If x and y are integers, is x^7 < 6^y?

[Vincen]

If x and y are integers, is x^7 < 6^y?

(1) x^3 = -125

(2) y^2 = 36

The OA is A.

How can I know that x^7 < 6^y without knowing the value of y? Experts, clarify this for me, please? Thanks.

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Hi Vincen,

We're told that X and Y are integers. We're asked if X^7 is less than 6^Y. This is a YES/NO question. We can solve it by TESTing VALUES and/or by using Number Property rules. To start, it's worth nothing that X^7 could be positive (if X is positive), 0 (if X is 0) or negative (if X is negative). However, 6^Y can ONLY be positive (regardless of the value of Y)...

1) X^3 = -125

Fact 1 tells us that X will be NEGATIVE (you don't technically have to calculate it, but the one solution to this equation is X = -5). Since X is negative, X^7 will also be negative. Since 6^Y is always positive, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

2) Y^2 = 36

The equation in Fact 2 has two solutions: +6 and -6. However, we know nothing about the value of X. Since X^7 could be negative or a gigantic positive number, the answer to the question could be YES or NO.
Fact 2 is INSUFFICIENT.

Final Answer: A

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