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# Is |x − 6| > 5 ?

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Is |x − 6| > 5 ?  [#permalink]

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16 Jan 2012, 22:50
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72% (01:27) correct 28% (01:35) wrong based on 455 sessions

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Is |x − 6| > 5 ?

(1) x is an integer
(2) x^2 < 1

M25-01

[Reveal] Spoiler:

When (x-6) is positive
x-6 > 5 => x > 11

When (x-6) is negative
6 - x > 5 => x < 1

So the question is (is this re-phrasing of question correct?) -
Is x > 11
or
Is x < 1

1)x is an integer - doesn't help much.

2)x^2 < 1 => x lies between -1 and 1 exclusive; means x is less than 1. answers the question.

Does this solution look okay? though it's not the most elegant. Considering |x-6| as distance is quite lucid.
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Re: Is |x − 6| > 5 ?  [#permalink]

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17 Jan 2012, 00:45
|x-6| > 5 if x>11 OR x<1

Using statement (1), we know that x is an integer. However, it may lie between 1 and 11 or not. Insufficient.

Using statement (2), x^2<1 => x lies between -1 and 1 (both not inclusive). This satisfies the condition that x<1. Sufficient.

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Re: Is |x − 6| > 5 ?  [#permalink]

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17 Jan 2012, 00:57
1
Apex231 wrote:
Is |x-6| > 5?

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

When (x-6) is positive
x-6 > 5 => x > 11

When (x-6) is negative
6 - x > 5 => x < 1

So the question is (is this re-phrasing of question correct?) -
Is x > 11
or
Is x < 1

1)x is an integer - doesn't help much.

2)x^2 < 1 => x lies between -1 and 1 exclusive; means x is less than 1. answers the question.

Does this solution look okay? though it's not the most elegant. Considering |x-6| as distance is quite lucid.

Yes, all of your work looks perfect. I personally prefer the 'distance approach' (|x - 6| is just the distance between x and 6 on the number line, so the question is just asking if that distance is greater than 5, from which we see right away that the question is asking if we can be sure that either x > 11 or x < 1), but the algebraic cases approach also works, of course.
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Re: Is |x − 6| > 5 ?  [#permalink]

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Updated on: 27 Nov 2013, 01:46
2
Is |x − 6| > 5 ?

(1) x is an integer
(2) x^2 < 1

M25-01
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Kindly press +1 Kudos if my post helped you in any way

Originally posted by sunita123 on 26 Nov 2013, 18:32.
Last edited by Bunuel on 27 Nov 2013, 01:46, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Is |x − 6| > 5 ?  [#permalink]

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26 Nov 2013, 21:43
my understanding of the ques -- Is |x−6|>5 ? i.e. is 1<x<11 ? is x between 1 and 11
(1) x is an integer -- insuff as there can be infinite values

(2) x^2<1 i..e. (x-1)(x+1) <0 so both the terms have opposite sign and are consecutive so only possible values 1 and -1...so x is zero and is suff

so B seems to be the ans..that is stmt 2 is suff..Please confirm is B is the right ans.
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Re: Is |x − 6| > 5 ?  [#permalink]

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26 Nov 2013, 22:24
himapm1l wrote:
my understanding of the ques -- Is |x−6|>5 ? i.e. is 1<x<11 ? is x between 1 and 11
(1) x is an integer -- insuff as there can be infinite values

(2) x^2<1 i..e. (x-1)(x+1) <0 so both the terms have opposite sign and are consecutive so only possible values 1 and -1...so x is zero and is suff

so B seems to be the ans..that is stmt 2 is suff..Please confirm is B is the right ans.

yes, ans is B.
Still I have a question
when I solved |x−6|>5 , i got x<1 and x>11
but from your explanation, it says 1<x<11.
Can you pls clarify
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Re: Is |x − 6| > 5 ?  [#permalink]

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27 Nov 2013, 01:47
1
1
sunita123 wrote:
Is |x − 6| > 5 ?

(1) x is an integer
(2) x^2 < 1

M25-01

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

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

If $$x<6$$ --> $$-x+6>5$$ --> $$x<1$$.
If $$x\geq{6}$$ --> $$x-6>5$$ --> $$x>11$$.

So we have that inequality $$|x - 6| > 5$$ holds true for $$x<1$$ and $$x>11$$.

(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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Re: Is |x − 6| > 5 ?  [#permalink]

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06 Feb 2015, 16:32
Bunuel wrote:
sunita123 wrote:
Is |x − 6| > 5 ?

(1) x is an integer
(2) x^2 < 1

M25-01

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

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

If $$x<6$$ --> $$-x+6>5$$ --> $$x<1$$.
If $$x\geq{6}$$ --> $$x-6>5$$ --> $$x>11$$.

So we have that inequality $$|x - 6| > 5$$ holds true for $$x<1$$ and $$x>11$$.

(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.

Dear Bunuel, I have question when I tried under the case that X >0 I got that X >11 so I chose the common range

x>11 and when I tried under the case x <0 I got that x<1 so here I chose the common range x<0 is that

correct?
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Question M25-01: is |x-6| > 5  [#permalink]

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21 Sep 2016, 18:10
Just a question about the solution to this problem:

Is |x−6|>5 ?

(1) x is an integer

(2) x^2 < 1

The explanation provided is as follows:

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

If x<6, then −x+6>5 or x<1.

If x≥6, then x−6>5 or x>11.

My question is this: How did we come to the text in red? If x<6, why would the sign change on the 6? For x values from x=5 to x=2, we have x<6 and |x-6|<5, not >5

Appreciate any insight, even if its a link to a different forum thread. I tried searching for my question but had trouble funding something this specific.

(forgot to add above, official answer was B, (2) is sufficient but (1) is not.)
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Re: Question M25-01: is |x-6| > 5  [#permalink]

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21 Sep 2016, 18:55
Quote:
My question is this: How did we come to the text in red? If x<6, why would the sign change on the 6? For x values from x=5 to x=2, we have x<6 and |x-6|<5, not >5

|x-6| means distance of X from 6 on the number line. And distance will always be positive.

If x < 6, |x-6| becomes a negative integer, so we multiply it with -1.

|x-6| > 5 --> -(x-6) > 5 --> -x+6 > 5 --> X < 1

If x < >, |x-6| becomes a positive integer.

|x-6| > 5 --> (x-6) > 5 --> x-6 > 5 --> X > 11

So, X < 1 or X > 11

In above example,

|X| = k --> means x = -k or x = k but distance will be always positive K.
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Re: Is |x − 6| > 5 ?  [#permalink]

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21 Sep 2016, 22:10
blitheclyde wrote:
Just a question about the solution to this problem:

Is |x−6|>5 ?

(1) x is an integer

(2) x^2 < 1

The explanation provided is as follows:

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

If x<6, then −x+6>5 or x<1.

If x≥6, then x−6>5 or x>11.

My question is this: How did we come to the text in red? If x<6, why would the sign change on the 6? For x values from x=5 to x=2, we have x<6 and |x-6|<5, not >5

Appreciate any insight, even if its a link to a different forum thread. I tried searching for my question but had trouble funding something this specific.

(forgot to add above, official answer was B, (2) is sufficient but (1) is not.)

Merging topics. Please refer to the discussion above.
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DS - Absolute value and Inequalities  [#permalink]

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13 Jun 2017, 18:24
Is |x-6|>5 ?

(1) x is an integer

(2) x^2<1
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Re: DS - Absolute value and Inequalities  [#permalink]

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13 Jun 2017, 21:01
Answer is B. Basically the question boils down to, is 1<x<11.
Statement 1 is not sufficient as x can be any integer.
Statement 2 basically says, -1<x<1. So this is sufficient.
Ans B.

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Re: Is |x − 6| > 5 ?  [#permalink]

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13 Jun 2017, 22:38
hotcool030 wrote:
Is |x-6|>5 ?

(1) x is an integer

(2) x^2<1

Merging topics. Please refer to the discussion above.
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Re: Is |x − 6| > 5 ?  [#permalink]

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08 Mar 2018, 12:31
Hi All,

We're asked if |X-6| > 5. This is a YES/NO question. This question is perfect for TESTing Values.

Fact 1: X is an integer.

If X = 6, then the answer to the question is NO
If X = 100, then the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: X^2 < 1

Here, we have a really limited range….

-1 < X < 1

No matter what we pick for X, the answer remains consistent...
If X = .99, then the answer to the question is YES
If X = 0, then the answer to the question is YES
If X = -.99, then the answer to the question is YES
Fact 2 is SUFFICIENT.

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Re: Is |x − 6| > 5 ?   [#permalink] 08 Mar 2018, 12:31
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