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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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20 Apr 2010, 07:04
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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]

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20 Apr 2010, 08:00
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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.

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

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20 Apr 2010, 08:50
Great explanation Bunuel!

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

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24 Apr 2010, 10:23
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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24 Apr 2010, 17:06
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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07 Nov 2011, 01:36
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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07 Nov 2011, 03:54
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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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17 Jun 2013, 05:05
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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28 Sep 2013, 06:41
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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28 Sep 2013, 06:52
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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12 Dec 2014, 19:27
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Re: What is the value of integer x ? [#permalink]

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15 Feb 2016, 09:11
Hello from the GMAT Club BumpBot!

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

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08 Sep 2017, 12:30
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: What is the value of integer x? [#permalink]

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08 Sep 2017, 14:18
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

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

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08 Sep 2017, 22:09
robertops wrote:
What is the value of integer x?

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

Merging topics. Please refer to the discussion above.
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Re: What is the value of integer x ?   [#permalink] 08 Sep 2017, 22:09
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