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Director  V
Joined: 18 Feb 2019
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GMAT 1: 460 Q42 V13 GPA: 3.6
If x is an integer, is x^2 > 25?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 64% (02:20) correct 36% (02:11) wrong based on 45 sessions

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If x is an integer, is x^2>25?

I. |x – 3|>5
II. (x + y)^2 > 49, where y is an integer such that |y|<2
Math Expert V
Joined: 02 Aug 2009
Posts: 8006
Re: If x is an integer, is x^2 > 25?  [#permalink]

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1
If x is an integer, is x^2>25?
$$x^2>25.....-5>x or x>5$$

I. |x – 3|>5
two cases....x-3>5...x>8...YES.
Also -(x-3)>5.....x-3<-5....x<-2
if x is -3, NO..
Insuff

II. (x + y)^2 > 49, where y is an integer such that |y|<2
$$(x + y)^2 > 49.....x+y<-7 ..and.. x+y>7.$$
But -2<y<2
a) x+y<-7.......when x=2, x+2<-7...x<-9. Also x=-2, x-2<-7...x<-5....YES x<-5 in every case
b) x+y>7.......when x=2, x+2>7...x>5. Also x=-2, x-2>7...x>9....YES x>5 in every case

B
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Re: If x is an integer, is x^2 > 25?  [#permalink]

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kiran120680 wrote:
If x is an integer, is x^2>25?

I. |x – 3|>5
II. (x + y)^2 > 49, where y is an integer such that |y|<2

#1
|x – 3|>5
x=8 and 2
not sufficient
#2
(x + y)^2 > 49, where y is an integer such that |y|<2[
y has to be between -2>y<2
so value of x will always be x^2>25
IMO B
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If x is an integer, is x^2 > 25?  [#permalink]

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kiran120680 wrote:
If x is an integer, is x^2>25?

I. |x – 3|>5
II. (x + y)^2 > 49, where y is an integer such that |y|<2

Given : x is an integer.

Question : Is x < - 5 or x > 5 ?

St 1: |x - 3| > 5

x - 3 > 5 or x > 8

Or x - 3 < -5 or x < -2

Therefore, 8 > 5 but -2 is not less the -5 .

(x + y) ^ 2 > 49

x + y > +/-7

x + y < - 7 --- (I) or x + y > 7 (II)

|y| < 2

y = -1, 0, 1

Put y = -1 and 1 in equation (I)

x - 1 < -7, so x < -6

x +1 < -7, so x < -8

Put y = -1 and 1in equation (II)

x - 1 > 7, so x > 8

x+1 > 7, so x > 6

So from statement 2, we get all the values of x in the range x < - 5 or x > 5

Hence Sufficient (B)

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"Do not watch clock; Do what it does. KEEP GOING." If x is an integer, is x^2 > 25?   [#permalink] 31 Mar 2019, 06:34
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