5 lb. Book of GRE Practice Problems by Manhattan Prep

Author:Manhattan Prep
Language: eng
Format: epub, mobi, pdf
Publisher: Manhattan Prep Publishing
Published: 2015-06-02T04:00:00+00:00

Since f(g(x)) = 1, solve the equation = 1:

4 – 3x = 5

–3x = 1

x = –

34. (E). The value of the investment doubled every 9 years. Calculate the amount of money at the end of each 9-year period:

Age Value

27 $25,125

27 + 9 = 36 $50,250

36 + 9 = 45 $100,500

45 + 9 = 54 $201,000

54 + 9 = 63 $402,000

At age 63, the investor had $402,000.

35. (D). Calculate each of the archer’s scores by plugging in the appropriate values for b, a, and s. For the first archer, b = a = s = 10 and the score is . For the second archer, b = half of 10 = 5, a = twice as many as 10 = 20, and s = 15. The score for the second archer is . The difference in scores is 20 – 2 = 18.

36. (E). Let k equal the constant added to a term to get the next term. If the second term = 27, then the third term = 27 + k, the 4th term = 27 + 2k, and the 5th term = 27 + 3k. The 5th term equals 84, so create an equation:

27 + 3k = 84

3k = 57

k = 19

To find the first term, subtract k from the second term. The first term = 27 – 19 = 8.

37. (C). This problem defines functions for the made-up symbols # and @. Substitute a = 1 and b = 2 into the function for a@b: 3(1) – 2(2) = –1. Substitute a = 3 and b = 4 into the function for a#b: . Now, subtract: (–1) – = –1 + = .

38. (D). This is an arithmetic sequence: each new number is created by adding 5 to the previous number in the sequence. Calculate the first few terms of the sequence: 1, 6, 11, 16, 21, and so on. Arithmetic sequences can be written in this form: an = a1 + k(n – 1), where k is the added constant and n is the number of the desired term. In this case, the function is: an = 1 + 5(n – 1). The 75th term of this sequence is a75 = 1 + 5(74) = 371.

To find the sum of an arithmetic sequence, multiply the average value of the terms by the number of terms. The average of any evenly spaced set is equal to the midpoint between the first and last terms. The average of the 1st and 75th terms is = 186. There are 75 terms. Therefore, the sum of the first 75 terms = 186 × 75 = 13,950.

39. (E). This is a geometric sequence: each new number is created by multiplying the previous number by 2. Calculate the first few terms of the series to find the pattern: 1, 2, 4, 8, 16, and so on. Geometric sequences can be written in this form: an = rn – 1, where r is the multiplied constant and n is the number of the desired term.

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