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# What is the value of x, if x is an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
What is the value of x, if x is an integer?  [#permalink]

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02 Sep 2016, 04:23
1
2
00:00

Difficulty:

75% (hard)

Question Stats:

48% (02:22) correct 52% (02:41) wrong based on 63 sessions

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What is the value of x, if x is an integer?

(1) $$\sqrt{(x+4)*(x-5)} < 11$$

(2) $$\sqrt{(x+4)*(x-5)} > 10$$

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Current Student
Joined: 09 Jul 2016
Posts: 25
Re: What is the value of x, if x is an integer?  [#permalink]

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02 Sep 2016, 05:44
1
From Statement 1, squaring both sides

(x+4)(x-5) < 121

x can take any value. Not sufficient.

From Statement 2, squaring both sides

(x+4)(x-5) > 100

x can take any value. Not sufficient.

Combining both, 100< (x+4)(x-5) < 121
Product has to be greater than 100, so we start by checking values of x as x=11,12,13 etc.
when x = 11, (11+4)(11-5)= 90
when x = 12, (12+4)(12-5)=112; Condition satisfied
when x=13, (13+4)(13-5) = 136;
Now x can also be negative
Checking for -11, (-11+4)(-11-5) = 112; Condition satisfied
So, value of x could be 12 or -11. Hence answer is E
Intern
Joined: 15 Dec 2014
Posts: 8
Re: What is the value of x, if x is an integer?  [#permalink]

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02 Sep 2016, 19:55
1
1: (x+4)(x-5)<121
or x(x-1)<141 not sufficient as there are many values of x satisfying the equation

2: x(x-1)>120 not sufficient

1 and 2 :

120<x(x-1)<141
x= -11 and 12 both satisfy
hence E
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Joined: 09 Sep 2013
Posts: 9851
Re: What is the value of x, if x is an integer?  [#permalink]

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13 Apr 2018, 07:51
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Re: What is the value of x, if x is an integer?   [#permalink] 13 Apr 2018, 07:51
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