Admission Tests Admission Tests Certifications GMAT-QUANTITIVE Questions & Answers

• Question 251:

  Two cars leave the same city traveling on the same road in the same direction. The second car leaves one hour after the first. How long will it take the second car to catch up with the first?

  (1)

  The second car is traveling 10 miles per hour faster than the first car.

  (2)

  The second car averages 60 miles per hour.

  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

  In this type of question, remember the formula distance = rate -time. Let t = the time it takes the second car to catch up to the first. The fact that the second car is traveling 10 miles per hour faster than the first is not helpful by itself. We need to know more about either the distance traveled or the time traveled. Statement

  (2) alone also does not give enough information because we do not know the distances traveled. If we use

  both statements together, the first car's distance is 50 ( t +

  1) and the second car's distance is 60 t.When the second car catches up, their distances will be the same.

  Setting the two distances equal to each other gives the equation 50t + 50 = 60t.We can

  

  . t = 5 hours.

• Question 252:

  What is the area of the circle?

  (1)

  The radius is 6.

  (2)

  The circumference is 12.

  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

  

  , so the radius of the circle must be found in order to use the formula. Statement (1) gives you the radius. Using statement (2), the formula can be found by the fact that the circumference is ?the diameter. If the diameter is 12, then the radius is 6. Stop; you do not actually need to compute the area. Either statement can be used to solve the problem.

• Question 253:

  What is the positive value of z?

  (1)

  3y + z = 4

  (2)

  z2 -z = 12

  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

  Statement (1) contains two variables; you would need more information to solve for z. Statement (2) can be put into the form z2 -z -12 = 0. This equation can be solved by either factoring or by using the quadratic formula, and is sufficient to answer the question.

• Question 254:

  Between what two numbers is the measure of the third side of the triangle?

  (1)

  The sum of the two known sides is 10.

  (2)

  The difference between the two known sides 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: C

  The sum of the two smaller sides of a triangle must be greater than the longest side. To find the third side, subtract the two known values to get the lower bound and add the two known values to get the upper bound. The value of the third sides must be between these two numbers. Therefore, both statements are necessary.

• Question 255:

  

  What is the value of a + b?

  (1)

  a2 + b2 = 13

  (2)

  2b =

  A.

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

  B.

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

  C.

  statement (1) or statement (2).

  D.

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

  Correct Answer: C

  Remember that (a + b)2 = a2 + 2ab + b2. From statement (1), we know that a2 + b2 = 13. By cross multiplying in statement (2), we get 2ab = 12. Since we know the values of a2 + b2 and 2ab, and (a + b)2 = a2 + 2ab + b2, we can now take the square root of the sum to find the value of a + b.

• Question 256:

  Find the value of x.

  

  (1)

  The length of BC is 2

  .

  (2)

  The length of AC is 4.

  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

  

  

  From the diagram, if the measure of angle C is 30 degrees and angle B is a right angle, then

  

  ABC is a 30--60--90 right triangle. Using statement (1), if the measure of BC is 2 , then the shortest side x must be

  

  , which reduces to 2. Using statement (2), if the length of AC is 4 and AC is the hypotenuse of the triangle, then the shortest side of the triangle x is equal to

  = 2. Either statement is sufficient.

• Question 257:

  The circles in the diagram are concentric circles. What is the area of the shaded region?

  

  (1)

  The area of the inner circle is 25.

  (2)

  The diameter of the larger circle is 20.

  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

  To find the area of the shaded region, you need the area of the inner circle subtracted from the

  

  , you need to know at least the radius of each circle. Statement (1) gives you the area of the inner circle only, but no information about the outer circle. Statement (2) tells you the diameter of the outer circle is 20, so the radius is 10. Both statements are needed to answer the question.

• Question 258:

  Is x + y > 2z ?

  

  (1)

  ABC is equilateral.

  (2)

  AD BC

  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

  Statement (1) is sufficient. If the triangle is equilateral, then all sides and all angles are congruent. This would make x + y = 60 and z = 60; this is enough information to answer the question. From

  

  is the altitude drawn to side

  

  , and that ADB and ADC are both right triangles.

• Question 259:

  A rectangular courtyard with whole-number dimensions has an area of 60 square meters. Find the length of the courtyard.

  (1)

  The width is two more than twice the length.

  (2)

  The length of the diagonal of the courtyard is 13 meters.

  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

  Let x = the length of the courtyard. Statement (1) states that 2x + 2 = the width of the courtyard. Using the formula area = length -width, we get the equation 60 = x (2x + 2), which can be solved for x. Statement (1) is sufficient. Using statement (2), the diagonal divides the courtyard into two congruent right triangles. If the diagonal is 13 meters, and the dimensions are whole numbers, this must be a 5--12--13 right triangle. The length is 5 meters, and statement (2) is also sufficient.

• Question 260:

  What is the numerical value of x2 -25?

  (1)

  x -5 = 3

  (2)

  4 -x = 5

  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 x2 -25 is the difference between two perfect squares, its factors are ( x -5) and ( x + 5). Statement

  (1) gives the value of x -5. Statement (2) can be changed from 4 -x = 5 to 4 = x + 5 by adding x to both sides of the equation. Since you now know the numerical value of each factor, you can find the numerical value of x2 -25.