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# If x is a positive integer, x=? (1) [(x-5)(x+4)]^1/2 > 10 (2) [(x-5)(x

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Manager
Joined: 30 May 2018
Posts: 88
GMAT 1: 620 Q42 V34
WE: Corporate Finance (Commercial Banking)
If x is a positive integer, x=? (1) [(x-5)(x+4)]^1/2 > 10 (2) [(x-5)(x  [#permalink]

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06 Apr 2019, 03:27
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00:00

Difficulty:

55% (hard)

Question Stats:

59% (02:09) correct 41% (02:42) wrong based on 37 sessions

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If x is a positive integer, x=?

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

(2) $$\sqrt{(x-5)(x+4)} < 11$$
Senior Manager
Joined: 25 Feb 2019
Posts: 335
Re: If x is a positive integer, x=? (1) [(x-5)(x+4)]^1/2 > 10 (2) [(x-5)(x  [#permalink]

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06 Apr 2019, 03:59
1
After solving first statement we get ,

x greater the 11.4 approx

x can have many values insufficient

statement 2
we get x less than 12.12 approx

alone insufficient

putting together ,

we get integer value as 12

IMO C

award kudos if helpful

Posted from my mobile device
Manager
Joined: 30 May 2018
Posts: 88
GMAT 1: 620 Q42 V34
WE: Corporate Finance (Commercial Banking)
Re: If x is a positive integer, x=? (1) [(x-5)(x+4)]^1/2 > 10 (2) [(x-5)(x  [#permalink]

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06 Apr 2019, 04:21
m1033512 wrote:
After solving first statement we get ,

x greater the 11.4 approx

x can have many values insufficient

statement 2
we get x less than 12.12 approx

alone insufficient

putting together ,

we get integer value as 12

IMO C

award kudos if helpful

Posted from my mobile device

How did u get 11.4 and 12.12 ? Please show steps.
Senior Manager
Joined: 25 Feb 2019
Posts: 335
Re: If x is a positive integer, x=? (1) [(x-5)(x+4)]^1/2 > 10 (2) [(x-5)(x  [#permalink]

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06 Apr 2019, 05:04
for first statement tonhold true,

we should have
(x-5)*(x+4) >100

x^2-x-20 >100
x^2-x-20-100>0

please solve this quadratic inequation and find the range of values of x

similarly simplify and solve statement 2 also and find the range value of x

and by combining both the statements you will get only 12 is the integer values satisfying this .

Hope this helps

It is very difficult to type all the steps here ......

Posted from my mobile device
Re: If x is a positive integer, x=? (1) [(x-5)(x+4)]^1/2 > 10 (2) [(x-5)(x   [#permalink] 06 Apr 2019, 05:04
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# If x is a positive integer, x=? (1) [(x-5)(x+4)]^1/2 > 10 (2) [(x-5)(x

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