Admission Tests Admission Tests Certifications GMAT-QUANTITIVE Questions & Answers

• Question 241:

  A fence has a square gate. What is the height of the gate?

  (1)

  The width of the gate is 30 inches.

  (2)

  The length of the diagonal brace of the gate is 30

  

  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: D

  

  Knowing that the gate is square and the diagonal is 30

  

  , the Pythagorean theorem can be used with x as the side of the square. x2 + x2 = (30

  )2 . Or you may recall that the length of a leg will

  

  be because it is an isosceles triangle. Thus, statement (2) is sufficient. Since statement (1) gives the width and the gate is a square, then the height is the same as the width. Either statement is sufficient.

• Question 242:

  The formula for compounded interest can be defined as A = p (1 + r)n, where A is the total value of the investment, p is the principle invested, r is the interest rate per period, and n is the number of periods. If a $1,000 principle is invested, which bank gives a better interest rate for a savings account, Bank A or Bank B?

  (1)

  The interest rate at Bank A is 4% compounded annually.

  (2)

  The total amount of interest earned at Bank B over a period of five years is $276.28.

  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 order to have enough information to substitute into the formula, you would need both statements. Use p = $1,000, r = 0.04 and n = 5 to compare Bank A to Bank B. Again, you do not need to actually compute the interest earned once you can answer the question.

• Question 243:

  Is ABC similar to ADE?

  

  (1)

  BC is parallel to DE

  (2)

  AD = AE

  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. In a triangle, when a line is drawn parallel to a base, the line divides the sides it intersects proportionally. This would make ABC similar to ADE. Using statement (2), knowing that AD = AE is not enough information to assume that other parts are proportional.

• Question 244:

  Jacob is a salesperson. He earns a monthly salary plus a commission on all sales over $4,000. How much did he earn this month?

  (1)

  His monthly salary is $855 and his total sales over $4,000 were $4,532.30.

  (2)

  His total sales for the month were $8,532.30.

  A.

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

  statement (1) or statement (2).

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

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

  Correct Answer: C

  Neither statement is sufficient. The question never states the amount of commission, nor the commission rate, he gets on sales over $4,000.

• Question 245:

  What is the slope of line m?

  (1)

  Line m intersects the x-axis at the point (4, 0).

  (2)

  The equation of line m is 3y = x ?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: B

  Statement (2) is sufficient. Change the equation to y = mx + b form, where m is the slope of the

  

  . The slope of the line is

  . Statement (1) is not sufficient because we cannot tell the slope of line by only looking at the x- intercept.

• Question 246:

  Daniel rides to school each day on a path that takes him first to a point directly east of his house and then from there directly north to his school. How much shorter would his ride to school be if he could walk on a straight-line path directly to school from his home, instead of east and then north?

  (1)

  The direct straight-line distance from home to school is 17 miles.

  (2)

  The distance he rides to the east is 7 miles less than the distance he rides going north.

  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 solve this problem, you need to find the distance east and north that he travels. Since he goes directly east and then directly north, his path forms a right angle, which in turn is part of a right triangle. His straight-line distance to school is the hypotenuse of the right triangle formed by his paths. Although statement (1) gives you the hypotenuse, you do not know enough information to solve for the other sides. Statement (2) gives the relationship between the two legs of the right triangle, but again this is not enough information. Using the information from both statements, you can write an equation using the Pythagorean theorem: a2 + b2 = c2. Let x = the distance he travels east and x + 7 = the distance he travels north. x2 + (x + 7)2 =172. This equation can now be solved for the missing legs and therefore the solution to the problem.

• Question 247:

  What percent of the class period is over?

  (1)

  The time remaining is

  of the time that has passed.

  (2)

  The class period is 42 minutes long.

  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

  

  

  Let x equal the amount of time passed. Since the time remaining is

  

  of the time that has passed, this time can be represented as

  

  x. Converting to decimal form may make this problem easier, so change

  

  x to .25x. Since 1x is the time passed and .25x is the time remaining, then 1x + .25x is the total time. This is equal to 1.25x. To calculate the percent of the period that is over, use the proportion

  

  Now set up a proportion using the time passed as the part and the total time for the class as the whole. Cross-multiply to get 1.25x = 100.

  

  x = 80%

  80% of the class period is over.

  For this particular question, the number of minutes in the class period is not needed to solve the problem.

• Question 248:

  What is the total cost of six pencils and four notebooks?

  (1)

  Ten pencils and nine notebooks cost $11.50.

  (2)

  Twelve pencils and eight notebooks cost $11.00.

  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 (2) is the same as the original question doubled. Divide $11.00 by 2 to answer the question. Statement (1) is not sufficient by itself.

• Question 249:

  What is the ratio of the corresponding sides of two similar triangles?

  (1)

  The ratio of the perimeters of the two triangles is 3:1.

  (2)

  The ratio of the areas of the two triangles is 9:1.

  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. The ratio of the perimeters of two similar triangles is equal to the ratio of the corresponding sides. Also, the ratio of the areas of two similar triangles is equal to the squares of the ratios of the corresponding sides.

• Question 250:

  In right triangle XYZ, the my = 90 .What is the length of XZ?

  (1)

  The length of YZ = 6.

  (2)

  m z = 45

  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

  Statement (1) gives information about one of the three sides of the triangle, but this is not enough to solve for XZ. Statement (2) tells you that the right triangle in this problem is a 45--45--90 right triangle, or an isosceles right triangle. However, this also is not enough information to find XZ. By

  

  .