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What is integer x?

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What is integer x?

by M7MBA » Sat Dec 30, 2017 7:22 am
What is integer x? $$(1)\ \ \ \ x^x=|x|\ $$ $$(2)\ \ \ \ x^2=|x^3|$$ The OA is the option A.

I don't know how to find the correct answer. Experts, could you give me your explanation? Thanks.
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Source: — Data Sufficiency |
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by M7MBA » Sun Jan 07, 2018 11:30 am
Experts, can you help me? I still don't know how to solve this DS question.

Thanks.
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by Jay@ManhattanReview » Tue Jan 09, 2018 3:45 am
M7MBA wrote:What is integer x? $$(1)\ \ \ \ x^x=|x|\ $$ $$(2)\ \ \ \ x^2=|x^3|$$ The OA is the option A.

I don't know how to find the correct answer. Experts, could you give me your explanation? Thanks.
(1) x^x = |x|

We cannot consider x = 0 as 0^0 is undefined.
x can be 1 as 1^1 = 1 and |1| = 1.
x cannot be -1 as (-1)^(-1) = 1/(-1) = -1 ≠ |1| (= 1).
There is no need to consider other positive integer values as for those values x^x >> |x|. Thus x = 1. Sufficient.

(2) x^2 = |x^3|

x can be any integer among 0, 1 and - 1.

At x = 0, we have x^2 = |x^3| => 0^2 = |0^3| => 0 = 0.
At x = 1, we have x^2 = |x^3| => 1^2 = |1^3| => 1 = 1.
At x = -1, we have x^2 = |x^3| => (-1)^2 = |(-1)^3| => 1 = 1.

No unique value. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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