Admission Tests Admission Tests Certifications GMAT-QUANTITIVE Questions & Answers

• Question 71:

  What is the value of (X2 + Y2)?

  (1)

  4X2 -7 = 17 -4Y2.

  (2)

  (X + Y)2 = 6 + 2XY.

  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

  Statement (1) can be written as 4X2 + 4Y2 = 24 X2 + Y2 = 6. (1) is sufficient. Statement (2) can be simplified: X2 + 2XY + Y2 = 6 + 2XY X2 + Y2 = 6. This statement is also sufficient.

• Question 72:

  If Y is a positive integer, does Y have four distinct positive factors?

  (1)

  Y = 8.

  (2)

  Y is a multiplication of two different odd numbers.

  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

  Statement (1) is sufficient since 8 has the following factors: 1, 2, 4 and 8. Statement (2) is not sufficient. For example, take 1 and 3, the product is 3, which has only two factors. But if you take 3 and 5, the product is 15 and we have 1,3,5 and 15 as factors of y, and we have four factors.

• Question 73:

  If X is a positive integer, does X have six distinct positive factors?

  (1)

  X is the product of four different positive primes.

  (2)

  X = 18.

  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

  You can find out how many factors a number has if you know what that number is, or something about its prime factorization. Look for this as you move on to the statements. Statement (1) is sufficient. If X is the product of four different prime numbers it will have six different factors; 1, the four prime numbers, and itself. Statement (2) is also sufficient. 18 has 6 different factors: 1, 2, 3, 6, 9 and 18.

• Question 74:

  The total volume of a swimming pool, when filled to capacity, is 2,652 gallons. How long will it take for the pool to fill up?

  (1)

  Water is being purred into the empty pool at the rate of 120 gallons per minute.

  (2)

  It takes 5 hours to empty the pool when it is half full.

  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

  It is sufficient to know the rate of water being purred and that the pool was empty to calculate the time

  needed for the pool to fill up:

  Therefore, statement 1 is sufficient. Statement 2 does not give information regarding the rate of filling the

  pool, thus, it is not sufficient.

• Question 75:

  What is the average of a sequence of integers?

  (1)

  There are 15 integers in the sequence.

  (2)

  The sum of the integers in the sequence is 1275.

  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

  An average of a set of integers is calculated as the sum of the integers divided by the number of integers in the sequence. Statement 1, gives the number of integers, which is not enough by itself. Statement 2, gives the sum of the integers in the sequence, which is not enough by itself. Using the data from both statements is enough to find the average.

• Question 76:

  What percent of the employees In X Company are managerial employees?

  (1)

  30% of the employees are technical.

  (2)

  There are exactly 45 clerical employees in the X Company.

  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 fact that 30% are technical or that 45 are clerical, does not tell anything about the rest of the workers. In this question, 3 types of workers appear, technical, clerical and managerial. However, there is no mention of whether other types of workers exist also. Since we cannot assume there are no other types, we cannot answer the question.

• Question 77:

  If A, B and C are integers. Is AB a factor of C?

  (1)

  A is a factor of B.

  (2)

  B is a factor of C.

  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

  Plug in numbers: A=4, B=8, C=16. A is a factor of B and B is a factor of C, However, AB=32 is not a factor of C=16.

• Question 78:

  Is (a+b)2 + (a+b)3 even?

  (1)

  a and b are positive.

  (2)

  a>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.

  Correct Answer: D

  Each statement alone is sufficient since there are only three possibilities:

  (1)

  a and b are even.

  (2)

  a and b are both odd.

  (3)

  One is odd and the other is even.

  Any of the options give us an even result, thus, the expression is always even.

• Question 79:

  At a certain library, there are fiction and non-fiction books only. How many of the books are non-fiction books?

  (1)

  There are 13,200 books at the library.

  (2)

  35% of the books at the library are non-fiction books.

  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

  The first statement alone does not give the information needed to know how many of the 13,200 books are fiction and how many are non-fiction. The second statement does not tell us 35% of what number are nonfiction books. The two statements together, give us enough information to calculate 35% of 13,200 and find the number of non-fiction books.

• Question 80:

  Is a>b?

  (1)

  a2 > b2

  (2)

  a+d > b+d

  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

  Plug in numbers. The first statement will work when a=3 and b=2, for example and then a2=9 and b2=4. However, it will not work when a=(-2) and b=(-3), then a2=4, and b2=9. The second statement is sufficient, it is possible to subtract d from both sides of the inequality and get: a+d-d>b+d-d, or a>b.