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67 Find x from the inequality

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by ern5231 » Sat Sep 26, 2009 4:00 am
x is an integer. What is the value of x in the expression 4 <(x-1) ^ 2 <16?

A.0
B.1
C.2
D.3
E.4

Cant we reduce this expression to 2<x-1<4? Then we get the answer as E. But the answer given is C.Please explain.
Last edited by ern5231 on Sun Oct 04, 2009 12:49 am, edited 1 time in total.
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Re: Find x from the inequality

by mohitsharda » Sat Sep 26, 2009 6:45 am
ern5231 wrote:x is an integer. What is the value of x in the expression 4 <(x-1) ^ 2 <16?

A.0
B.1
C.2
D.3
E.4

Cant we reduce this expression to 2<x-1<4? Then we get the answer as E. But the answer given is C.Please explain.
x = 2 => expression becomes (2-1)^2 = 1
So, that should clearly not be the answer.
It should be 4.. maybe the given answer is wrong.
MS
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by rajiishere » Sun Sep 27, 2009 5:47 am
If x is 2, then (x-1)^2 is (2-1)^2 which is 1. 4 is not less than 1. So, 2 could not be the answer. 4 should be the answer.
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by ern5231 » Sun Oct 04, 2009 12:48 am
Ok..but the OA is 2. Any views?
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by glorydefined » Sun Oct 04, 2009 3:18 am
wats the source of the question?? answer looks 4 to me as well
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by marie » Sun Oct 04, 2009 6:27 am
The answer is 4. There are multiple ways to attack this problem. Here's one;

4<(x-1)^2<16
4<x^2-2x+1<16
subtract 4 from all segments
0<x^2-2x-3<12
0<(x-3)*(x+1)<12
when x = 3 the quadratic is equal to zero. The above suggests the quadratic must be greater than zero and less than 12. Therefore x must = any number greater than 3 but less than 5. x= 4
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