xa = 1
a > 0
QUANTITY A QUANTITY B- x 1 A B C D
b
√c = a
QUANTITY A QUANTITY B- ba^22 c A B C D
Exercise Answers
Discrete Quantitative Questions
- E To solve for x, you should express all the terms with a base of 2: 4^2 = (2^2 )^2 =
24. 16^5 = (2^4 )^5 = 2^20. Thus:
(2^4 )(2^20 ) = 2^24 = 2x
↓
x = 24 - 5 When simplifying exponential expressions, you should express all bases in
their prime forms. Express 21 in terms of base 7 and 3: 211,003 = (7 × 3)1,003 =
(71,003)(31,003). The fraction now reads:
(71,003)(31,003)
(31,002)(71,001) = (7
(^2) )3 = 147
- C Note that you are adding the same term (5x) five times. Thus:
5 x + 5x + 5x + 5x + 5x = 5(5x) = (5^1 )(5x) = 5(x+1) = 5^6
x + 1 = 6
x = 5 - B Since the two sides of this equation are equal, they must have the same
prime factorization. Thus the exponent on the 2 on the left side of the equation
represents the number of times 2 appears in the prime factorization of 576,
and the exponent on the 3 on the left side of the equation represents the
number of times that 3 appears in the prime factorization of 576. To solve for
these exponents, you should express 576 in terms of base 2 and 3:
576 = 2(288)
576 = (2)(2)(14 4)
576 = (2)(2)(12)(12)
576 = (2)(2)(4 × 3)(4 × 3)
576 = (2)(2)(2 × 2 × 3)(2 × 2 × 3)
576 = (2^6 )(3^2 )
280 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 280 12/05/17 11:54 am