Is a |b| ? (1) 2^(a - b) 16 (2) |a - b|

Question

Is  a > |b|  ?

(1)  2^{(a - b)} > 16 
(2)  |a - b| < b

gmatophobia · Answer

Question: Is a > |b| ? Does b lie between -a and a ? -a < b < a Statement 1 (1) 2^{(a - b)} > 16 2^{(a - b)} > 2^{4} a - b > 4 a > b + 4 Case 1: ---------- -b ---------- b ---------- a --------- 2b ---------- Case 2: ---------- b ------- a --- -b ---------- As we are getting two possible answers, the statement is not sufficient. Statement 2 (2) |a - b| < b -b < a - b < b Adding "b" 0 < a < 2b Case 1: ---------- 0 ---------- b ------ a --- 2b --------- Case 2: ---------- -b --- 0 --- a --- b ---------- 2b --------- Combining As a > 0, and a < 2b, therefore b > 0 From statement 1, we know that a > b +4, hence a lies to the left of b on the number line and not between b and -b. The statement is sufficient. Option C

Is a > |b| ? (1) 2^(a - b) > 16 (2) |a - b| < b

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