Admission Tests Admission Tests Certifications GMAT-QUANTITIVE Questions & Answers

• Question 281:

  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.

  Correct Answer: D

  Explanation: 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.

• Question 282:

  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.

  Correct Answer: A

  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.

• Question 283:

  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.

  Correct Answer: B

  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) is 150 to get: 150Q + 75W = 18,000.

  Statement (2) is sufficient by itself.

  The correct answer is B.

• Question 284:

  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.

  Correct Answer: C

  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.

• Question 285:

  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.

  Correct Answer: D

  Explanation: 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.

• Question 286:

  Which expression is larger 1/(5 - X) or X/5?

  (1)

  X < 8.

  (2)

  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.

  Correct Answer: E

  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.

• Question 287:

  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.

  Correct Answer: D

  Explanation: 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.

• Question 288:

  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.

  Correct Answer: B

  Explanation: 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.

• Question 289:

  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.

  Correct Answer: B

  Explanation: 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.

• Question 290:

  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.

  Correct Answer: C

  Explanation: 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.