Is x/(yz) 0 (1) yz x^2 (2) x

Question

Is  \frac{x}{yz}>0 ？
 
(1)  yz>x^2

(2)  x<y+z

gmatophobia · Answer

Question : \frac{x}{yz}>0 Inference : For this to be true - x > 0 yz > 0 OR x < 0 yz < 0 Statement 1 (1) yz>x^2 As x^2 is non-negative, yz is positive in this case. Hence we can conclude that yz > 0. We however don't know the value of x, hence the statement alone is not sufficient. Eliminate A and D. Statement 2 (2) x 0 and yz > 0 ⇒Is \frac{x}{yz}>0 ？ -- Yes ! Case 1 : ----- x -----(y+z)------- y ---------- x ------ 0 ------- In this case, x < 0 and yz > 0 ⇒Is \frac{x}{yz}>0 ？ -- No! As we have two contradicting answers from statement 2, the statement alone is not sufficient. Hence we can eliminate B. Combined The statements combined don't help either as the sign of x can be positive or negative in both of the above statements. Hence the ambiguity on the sign of x remains when we use both the statements combined. Option E

Is x/(yz) > 0 (1) yz > x^2 (2) x < y + z

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