Admission Tests Admission Tests Certifications GMAT-QUANTITIVE Questions & Answers

• Question 671:

  If y = 6x, then 6y equals

  A. 6x

  B. 6x+1

  C. 6x + 6

  D. 6x

  E. 6x -1

  Correct Answer: B

  Since y = 6x, multiplying each side of the equation results in 6y = 6 (6x). Recall that since 6 = 61, 6x × 61 = 6 x + 1 by the laws of exponents.

• Question 672:

  If x, y, and z are real numbers, which is always true?

  I) x (yz) = (xy) z

  II) x/y = y/z

  III) z (x + y) = zx + zy A. I only

  B. II only

  C. I and II only

  D. I and III only

  E. I, II, and III

  Correct Answer: D

  Statement I is an example of the associative property of multiplication and statement III is an example of the distributive property. These properties will hold for any real numbers that are substituted into them. Statement II is not a property of real numbers and may be true for certain numbers, but not for every real number.

• Question 673:

  If x $ y is defined as 2(x + y) 2, then what is the value of 2 $ 3?

  A. 25

  B. 36

  C. 50

  D. 100

  E. 144

  Correct Answer: C

  For this type of problem, substitute the values you are given for x and y. In this case, x = 2 and y = 3. The expression becomes 2 (2 + 3)2. Using the order of operations, perform the operation within the parentheses first and then the exponent. 2 (5)2 = 2 (25).Multiply to get 50.

• Question 674:

  If 3x + 1 = 81, then x – 1 = A. 2

  B. 3

  C. 4

  D. 9

  E. 27

  Correct Answer: A

  Solve for x first. Since 3x+1 = 81, and 81 is 34, make an easier equation just based on the exponents. This would be x + 1 = 4. x = 3. Therefore, x – 1 = 3 – 1 = 2.

• Question 675:

  For dinner at a restaurant, there are x choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?

  A. x + y + z + 1

  B. xyz + xz

  C. xy + z + 1

  D. xyz + 1

  E. xyz + 1/2

  Correct Answer: B

  Use the counting principle: Take the number of choices you have for each course and multiply them together to get the total possible combinations. x × (y + 1) × z. Use the distributive property to simplify to xyz + xz.

• Question 676:

  If the volume of a cube is x3 cubic units, what is the number of square units in the surface area of the cube?

  A. x2

  B. x3

  C. x6

  D. 6x2

  E. 6x3

  Correct Answer: D

  If the volume of the cube is x3, then one edge of the cube is x. The surface area of a cube is six times the

  area of one face, which is x times x. The total surface area is 6x2.

• Question 677:

  If x –3 is a multiple of two, what is the next larger multiple of two?

  A. 2x

  B. x -2

  C. x -1

  D. x -5

  E. x + 2

  Correct Answer: C

  The next larger multiple of two would be x – 3 + 2, which is x – 1. In this case, remember that any even number is a multiple of two and all evens are two numbers apart. If x – 3 is a multiple of two, you can assume that it is also an even number. This number plus two would also produce an even number.

• Question 678:

  If it costs d dollars to make the first 100 copies of a poster and e dollars for each poster after that, what is the total cost of 125 posters?

  A. 25d + 100e

  B. 100d + 25e

  C. 125de

  D. d + 25e

  E. 125/de

  Correct Answer: D

  It costs d for the first 100 posters plus the cost of 25 additional posters. This translates to d + 25e, since e is the cost of each poster over the initial 100.

• Question 679:

  If the average (arithmetic mean) of x, x + 2, and x + 4 is 33, what is the value of x?

  A. 30

  B. 31

  C. 32

  D. 32

  E. 37

  Correct Answer: B

  x, x + 2, and x + 4 are each two numbers apart. This would make x + 2 the average of the three numbers. If x + 2 = 33, then x = 31.

• Question 680:

  How many degrees is the smaller angle?

  

  A. 44

  B. 88

  C. 92

  D. 132

  E. 180

  Correct Answer: B

  Note that the figure is not drawn to scale, so do not rely on the diagram to calculate the answer.

  Since the angles are adjacent and formed by two intersecting lines, they are also supplementary.

  Combine the two angles and set the sum equal to 180.2x + 3x – 40 = 180. Combine like terms and add 40

  to both sides. 5x – 40 + 40 = 180 + 40. 5x = 220. Divide both sides by 5 to get x = 44. Then 2x = 88 and 3x

  – 40 = 92. The smaller angle is 88.