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24 Is integer y > 0 (1) (2 + y) > 0 (2) (2 + y)2 > 0
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ANSWER: A (1) alone is sufficient because this statement means that y < -3, which means that y is not greater than 0 (2) alone is insufficient, because the statement could work for values of y that are both greater and less than 0, such as 1 and -1
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27 The figure above represents a window, with the shaded regions representing openings for glass and the pale regions representing the wood panels between and around the glass If the window is 45 feet high by 25 feet wide, and if each of the wooden panels is exactly 4 inches thick, what is the total surface area, in square inches, of glass in the window (1 foot = 12 inches; figure not drawn to scale) A B C D E 189 378 448 756 1,620
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25 If 4 and 11 are the lengths of two sides of a triangular region, which of the following can be the length of the third side I 5 II 13 III 15 A I only B II only C I and II only D II and III only E I, II, and III
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ANSWER: B A leg of a triangle cannot be greater than or equal to the sum of the other two legs This principle eliminates both I (11 > 5 + 4) and III (4 + 11 = 15) Therefore, II is the only acceptable length
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26 A certain truck uses 18 gallons of diesel fuel in traveling 270 miles In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck s fuel mileage be increased A B C D E 8 9 12 15 27
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ANSWER: D For this problem, you could calculate the dimensions of each of the four pieces of glass, but it is probably simplest to calculate the area of glass as if the four pieces were just one rectangular area of glass If the window is 45 feet high, then it is 45 12 = 54 inches high 54 inches minus the 3 4 inches for the wooden panels means that the glass in the window is 54 - 12 = 42 inches high The window is 25 feet wide = 30 inches; 30 inches minus 12 inches for the panels means that the glass is 18 inches wide 42 18 = 756 square inches Note that the figure is not drawn to the dimensions given in the question
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28 If 3( x 2 + x ) 7 = x 2 + 2( 4 + x 2 ) , then x = A B C D E 5 6 9 15 25
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You can restate the equation as
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ANSWER: A
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3x 2 + 3x 7 = 3x 2 + 8, so 3x = 15, and x = 5
PRACTICE TEST 1
$365
29 Suzie s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $650 On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $760 How much more do pairs of boots cost than pairs of shoes at Suzie s Discount Footwear A B C D E $250 $500 $550 $750 $1500
31 A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes Each hat is valued at $750 If the company s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order A B C D E $960 $1,350 $1,725 $2,050 $2,250
ANSWER: B One approach to this question is to set up the two equations and then eliminate one variable to solve for the other If s represents the prices of shoes and b represents the price of boots, then 22s + 16b = 650 and 8s + 32b = 760 To eliminate b, multiply both sides of the first equation by 2 and then subtract the second equation from the modified first equation, and you get 44s - 8s + 32b - 32b = 1,300 - 760; therefore, 36s = 540, and shoes cost $15 Plug this value into one of the equations and you get b = $20 $20 - $15 = $5
ANSWER: E An 8 10 12-inch box contains 960 cubic inches 288,000 total cubic inches divided by 960 cubic inches per box equals 300 boxes 300 boxes times $750 per hat equals $2,250
32 Chauncy, an English bulldog, received 1,618 votes in the Mr Bulldog USA competition, giving him approximately 20 percent of the vote Approximately what percent of the remaining votes would he have needed to receive in order to win 30 percent of the total votes A B C D E 10% 125% 15% 175% 20%
30 For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3 I Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number II Dividing each of the numbers by 3 and then adding the results together III Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9 A B C D E I only II only I and II only II and III only None of the above
ANSWER: B If 1,618 was 20 percent of the vote, then there were approximately 8,090 votes (1,618/02 = 8,090) 30 percent of 8,090 would be 2,427 2,427 - 1,618 = 809 additional votes that Chauncy would have needed in 809 order to reach 30 percent = 8,090 1,618 0125 = 125%
33 If 8 skiers raced down a course multiple times in one day, and each skier used a different pair of skis on each run, what is the maximum number of different skis used by the 8 skiers during the day (1) No skier shared any skis with any other skier (2) Each skier made exactly 12 runs during the day
ANSWER: B Choose any three numbers and test them on statements I, II, and III You will quickly find that I and III are not always true II is always true, because mathematically it and the process in the question are doing the same thing summing the numbers and dividing by 3
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