or an even number, thus we cannot determine if the area of the triangle is an integer or not. The correct answer is E.
5. Statement (1) is insufficient since the size of the reservoir is irrelevant. Statement (2) is sufficient since it tells us that the second tanker has the same work rate as the first. So, it will take them both half the time it took the first tanker alone. The correct answer is B.
6. 3Q is a prime number so it can be divide equally by 3Q, by 1 and by the components 3 and Q. The smallest number therefore is 3. The correct answer is C.
7. The number of green and yellow balls in the box is A+2. The total number of balls is 4A +8. The probability of taking out a green or a yellow ball is: 41842=++AA. The correct answer is D.
8. The price of the ticket is unknown. It would be most convenient to plug in 100 as the price of the ticket. A 30% discount of 100 is $30, that amount remained the same after the price of a ticket increased by 50%. The new price of a ticket is $150, so 30/150 is 20%. The correct answer is B.
9. If you square each digit {0, 1, 2,..., 8, 9}, you will see that the possible last digits for a square are 0, 1, 4, 5, 6 and 9. Thus, if the last digit of A is 8, A cannot be a square and the square root of A is not an integer. Statement (1) by itself is sufficient. Statement (2) by itself is insufficient since there are numbers that are divisible by 6 and have an integer square root and numbers divisible by 6 that do not have an integer square root. The correct answer is A.
10. We want to find the number value of Q. In statement (1) we are given the ratio between Q and T, which is not sufficient. Statement (2) can be simplified: 277277214774)2(727QTQTQTQT=⇒+=+⇒+=+⇒+=+. We can see that the same ratio is given in statement (2) also and more data is required to answer the question. Both statements give the same information. The correct answer is E.
11. From the grade 40 at the end of the first year we learn that his age is 20. At the end of the second year, he will be 21 and his grade will be (21 x 2 + ½ x 40 = 62). At the end of the third year, he will be 22 and his grade will be (22 x 2 + ½ x 62 = 75). The correct answer is D.
12. Factorize C: C = A x A x A: C can be equally divided into 1, A, A2, and A3 =C 4 numbers total. The correct answer is B.
13. Find the factors of (405) 4 and see what the largest value of X can be. 405 = 81 x 5 = 9 x 9 x 5 = 3 x 3 x 3 x 3 x 5 (405) 4 = (3 x 3 x 3 x 3 x 5) 4 = 316 x 54. The largest possible value of 3X that is still a factor of (405) 4 is the largest possible value of X and that is 316. X = 16. The correct answer is C.
14. Statement (1) is sufficient. If X2 is a fraction, X must also be a fraction. Meaning that X3 and Y will also be fractions. Statement (2) is sufficient. If X3 is a fraction then X must be greater than X3, which is also equal to Y. We get that from X > Y, so X3 and Y are fractions.
The correct answer is D.
15. Statement (1) gives us the average speed of the turtle; this statement is insufficient since the time is not given.
Statement (2) is also insufficient by itself since we don’t know what the average speed is.
Both statements combined are sufficient since we can calculate the distance
2*T=D and 3(T-40)=D, solve to get D=240 meters. The correct answer is C.
16. We are told that the stock increases its value by a constant rate and therefore we need to find some kind of pattern in order to know the value every year.
Statements (1) and (2) taken together are sufficient since they give us the percent increase of the stock from 1991 to 1992, which is 15%. The value of the stock in 1998 can be easily calculated, add 15% every year until 1998. The correct answer is C.
17. Answer D is a multiplication of two consecutive numbers, therefore one of them must be even, and an even number multiplied by a different number is an even number. The correct answer is D.
18. 25,200 x 1.1 = 27,720. 27,720 x 0.9 = 24,948. The correct answer is C.
19. Dividing the requested amount of miles by the reference amount would give us the answer in inches. 383.6 / 28 = 13.7 inches. The correct answer is C.
20. The total working days for finishing a web page are (15 x 3) 45. If after one day 9 programmers quit, only 15 working days are done and the rest of the programmers (6) Need to finish (45 – 15) 30 days of work. It will take them 5 more days. The correct answer is C.
21. Tim is traveling at twice the speed of Élan, and so will be after they double their speeds. The ratio between their velocities will always be 2:1 and the ratio between the distances they will pass will also be 2:1 or 60 miles to 30 miles. Tim will go through 60 miles. The correct answer is D.
22. In order to calculate the time it would take to complete one rotation, you need the radius and the velocity. Statement (1) provides the radius of rotation and (2) provides the velocity.
The distance the spaceship has to travel in order to complete one rotation is )000,21(22⋅⋅=⋅⋅ππR and the speed is 35 miles per second. Divide the first by the second and you’ll get the time it would take the spaceship to complete one rotation.
The correct answer is C.
23. Since we need to compare between X and Y, look at both statements together.
(1) and (2) state that: 12X = 4C = 12Y4 X = Y4.
Take Y=-1, X=1: X is bigger than Y.
Take X=1 and Y=1: X is not bigger than Y.
The answer is not distinct and therefore more data is required in order to solve the question. The correct answer E.
24. If a circle inscribers a square then the diagonal of the square is the diameter of the circle, which is sufficient to find the perimeter.
Statement (1) tells us about the square that is inscribed with out any further data.
Statement (2) gives us the perimeter, which is equal to 4 times the side of the square.
If we know the side of the square, we know its diagonal.
Both statements, taken together, are sufficient. The correct answer is C.
25. Draw the x and y-axes, then plot the points and connect them. The length of the base is 6 units [from (6, 3) to (6, -3)] and the height is 2 units [from (6, 0) to (4, 0)].
Area of a triangle = (base × height) / 2, so (6 × 2)/2 is 6. The correct answer is D.
26. [6.5] x [2/3] + [2] x 7.2 + [8.4] – 6.6 = 6 x 0 + 2 x 7.2 + 8 - 6.6 = 15.8. The correct answer is C.
27. ()()0.001610161021025144444=×===−. The correct answer is E.
28. The first digit has 7 possibilities (10 – 0,3 and 6). The other three digits have 8 possibilities each. 7*8*8*8= 3584. The correct answer is B.
29. From (1) by itself we can only learn that 90 kids have good grades. This statement is insufficient.
From (2) we can learn that there are 100 girls in the group.
Combining the statements doesn’t help much since we know nothing about the overlapping of (1) and (2) and more data is required. The correct answer is E.
30. Statement (1) tells us that 10 cans cost 4.2 dollars instead of 5 dollars and therefore the last two cans were sold for 20 cents. This statement is sufficient.
Statement (2) also tells us that the entire amount of cans cost 4.2 and therefore this statement is also sufficient. The correct answer is D.
31. From (1) we know the value of Y only, which is 1.
From (2) and (1) we know the value of all the other parameters, X = 4 and ZW = 4.
Therefore, (1) and (2) together are sufficient. The correct answer is C.
32. The phone company already created 122*122 area codes, now it can create 124*124. 1242-1222=(124+122)(124-122) = 246*2 = 492 additional codes. The correct answer is C.
33. If the average of 7 numbers is 12.2, we can solve for their sum: 7 × 12.2 = 85.4. If four of these numbers total 42.8, then by subtracting 42.8 from 85.4, we get the sum of the other three numbers, 42.6. To find the average of these three numbers, we divide their sum by their number: 42.6/3 = 14.2. The correct answer is B.
34. Statement (1) is insufficient. Take A=0 and B=0, (1) is correct yet A4 is not bigger than B4.
Take different numbers, A=6 and B=12 A4 is larger than B4.
Statement (2) is sufficient. The only possible way that A will not be larger than B is if they are both zero. (2) Claims that A <>
35. Lets look at two cases, where each one will give out different results. One of the numbers is 15 and three more are 15, 15 and 15 (with an average of 15). The sum of all the numbers should be (20 x 5 = 100). The sum of the numbers we picked up is (15 x 4 = 60) and therefore the last number should be 40 which is greater than 15. The answer in this case is 1. Take another case: One of the numbers is 15 and three more are 14, 15 and 16 (with an average of 15). In this case there will be 2 numbers over 15. More data is required. The correct answer is E.
36. Getting three red out of 4 that are taken out has 4 options (4!/(3!*1!)) each option has a probability of (1/2)4 since drawing a red or blue has a 50% chance. 4*1/16= ¼ to get three red hats. The same goes for three blue hats so ¼+¼ =1/2. The correct answer is C.
37. (2X + Y)(2Z + W) = 4XZ + 2XW + 2ZY + WY. Now, plug in this data to get: 3 + 2 x 6 = 15. The correct answer is C.
GMAT Quantitative Test 1
37 Questions
75 minutes
These questions closely resemble real test questions collected by students from 1999 to 2003.
The answers and explanations were written by leading Test preparation professionals.
Have a good GMAT exam.
1. Roy is now 4 years older than Erik and half of that amount older than Iris. If in 2 years, Roy will be twice as old as Erik, then in 2 years what would be Roy’s age multiplied by Iris’s age?
(a) 8
(b) 28
(c) 48
(d) 50
(e) 52
2. An investment yields an interest payment of $228 each month. If the simple annual interest rate is 9%, what is the amount of the investment?
(a) $28,300
(b) $30,400
(c) $31,300
(d) $32,500
(e) $35,100
3. X, Y, Z, and W are integers. The expression X-Y-Z is even and the
Expression Y-Z-W is odd. If X is even what must be true?
(a) Y-Z must be odd.
(b) W must be even.
(c) W must be odd.
(d) W must be even.
(e) Z must be odd
4. X Y
X and Y are two sides of a triangle, is the area of the triangle an integer?
(1) X is a prime number.
(2) Y is an odd integer.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
5. Fuel tanker A can fill the underground reservoir in 12 minutes. How long will it take fuel tanker A and fuel tanker B to fill up the same reservoir together?
(1) The reservoir contains 3000 liters of fuel.
(2) Fuel tanker B alone will require the same number of hours to fill the same reservoir.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
6. Q is a prime number bigger than 10. What is the smallest positive number (except 1) that 3Q can be divided by equally?
(a) 3Q.
(b) Q
(c) 3
(d) Q+3
(e) 2Q
7. In a box there are A green balls, 3A + 6 red balls and 2 yellow ones.
If there are no other colors, what is the probability of taking out a green or a yellow ball?
1/5.
½.
1/3.
¼.
2/3.
8. Kelly used to get a 30% discount on movie tickets. When the price of the movie ticket increased by 50%, the amount of discount in dollars remained the same. What is Kelly's discount with the new Ticket price in percent terms?
(a) 10%
(b) 20%
(c) 25%
(d) 35%
(e) 38%
9. Is the square root of A an integer?
(1) The last digit of A is 8 .
(2) A is divisible by 6.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
10. If Q and T are integers, what is the value of Q?
(1) Q = 2T/7.
(2) 4)2(727+=+QT
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
11. In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey’s grade at the end of the first year is 40, what will be his grade at the end of the third year?
(a) 44.
(b) 56.
(c) 62.
(d) 75.
(e) 80.
12. A is a prime number (A>2). If C = A3, by how many different integers can C be equally divided?
(a) 3.
(b) 4.
(c) 5.
(d) 6.
(e) 7.
13. If X is a positive integer and (405) 4 is a multiple of 3X, what is the largest possible
alue of X?
(a) 5.
(b) 12.
(c) 16.
(d) 20
(e) 26.
14. X, Y>0, If X3 = Y, is Y a fraction?
(1) X2 is a fraction.
(2) X > Y.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
y itself is not.
(B) Statement (2)BY ITSELF is sufficient to answer the question, but statement (1)
y itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
15. A turtle is crossing a field, how many meters total did he pass?
(1) The average speed of the turtle is 2 meters per minute.
(2) Had the turtle walked 1 meter per minute faster than his average speed it would
ave finished the same path 40 minutes earlier.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
y itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
y itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
16. The net value of a certain stock increased at a constant rate during the ten-year period between 1990 and 2000. What was the value of the stock in the year 1998?
(1) In 1991, the value of the stock was 130 U.S dollars.
(2) In 1992, the value of the stock was 149.5 U.S dollars.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2)
by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1)
by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the
question, requiring more data pertaining to the problem.
17. N is a prime number bigger than 5. Which of the following expressions must be
even?
(a) (N+2)2.
(b) N2+2.
(c) N(N+2).
(d) (N+1)(N+2).
(e)(N – 2)2.
18. The original price of a car was $25,200. Because the car owner thought he could get more money for the car, he increased the price of the car to 110% of its original price. After a week, the car had not sold, so the owner then discounted the price by 10%, and the car was finally sold. What price was the car sold for?
(a) $25,200
(b) $25,000
(c) $24,948
(d) $24,542
(e) $23,658
19. On a map, 1 inch represents 28 miles. How many inches would be necessary to represent a distance of 383.6 miles?
(a) 5.2
(b) 7.4
(c) 13.7
(d) 21.2
(e) 28.7
20. 15 Java programmers, working in a constant pace, finish a web page in 3 days. If after one day, 9 programmers quit, how many more days are needed to finish the remainder of the job?
(a) 2.
(b) 4.
(c) 5.
(d) 6.
(e) 8.
21. Tim and Élan are 90 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?
(a) 30 miles.
(b) 35 miles.
(c) 45 miles.
(d) 60 miles.
(e) 65miles.
22. A spaceship in orbit rotates around the planet Pluto. How many full rotations can the spaceship complete in 20 hours.
(1) The radius of a single rotation is 21,000 miles.
(2) The spaceship travels at 35 miles per second.
(a) Statement (1)BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
23. Is X > Y?
(1) 12X = 4C.
(2) C = 3Y4.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statementstatement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
24. What is the circumference of circle O?
(1) The circle inscribes a square.
(2) The perimeter of the square is 10.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
25. In a rectangular coordinate system, what is the area of a triangle whose vertices have the coordinates (4, 0), (6, 3), and (6, -3)?
(a) 7.5
(b) 7
(c) 6.5
(d) 6
(e) 5.5
26. For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] – 6.6?
(a) 12.6.
(b) 14.4.
(c) 15.8.
(d) 16.2.
(e) 16.4.
27. What is the decimal equivalent of ()514?
(a) 0.0032
(b) 0.032
(c) 0.00625
(d) 0.003125
(e) 0.0016
28. How many four-digit numbers that do not contain the digits 3 or 6 are there?
(a) 2401
(b) 3584
(c) 4096
(d) 5040
(e) 7200
29. How many of the girls in a group of 200 children have an average score of 80 in their final exams?
(1) 45% of the children have an average score of 80 in their final exams.
(2) 50% of the children in the group are girls.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
30. A paint shop sells spray cans at a flat charge of 50 cents per can. If a customer bought 10 cans and the owner decided to give that customer a special discount on the last two cans, what was the price of the two discounted cans?
(1) The customer paid four dollars and twenty cents total for the ten cans.
(2) The customer bought the ten cans for an average price of 42 cents per can.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
31. Does the product of XYZW = 16?
(1) Y = 1.
(2) X = 4Y and ZW = 4Y2
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
32. The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. If the company used 122 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 124 signs?
(a) 246
(b) 248
(c) 492
(d) 15,128
(e) 30,256
33. The average (arithmetic mean) of seven numbers is 12.2. If the sum of four of these numbers is 42.8, what is the average of the other 3 numbers?
(a) 12.4
(b) 14.2
(c) 16.8
(d) 18.6
(e) 19.2
34. If A = 2B, is A4 > B4?
(1) A2 = 4B2.
(2) 2A + B <>
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
35. 5 numbers are randomly chosen. If their average is 20, how many of the numbers are larger than 15?
(1) One of the numbers is 15. (2) The average of three of the numbers is 15.
(a) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(b) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(c) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(d) Either statement BY ITSELF is sufficient to answer the question.
(e) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
36. A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every that to the drawer before taking out the next?
(a) 1/8
(b) ¼
(c) ½
(d) 3/8
(e) 7/12
37. If 4XZ + YW = 3 and XW + YZ = 6, what is the value of the expression (2X + Y)(2Z + W)? (a) 9. (b) 12. (c) 15. (d) 16. (e) 18.
