Admission Tests Admission Tests Certifications GMAT-QUANTITIVE Questions & Answers

• Question 231:

  What is the sum of the two smallest integers in a set of different positive integers?

  (1)

  There are 4 integers in the set.

  (2)

  The average of the integers in the set is 3.

  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 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.

• Question 232:

  What was the total amount John earned on his two investments?

  (1)

  John received an annual interest of 5% on one investment and 13% on the other.

  (2)

  John invested a total of $15,000 on both investments.

  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

  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.

• Question 233:

  What is the value of (a+b)?

  (1)

  a2-b2=133.

  (2)

  a-b=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: C

  Since a2-b2=(a+b)(a-b), 133=(a+b)7, and (a+b)=19. Both statements are needed to solve the question.

• Question 234:

  What is the value of X+Z?

  (1)

  X+Y=11

  (2)

  Z+Y=13

  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

  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: x+y=11y+z=13 y=11-xy=13-z 11-x=13-z z-x=13-11

  It is only possible to find z-x.

• Question 235:

  Is the product XY divisible by 22?

  (1)

  X is divisible by 4.

  (2)

  Y is divisible by 11.

  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 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.

• Question 236:

  Is the integer X even?

  (1)

  X is divisible by 7.

  (2)

  X is divisible by 11.

  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 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.

• Question 237:

  What is the area of the shaded region?

  

  (1)

  ABC is equilateral.

  (2)

  The length of

  

  is 16 inches.

  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

  Because you know that the triangle is equilateral from statement (1), you also know that each side has the same measure and that each angle is 60 degrees. This does not, however, tell you the length of the diameter or radius of the circle, which you need to know in order to find the area. Statement (2) alone is also insufficient because it tells you the length of one side of the triangle, but no other information about the figure. Using both statements together, the diameter is then 16; thus, the radius is 8. Therefore, the area of the semicircle can be calculated.

• Question 238:

  Michael left a city in a car traveling directly west. Katie left the same city two hours later going directly east traveling at the same rate as Michael. How long after Katie left will they be 350 miles apart?

  (1)

  An hour and a half after Katie left they are 250 miles apart.

  (2)

  Michael's destination is 150 miles farther than Katie's.

  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: A

  Using distance = rate -time and the facts from statement (1), you can calculate the time they will be 350 miles apart. You are told that they are traveling at the same rate. To solve for the rate, you can use the equation that relates Michael's distance plus Katie's distance, which equals 250 miles at a time of 1.5 hours. Once the rate is known you can then solve for the time when they are 350 miles apart. Statement

  (2) is unnecessary information and does not help you to solve for the time.

• Question 239:

  A circle and a straight line are drawn on the same coordinate graph. In how many places do the two graphs intersect?

  (1)

  The equation of the circle is x2 + y2 = 25.

  (2)

  The y-intercept of the straight line is 6.

  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: E

  From statement (1), the circle is centered at the origin and has a radius of 5. This obviously is not sufficient because it does not tell you anything about the line. Even though statement (2) gives you the y-intercept of the line, since you do not know the slope, the line could intersect the circle in 0, 1, or 2 different places. Neither statement is sufficient.

• Question 240:

  Find the area of the shaded region.

  

  (1)

  m A = 43°.

  (2)

  AB = 10 cm.

  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: E