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1991sehwag
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The question here is
whether W > 1 or W > 11

Stmt1 only tells W is an integer. It can be negative, zero or positive. Hence stmt1 is not sufficient
stmt2 :W^2 - 1 < 0 which means -1 < W < 1 which clearly means W is neither greater than 1 nor 11. Hence sufficient.

So the answer is B.
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tcsanimesh
The question here is
whether W > 1 or W > 11

Stmt1 only tells W is an integer. It can be negative, zero or positive. Hence stmt1 is not sufficient
stmt2 :W^2 - 1 < 0 which means -1 < W < 1 which clearly means W is neither greater than 1 nor 11. Hence sufficient.

So the answer is B.


Isn't w < -1 and w >11 ?
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(1) if w is an integer

w = 66, then |w-6| = 60 >5 TRUE
w = 6, then |w-6| =0 >5 FALSE
not suff.

(2) w^2 <1
(w+1)(w-1)<0
So, -1< w<1

Now, checking extremes & in between values.

w= -0.99 -> |w-6| = 6.99 >5 TRUE
w= 0.99 -> |w-6| = 5.01>5 TRUE
w= 0 -> |w-6| =6 >5 TRUE
Any value from in (-1,1) will satisfy this.

So, (2) is suff.

Hope it helps!
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1991sehwag
Is |w-6| > 5 ?

(1) w is an integer

(2) w^2 < 1

You can solve the inequality in the question:

Two scenarios:

> w – 6 > 5 → w > 11

> w – 6 < -5 → w < 1

Therefore, the answer is YES if w < 1 or w > 11.

Stat (1)
w could be 0 or 2, so the answer could be YES or NO.
Insufficient

Stat (2)
This means that -1 < w < 1. Therefore, w < 1 will always be true, so the answer will always be YES.
Sufficient

(b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
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