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23 The flat triangular lot depicted above is available for development If x + x = 150
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meters, what is the area of the lot in square meters
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A 125
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B 150 3 C 1,500 D 1,250 3 E 2, 500 3
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ANSWER: D You can tell from the statement x + x = 150 that x = 100 meters, and since one 2 x of the legs of the right triangle is 2 and the hypotenuse is x, you can tell that this is a 30 60 90 triangle, and the legs of the triangle are then 50 and 50 3 The area of a triangle is one-half base times height, so (50)(50 3 ) = 2 2, 500 3 = 1, 250 3 2
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21 If x is a positive number and 1/2 the square root of x is the cube root of x, then x = A B C D E 64 32 16 4 1
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ANSWER: A The fastest approach to a question like this is probably to plug in the answer choices and see which one fits If x = 64, then 1/2 of the square root is 4, which is also the cube root of 64, so A is the answer
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24 For any numbers w and z, w z = w 3z(8 w2) If both z and w z are positive numbers, which of the following could be a value of w A B C D E 9 3 0 2 9
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27 What is the value of 5x 2 19x 37 for x = 03 A B C D E 472 382 358 268 057
ANSWER: E The most direct approach here is probably to plug in the answers and see which one gives a positive value for w z A and B are out because (8 - w 2) results in a negative number while w 3z is positive, C is out because 0 is not a positive number, D is out because w 3z is negative while (8 - w 2) is positive; only E meets the conditions, because both (8 - w2) and w 3z are negative, yielding a positive value for w z
ANSWER: D The equation 5(-03 -03) -19(- 03) -37 = 045 + 057 - 37 = - 268
28 Two cyclists are racing up a mountain at different constant rates Cyclist A is now 50 meters ahead of cyclist B How many minutes from now will cyclist A be 150 meters ahead of cyclist B (1) 5 minutes ago, cyclist A was 200 meters behind cyclist B (2) Cyclist A is moving 25% faster than cyclist B
ANSWER: A To answer this question, we need to know how much faster cyclist A is moving than cyclist B (1) gives us this information, because we know that cyclist A gained 250 m on cyclist B in 5 minutes, so he is traveling 50 m/minute faster; (1) is sufficient (2) is insufficient, because their relative rate of motion is useful here only if it can be converted into actual measures of meters over time, which (2) cannot
1+1 4 5 25 1 = 8 A 2 5 B 9 20 C 9 8 D 9 5 E 18 5
ANSWER: E The fraction is the same thing as 9 20 = 72 = 18 1 20 5 8
29 Is integer x divisible by 48 (1) x is divisible by 16 (2) x is divisible by 12
ANSWER: C (1) alone is insufficient because the set of numbers divisible by 16 contains some numbers divisible by 48 (eg, 48, 96), but also some numbers not divisible by 48, such as 16, 32, and so on (2) alone is insufficient for the same reason If the two statements are combined, the set of numbers divisible by both 16 and 12 are all divisible by 48; plug in numbers to verify that this is true It works because 48 is the lowest common multiple of these two numbers
26 Last year s receipts from the sale of greeting cards during the week before Mother s Day totaled \$189 million, which represented 9 percent of total greeting card sales for the year Total greeting card sales for the year totaled how many million dollars A B C D E 17,010 2,100 1,890 1,701 210