Admission Tests Admission Tests Certifications GMAT-QUANTITIVE Questions & Answers

• Question 271:

  What is the value of x?

  (1)

  x + y = 6

  (2)

  2x -y = 9

  A.

  Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.

  B.

  Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.

  C.

  The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).

  D.

  The problem can be solved using EITHER statement (1) only or statement (2) only.

  E.

  The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

  Correct Answer: C

  Since this question has two variables and two equations, they can be used together to solve for x and y. If both equations are combined, the result is 3x = 15. Obviously x and subsequently y can be solved for now, but you do not need to finish the problem once you have reached this conclusion.

• Question 272:

  What is the measure of an interior vertex angle of a pentagon?

  (1)

  The measure of each adjacent exterior angle is 72.

  (2)

  The pentagon is a regular polygon.

  A.

  Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.

  B.

  Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.

  C.

  The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).

  D.

  The problem can be solved using EITHER statement (1) only or statement (2) only.

  E.

  The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

  Correct Answer: D

  Either statement is sufficient. Statement (1) is sufficient because if the measure of each adjacent exterior angle is 72, then the measure of the interior angle is 180 ?72 = 108. Statement (2) is also sufficient. Regular polygons contain congruent sides and congruent angles. If the pentagon is made up of 540 degrees, then 540 _ 5 = 108 in each angle.

• Question 273:

  Is rectangle ABCD a square?

  (1)

  m ABC = 90

  (2)

  AC CD

  A.

  Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.

  B.

  Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.

  C.

  The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).

  D.

  The problem can be solved using EITHER statement (1) only or statement (2) only.

  E.

  The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

  Correct Answer: B

  Since you know that ABCD is a rectangle, you already know that each vertex angle is 90 degrees. Statement (1) does not tell you any additional information about ABCD. Statement (2) states that the diagonals are perpendicular; a rectangle with perpendicular diagonals is a square. Statement (2) is sufficient.

• Question 274:

  Is r -5 a real number?

  (1)

  r is a rational number.

  (2)

  2

  

  is an irrational number.

  A. Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.

  B. Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.

  C. The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).

  D. The problem can be solved using EITHER statement (1) only or statement (2) only.

  E. The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

  Correct Answer: D

  Any real number is either rational or irrational and subtracting 5 from any rational or irrational will also be a real number. Statement (1) is sufficient. Statement (2) implies that if the square root of a number is irrational, the original number was either rational or irrational. Statement (2) is sufficient.

• Question 275:

  What is the value of x + 2y?

  (1)

  2x + 4y = 20

  (2)

  y = 5 -x

  A.

  Statement (1), BY ITSELF, will suffice to solve the problem, but NOT statement (2) by itself.

  B.

  Statement (2), BY ITSELF, will suffice to solve the problem, but NOT statement (1) by itself.

  C.

  The problem can be solved using statement (1) and statement (2) TOGETHER, but not ONLY statement (1) or statement (2).

  D.

  The problem can be solved using EITHER statement (1) only or statement (2) only.

  E.

  The problem CANNOT be solved using statement (1) and statement (2) TOGETHER.

  Correct Answer: D

  If you take statement (1) and divide each term by 2, the result is x + 2y = 10. Thus, x + 2y is

  

  x to both sides and multiply each term by 2, the result is also x + 2y = 10. Therefore, either statement is sufficient.

• Question 276:

  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

  Correct Answer: B

  Explanation: 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.

• Question 277:

  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.

  Correct Answer: A

  Explanation: 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.

• Question 278:

  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.

  Correct Answer: D

  Explanation: 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.

• Question 279:

  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.

  Correct Answer: E

  Explanation: 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. 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.

• Question 280:

  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: We are to find if X is an even number.

  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