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What is the value of integer x ?

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What is the value of integer x ?  [#permalink]

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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
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Re: Tough Inequation DS: What is the value of integer x ?  [#permalink]

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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]

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Re: Tough Inequation DS: What is the value of integer x ?  [#permalink]

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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]

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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]

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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]

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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]

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New post 17 Jun 2013, 04:05
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: What is the value of integer x ?  [#permalink]

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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]

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New post 28 Sep 2013, 05:52
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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Re: What is the value of integer x?  [#permalink]

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New post 08 Sep 2017, 13:18
robertops wrote:
What is the value of integer x?

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




1) 4<(x-1)^2<16
3<x<5 or -3<x<-1
X=-2 or 4
A D eliminated

2) 4<x^2-1<16
5<x^2<16
x= -3,3,-4,4
B eliminated

Combine 1&2

X=4 is the answer

C is ANSWER

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Re: What is the value of integer x ?  [#permalink]

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New post 23 Oct 2018, 07:47
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Re: What is the value of integer x ?   [#permalink] 23 Oct 2018, 07:47
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