GRE
Practice Test 9
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In the figure above, a square and an equilateral triangle share a common side.

Quantity A Quantity B
The area of the square Twice the area
of the triangle
  • Solution

The price of an apple equals the price of a pear.
The price of a melon is twice the price of a pear.

Quantity A Quantity B
The cost of eight apples,
nine pears, and three
melons		 The cost of seven apples,
four pears, and six melons
  • Solution

    (C) Let x = price of apple = price of pear, and then 2x = price of melon. Quantity (A) is 8x + 9x + 3(2x) = 17x + 6x = 23x. (B) is 7x + 4x + 6(2x) = 11x + 12x = 23x, as well. So the quantities are equal, (C).

–2|x – 5| = –12

Quantity A Quantity B
x 0
  • Solution

    (D) Recall that absolute value equations generally have two solutions. Divide both sides by –2 to obtain |x – 5| = 6. Therefore, x – 5 = 6, or x – 5 = –6. Adding 5 to both sides in each equation yields x = 11 or x = –1. Since one possible x value is greater than 0, while the other is less than 0, there is not enough information to determine, and (D) is correct.

Quantity A Quantity B
Length AB Length CD
  • Solution

Ed’s three friends each live within 20 miles of his house but more than 10 miles from his house. Triangle T is the triangle linking the three friends’ houses.

Quantity A Quantity B
The perimeter of
triangle T		 45 miles
  • Solution

Quantity A Quantity B
The distance traveled in 40
seconds by a marble rolling
at 1.8 meters per second		 The distance traveled in
4 minutes by a marble
rolling at 35 centimeters
per second
  • Solution

Set S = {2, 4, 6, 11} Set T = {50, 100, 200}

Quantity A Quantity B
The number of distinct
products that can be formed
when an element of Set S is
multiplied by an element of
Set T		 The number of distinct
sums that can be formed
when an element of Set S is
added to an element of
Set T
  • Solution

    (B) It may appear that there are four choices for the element from Set S times three choices for the element from Set T, making both quantities equal 4 × 3 = 12, choice (C). But when you begin multiplying elements of S by elements of T, notice that many of the products formed are not distinct. For example, 2 × 100 = 4 × 50. So Quantity (A) < 12. In Quantity (B), there are 4 × 3 = 12 distinct sums formed, because the large spread of values in Set T ensures no duplication. Thus, (B) must be greater.

Into empty Jar X, Jen places two black marbles and three white marbles.
Into empty Jar Y, she places five black marbles and four white marbles.
She then draws one marble at random from each jar.

Quantity A Quantity B
The probability that both
marbles drawn are black		 The probability that both
marbles drawn are white
  • Solution

Question is based on the following incomplete table, which shows the number of shirts sold by sleeve length and color in 1 year.

How many red short sleeve shirts were sold?

  • Solution

Question is based on the following incomplete table, which shows the number of shirts sold by sleeve length and color in 1 year.

If every shirt sold for $13.50, how much more money was earned from the sale of all short sleeve shirts than from the sale of all red shirts?

$ 

  • Solution

The function y = f(x) is graphed above. What is the value of f(f(1))?

  • Solution

     

    (5) First compute f (1) by finding the point on the graph where x = 1, P, and then reading across horizontally to find the y-value associated with this point, 4. Then f (f (1)) = f (4). Now find a point on the graph where x = 4, Q, by reading straight up vertically from the number 4 on the x axis. The y-value associated with this point is 5.

A nurse is combining one solution with an 8% concentration of acid in water with another solution that has a 15% concentration of acid in water. If the nurse uses 120 ml of the 8% solution, what volume of the 15% solution should be used to obtain a mixture with 12% concentration?

ml

  • Solution

    (160 ml) The nurse uses 120 ml of the 8% solution, which must contain 120 × .08 = 9.6 ml of acid. Let x = the volume of 15% solution that he or she uses. When the solutions are combined, there will be 120 + x total solution, of which 9.6 + .15x is acid. Since the combined solution is meant to have a 12% concentration, 12% of the total must equal the acid volume. That is, .12(120 + x) = 9.6 + .15x. Then 14.4 + .12x = 9.6 + .15x. Combine like terms by subtracting 9.6 and .12x from each side: 4.8 = .03x. Finally, divide by .03 on each side to obtain 160 ml = x.

The cost c, in dollars, of buying shirts as a function of x, the number of shirts bought is given by c(x) = 3.75x + 180. The cost of buying 995 shirts is how much more than the cost of buying 775 shirts?

$

  • Solution

    ($825) The shortcut: the number in front of x—also called the coefficient of x—in the equation c(x) = 3.75x + 180 represents the per item cost. In other words, $3.75 is the price per shirt. So when 995 – 775 = 220 more shirts are bought, the cost differential is 3.75 × 220 = $825.
    *The cost of 995 shirts is c(995) = 3.75(995) + 180 = $3,911.25. The cost of 775 shirts is c(775) = 3.75(775) + 180 = $3,086.25. The difference is 3,911.25 − 3,086.25 = $825.

Question is based on the following table, which shows the weekly spending of a small business on office supplies.

For what values of x are both the mean (average) and the median weekly spending for the entire period between 60 and 70 dollars?
Indicate all that apply.

A. 65
B. 72
C. 80
D. 83
E. 89

  • Solution

Question is based on the following table, which shows the weekly spending of a small business on office supplies.

If the Week 6 spending alone accounts for at least 80% of all spending for the entire period, what is the minimum value of x?

  • Solution

    (1,356) If x alone accounts for at least 80% of total spending, then x ≥ .80 × (339 + x). Distribute the .8, and x ≥ 271.2 + .8x. Subtract .8x from both sides to obtain .2x ≥ 271.2. Finally, divide both sides by .2, and x ≥ 1,356.

Machine A can produce a case of nails in 15 hours. Machine B can produce a case of nails in 12 hours. When both machines are running at the same time, how many hours will it take to produce nine cases?

  • Solution

The cube above has volume equal to 64 cubic feet. If Points M and N are the midpoints of two edges of the cube, what is length MN, in feet?

  • Solution

A boy is photocopying a rectangular poster. He sets the copier to increase the length of the poster by 30% and the width of the poster by 40%. The increase in the area of the poster is equal to x%. What is the value of x?

  • Solution

Books sell for $5 to $10 each. Magazines sell for $3 to $5 each. Zoe bought four books and five magazines. Which of the following could be the amount of money she spent?
Indicate all that apply.
A. $30
B. $36.25
C. $48.50
D. $59.95
E. $64
F. $70

  • Solution

    (B, C, D, E)

    Find the minimum Zoe could have spent by choosing the least price for both books and magazines. Then her total is 4 × 5 + 5 × 3 = 20 + 15 = $35. Find the maximum expenditure by choosing the greatest price for both books and magazines. Then her total is 4 × 10 + 5 × 5 = 40 + 25 = $65.

    So she spent from $35 to $65, (B), (C), (D), and (E).

If 3x – 13 > –38 and 4 – 5x > 38, then x could equal which of the following?
Indicate all that apply.

A. –5.5
B. –6.5
C. –7.5
D. –8
E. –9
F. –10

  • Solution

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