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Is |x 6| > 5 ? (1) x is an integer (2) x^2 < 1

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Apex231
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Is |x 6| > 5 ? (1) x is an integer (2) x^2 < 1 [#permalink] New post   16 Jan 2012, 22:50
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72% (01:26) correct 28% (01:33) wrong based on 594 sessions
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Is |x − 6| > 5 ?

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

M25-01

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[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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B
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Re: Is |x 6| > 5 ? (1) x is an integer (2) x^2 < 1 [#permalink] New post   17 Jan 2012, 00:45
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|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.

The answer is therefore (B).
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Re: Is |x 6| > 5 ? (1) x is an integer (2) x^2 < 1 [#permalink] New post   17 Jan 2012, 00:57
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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 ? (1) x is an integer (2) x^2 < 1 [#permalink] New post   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: Is |x 6| > 5 ? (1) x is an integer (2) x^2 < 1 [#permalink] New post   21 Sep 2016, 18:55
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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 ? (1) x is an integer (2) x^2 < 1 [#permalink] New post   08 Mar 2018, 12:31
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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.

Final Answer:
Show Spoiler
B


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Re: Is |x 6| > 5 ? (1) x is an integer (2) x^2 < 1 [#permalink] New post   08 May 2023, 15:38
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Is \(|x - 6| > 5\) ?

Is \(|x - 6| > 5\) ?

Is \(x - 6 < -5\) or \(x - 6 > 5\)?

Is \(x < 1\) or \(x > 11\)?

Another way to evaluate "Is |x - 6| > 5?" is to use the distance concept. \(|x - 6|\) represents the distance between \(x\) and 6 on the number line. For that distance to be greater than 5, \(x\) must be either less than 1 or greater than 11:

--------1--------6--------11--------

(1) \(x\) is an integer.

This statement is clearly not sufficient, as \(x\) could be any integer value.

(2) \(x^2 < 1\).

The above implies that \(-1 < x < 1\). Since \(-1 < x < 1\), then \(x\) is less than 1, and thus the answer to the question is YES. Sufficient.


Answer: B
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Re: Is |x 6| > 5 ? (1) x is an integer (2) x^2 < 1 [#permalink]
08 May 2023, 15:38
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