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Re: Tough Inequation DS: What is the value of integer x ? [#permalink]
20 Apr 2010, 07:00

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MBAUncle wrote:

What is the value of integer x ?

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

OA is C

If it is asking for the value of X, should an interval be enough to answer the question ?

Note: x is an integer.

(1) 4<(x-1)*(x-1)<16 --> 4<(x-1)^2<16 --> (x-1)^2 is a perfect square between 4 and 16 --> there is only one perfect square: 9 --> (x-1)^2=9 --> x-1=3 or x-1=-3 --> x=4 or x=-2. Two answers, not sufficient.

(2) 4<(x+1)*(x-1)<16 --> 4<x^2-1<16 --> 5<x^2<17 --> x^2 is a perfect square between 5 and 17 --> there are two perfect squares : 9 and 16 --> x^2=9 or x^2=16 --> x=3 or x=-3 or x=4 or x=-4. Four answers, not sufficient.

(1)+(2) Intersection of values from (1) and (2) is x=4. Sufficient.

When you take the square root (which you can because all terms are positive), you get 2 < |x - 1| < 4 If x is to be an integer, |x - 1| = 3 x can be 4 or -2

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