If x is an integer, is x2 25? (1) |x – 3| 5 (2) (x + y)2 49, whe

Question

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

chetan2u · Answer

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 -27.......when x=2, x+2>7...x>5. Also x=-2, x-2>7...x>9....YES x>5 in every case B

Archit3110 · Answer

#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

AkshdeepS · Answer

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)

ArunSharma12 · Answer

Given: x^2 > 25? x<-5 or x >5? statement 1: x-3> 5 or x-3<-5 x>8 or x<-2 x can be -3 falling outside the range x can be -6 falling within the range not sufficient statement 2: -2 < y < 2 (x + y) > 7 or x+y<-7 x > 7-y or x < -7-y x > 7 - y, in order to get the minimum value take maximum value of y: 1 x > 7 -1 or x> 6 x < -7-y, in order to get the maximum value take minimum value of y: -1 x < -7+1 or x < -6 x > 6 or x < -6 this is sufficient

rokhan · Answer

you assume y to be an integer in statement 2 when it's not mentioned explicitly. y could be 1.9 or -1.9. Doesn't change the answer in this case though

ArunSharma12 · Answer

It is not given in the question stem but it is given in statement 2.

Kritisood · Answer

hey  arunsharma

can we write statement 2 as x+y>7?

ArunSharma12 · Answer

hi  Kritisood ,

statement 2 is of the form  a^2>b^2 
if we know that a & b are not 0 and have a positive value then yes, I can write a > b.
otherwise I'll have to solve this inequality by finding the possible range for  (a+b)(a-b)>0 .
in this question we have to follow the latter approach as we do not know signs of x & y.

Kritisood · Answer

got it thanks
Also from st 2, we get -6<x<6 how is this sufficient to answer the question? we have to answer if -5<x<5
as per -6<x<6 the answer may (x=4) or may not (x=5/x=-5) be in the range of -5<x<5
am i missing something?  chetan2u

chetan2u · Answer

x^2 > 25 MEANS we are looking for whether x<-5 or x>5 (1) |x – 3| > 5 x-3>5.....x>8.... So surely x>5 Or 3-x>5.....x<-2.... x could be between -2 and -5, then NO, and ix x<-5 , yes Insuff (2) (x + y)^2 > 49, where y is an integer such that |y| < 2 \sqrt{(x + y)^2} > \sqrt{49}. Two possibilities a) x+y<-7, but -27, but -27....x>6. Thus if the min value of x>5, we can again say yes. Suff B Kritisood , now on your query. If statement II gives you the range - x<-6 and x>6, and you have to answer whether x<-5 and x>5, your answer will be yes. So you are looking for x<-5, and statement II tells you that x can be -7, -8 or less .... x will always be less than -5. Or you are looking for x>5, and statement II tells you that x can be 7, 8 or more.... x will always be greater than 5.

Kritisood · Answer

got it,  chetan2u  thanks for explaining.

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If x is an integer, is x2 > 25? (1) |x – 3| > 5 (2) (x + y)2 > 49, whe

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