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What is the value of integer x ?

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What is the value of integer x ? [#permalink] New post 20 Apr 2010, 06:04
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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
[Reveal] Spoiler: OA
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Re: Tough Inequation DS: What is the value of integer x ? [#permalink] New post 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.

Answer: C.
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Re: Tough Inequation DS: What is the value of integer x ? [#permalink] New post 20 Apr 2010, 07:50
Great explanation Bunuel!

Kudos!!
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Re: Tough Inequation DS: What is the value of integer x ? [#permalink] New post 24 Apr 2010, 09:23
Good question with a great explanation... Bunnel you are the champ :-)
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Re: Tough Inequation DS: What is the value of integer x ? [#permalink] New post 24 Apr 2010, 16:06
Bunuel, Just excellent!!!.
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What is the value of integer x ? (1) 4 < (x-1)*(x-1) < 16 [#permalink] New post 07 Nov 2011, 00:36
I have a doubt with that of choosing option 1.

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

4 < (x-1)^2 < 16

Taking square root.

2 < (x-1) < 4

This gives 2 scenarios. x>3 and x< 5

Since x is an integer, the option must be 4.

So the answer must be A rite .

Any inputs ??
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Re: DS question from 700 level DS qstns by Bunnel [#permalink] New post 07 Nov 2011, 02:54
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ksp wrote:
Question source :
tough-inequation-ds-what-is-the-value-of-integer-x-93008.html

The question is

What is the value of integer x ?

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

I have a doubt with that of choosing option 1.

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

4 < (x-1)^2 < 16

Taking square root.

2 < (x-1) < 4



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

Remember, \sqrt{x^2}\neq x
Instead, \sqrt{x^2} = |x|
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Re: What is the value of integer x ? [#permalink] New post 17 Jun 2013, 04:05
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Re: What is the value of integer x ? [#permalink] New post 28 Sep 2013, 05:41
I tried solving the first inequality and got this:
Statement 1:
4 < (x-1)*(x-1) < 16

--> x^2 -2x -3 < 12

--> x^2 - 2x - 15<0

--> (x+3) (x-5)<0

If x is an integer it means the function will be negative for the values x= -2, -1, 0, 1, 2, 3, 4.

What is the mistake here?
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Re: What is the value of integer x ? [#permalink] New post 28 Sep 2013, 05:52
Expert's post
emailmkarthik wrote:
I tried solving the first inequality and got this:
Statement 1:
4 < (x-1)*(x-1) < 16

--> x^2 -2x -3 < 12

--> x^2 - 2x - 15<0

--> (x+3) (x-5)<0

If x is an integer it means the function will be negative for the values x= -2, -1, 0, 1, 2, 3, 4.

What is the mistake here?


Why would you expand and manipulate 4 < (x-1)^2 < 16, when its already in its simplest form?

Anyway:
4 < (x-1)^2 < 16;
0 < x^2-2x-3 < 12 or -12 < x^2-2x-15 < 0;
-3<x<-1 or 3<x<5 --> x=-2 or x=4.

Hope this helps.
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COLLECTION OF QUESTIONS:
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Re: What is the value of integer x ?   [#permalink] 28 Sep 2013, 05:52
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