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.