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# m25,q1

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Joined: 06 Dec 2009
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28 Dec 2009, 14:04
Can anybody help me with this question?

Is $$|x - 6| > 5$$?

1. $$x$$ is an integer
2. $$x^2 < 1$$

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

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Math Expert
Joined: 02 Sep 2009
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28 Dec 2009, 18:53
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Expert's post
ppaulyni3 wrote:
Can anybody help me with this question?

Is |x - 6| > 5?

1. x is an integer
2. x^2 < 1

Let's work on the stem first. For which values of x, |x - 6| > 5 is true?

|x - 6| > 5
x<6 --> -x+6>5 --> x<1.
x>=6 --> x-6>5 --> x>11.

So for x from the ranges x<1 and x>11 the inequality |x - 6| > 5 holds true.

(1) x is an integer, clearly not sufficient. x can be 12 and the inequality holds true as we concluded OR x can be 5 and inequality doesn't hold true.

(2) x^2<1 --> -1<x<1, as all x-es from this range are in the range x<1, hence inequality |x - 6| > 5 holds true. Sufficient.

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17 Jan 2010, 08:30
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but in this case statement A contradicts to statement B. A states that x is an integer and B states that it is not.

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17 Jan 2010, 17:32
Tati wrote:
but in this case statement A contradicts to statement B. A states that x is an integer and B states that it is not.

Not so, taken together x can be zero which is an integer.
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09 May 2012, 22:46
Bunuel wrote:
Tati wrote:
but in this case statement A contradicts to statement B. A states that x is an integer and B states that it is not.

Not so, taken together x can be zero which is an integer.

If we need to indicate that x is an integer, shouldn't the answer be C?

Statement 1 alone: Insufficient.
Statement 2 alone:
-1<x<1
|-1-6| = 7. True.
However.
|1-6| = 5. False 5 is not larger than 5. Also insufficient.

Both statement together:
If say we take zero as an integer we need statement 1 to indicate that x is in fact an integer.

|0-6| = 6. True

Sufficient.

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10 May 2012, 01:18
leochanGmat wrote:
Bunuel wrote:
Tati wrote:
but in this case statement A contradicts to statement B. A states that x is an integer and B states that it is not.

Not so, taken together x can be zero which is an integer.

If we need to indicate that x is an integer, shouldn't the answer be C?

Statement 1 alone: Insufficient.
Statement 2 alone:
-1<x<1
|-1-6| = 7. True.
However.
|1-6| = 5. False 5 is not larger than 5. Also insufficient.

Both statement together:
If say we take zero as an integer we need statement 1 to indicate that x is in fact an integer.

|0-6| = 6. True

Sufficient.

No, when considering the second statement we don't need to know that x is an integer. The question asks: "is x<1 or x>11?" and (2) says that -1<x<1, so we can answer YES to the question. In your examples you can not consider x=-1 and x=1 since in the given range (-1<x<1) -1 and 1 are not inclusive.

Hope it's clear.
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10 May 2012, 11:55
Thank you for the clarification.

Say if statement 2 is larger than 11, but not smaller than 1. The statement will still be sufficient?

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Re: m25,q1   [#permalink] 10 May 2012, 11:55
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# m25,q1

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