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Is |w-6| > 5 ?
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1991sehwag
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Is |w-6| > 5 ? [#permalink] New post  Updated on: 18 Jan 2015, 01:55
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Is |w-6| > 5 ?

(1) w is an integer

(2) w^2 < 1
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Originally posted by 1991sehwag on 17 Jan 2015, 18:46.
Last edited by Bunuel on 18 Jan 2015, 01:55, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Is |w-6| > 5 ? [#permalink] New post  17 Jan 2015, 20:52
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Expert Reply
STAT1 itself is not sufficient as w can have any integer value
Ex: w = 100 will make the inequality true and w=0 can make the inequality false
So, NOT SUFFICIENT

STAT2: w^2 < 1 => -1<w<1

For all values of w in this range the inequality is true
Only for values of w >=1 the inequality will be false
SO, SUFFICIENT

Hence, answer will be B

Hope it helps!


1991sehwag wrote:
Is |w-6| > 5 ?

1) w is an integer

2) w^2 < 1

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Re: Is |w-6| > 5 ? [#permalink] New post  17 Jan 2015, 22:57
Expert Reply
Hi 1991sehwag,

This DS question can be solved with a bit of logic and TESTing VALUES.

We're asked if |W - 6| > 5. This is a YES/NO question.

Fact 1: W is an integer

IF....
W = 6
Then the answer to the question is NO.

IF....
W = 12
Then the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: W^2 < 1

This Fact severely restricts the possible values of W. The range is -1 < W < 1. W can get "really close" to 1 or -1, but CANNOT be either of those values.

IF...
W = .99999
Then the answer to the question is YES.

IF...
W = 0
Then the answer to the question is YES.

IF....
W = - .99999
Then the answer to the question is YES.
Fact 2 is SUFFICIENT.

Final Answer:
Show: ::
B


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Re: Is |w-6| > 5 ? [#permalink] New post  25 Jan 2015, 12:42
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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ryorye
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Re: Is |w-6| > 5 ? [#permalink] New post  24 Sep 2020, 09:21
tcsanimesh wrote:
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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Re: Is |w-6| > 5 ? [#permalink] New post  24 Sep 2020, 10:12
1
(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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Is |w-6| > 5 ? [#permalink] New post  24 Sep 2020, 12:56
Expert Reply
1991sehwag wrote:
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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