Answers and Explanations to Test 3

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.
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