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What is the value of integer x ?

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What is the value of integer x ?

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What is the value of integer x ?

(1) 4 < (x-1)*(x-1) < 16
(2) 4 < (x+1)*(x-1) < 16

OA C

Can some experts determine whether the statements are sufficient?

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Hi ardz24,

We're told that X is an INTEGER. We're asked for the value of X. A bit of 'brute force' math can help you to work through this question relatively quickly.

1) 4 < (x-1)(x-1) < 16

Since X has to be an INTEGER, you can start at X=0 and 'work up' to find a solution. X cannot be 0, 1, 2 or 3 (since none of those results would fit the given range. However, X = 4 does fit - but no other positive integer value will fit that range. The prompt did not state that X had to be positive though, so we also have to consider NEGATIVE solutions. 'Working down' from 0, you'll find that X = -2 is also a solution (but no other negative integer solution exists).
Fact 1 is INSUFFICIENT

2) 4 < (x+1)(x-1) < 16

The same approach that we used in Fact 1 can be used here. You'll find that X = 3 and X = 4 are solutions and X = -3 and X = -4 are also solutions.
Fact 2 is INSUFFICIENT

Combined, there is only one answer that 'fits' BOTH Facts: X = 4
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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ardz24 wrote:
What is the value of integer x ?

(1) 4 < (x-1)*(x-1) < 16
(2) 4 < (x+1)*(x-1) < 16
Statement 1:
4 < (x-1)² < 16.
Implication:
x-1=±3, with the result that (x-1)²=9.
If x-1 = 3, than x=4.
If x-1 = -3, than x=-2.
Since x can be different values, INSUFFICIENT.

Statement 2:
4 < x² - 1 < 16
5 < x² < 17.
Implication:
x²=9 or x²=16.
Options for x:
±3, ±4.
Since x can be different values, INSUFFICIENT.

Statements combined:
Of the options for x in Statement 1, only x=4 is among the options for x in Statement 2.
Thus, x=4.
SUFFICIENT.

The correct answer is C.

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