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|x-6|>5

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by GMATGuruNY » Sat Sep 06, 2014 12:14 am
j_shreyans wrote:Is |x−6|>5 ?

(1) x is an integer

(2) x^2<1

OAB
|a-b| = the DISTANCE between a and b on the number line.
Question stem, rephrased:
Is the distance between x and 6 greater than 5?

For x to be more than 5 places from 6, it must lie in one of the two RED RANGES shown below:
-----x-----1-----------6-----------11-----x-----

Statement 1: x is an integer
No way to determine whether x lies within one of the two red ranges.
INSUFFICIENT.

Statement 2: x²<1
For x² to be less than 1, -1 < x < 1.
Thus, x must lie in the red range to the left of 1 on the number line.
SUFFICIENT.

The correct answer is B.
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by j_shreyans » Sat Sep 06, 2014 2:13 am
Hey ,

I was solving like below:

|x-6|>5

x-6>5
x>11 -------

and |x-6|>5
-x+6>5
-x>-1
x<1 -----right?

Statement 1 is not sufficient

Statement 2 -- x^2<1

So x<1 and x<-1

then what should be my next step?????


Pls let me know.
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by Brent@GMATPrepNow » Sat Sep 06, 2014 5:54 am
j_shreyans wrote:Is |x−6| > 5 ?

(1) x is an integer

(2) x² < 1

OAB
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then -k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

Target question: Is |x−6| > 5?

This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

We'll apply rule #2 (above). If |x−6| > 5, then EITHER x−6 > 5 OR x-6 < -5
Simplify to conclude that EITHER x > 11 OR x < 1

So, we can REPHRASE the target question as....
REPHRASED target question: Is EITHER x > 11 OR x < 1? (this is a YES/NO question)

Statement 1: x is an integer
There are several values of x that satisfy this condition. Here are two:
Case a: x = 7, in which case the answer to the REPHRASED target question is NO, x is not either greater than 11 OR less than 1
Case b: x = 20, in which case the answer to the REPHRASED target question is YES, x is either greater than 11 OR less than 1
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x² < 1
This tells us that -1 < x < 1
This means that x is definitely less than 1.
So, the answer to the REPHRASED target question is YES, x is either greater than 11 or less than 1
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

For even more information on rephrasing the target question, you can read this article I wrote for BTG: https://www.beatthegmat.com/mba/2014/06/ ... t-question
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by Brent@GMATPrepNow » Sat Sep 06, 2014 5:56 am
j_shreyans wrote:Hey ,

I was solving like below:

|x-6|>5

x-6>5
x>11 -------

and |x-6|>5
-x+6>5
-x>-1
x<1 -----right?

Statement 1 is not sufficient

Statement 2 -- x^2<1

So x<1 and x<-1

then what should be my next step?????


Pls let me know.
This looks good, except it's unclear what role your calculations are playing.
You have taken the target question |x-6|>5 and concluded that EITHER x>11 OR x<1
This allows you to rewrite the target question as "Is it the case that x is either greater than 11 or less than 1?"

See my solution above for more detail.

Cheers,
Brent
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by GMATinsight » Sat Sep 06, 2014 9:36 am
j_shreyans wrote:Is |x−6|>5 ?

(1) x is an integer

(2) x^2<1

OAB
Question : Is |x−6|>5 ?
i.e. Is +(x−6)>5 ?
Is x−6>5 or -(x-6)>5?
Is x>11 or (x-6)<-5?
Question : Is x>11 or (x)<1?

Statement 1) x is an integer
NOT SUFFICIENT

Statement 2) x^2<1
i.e. -1 < x < 1
SUFFICIENT

Answer: Option B
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by GMATinsight » Sat Sep 06, 2014 9:38 am
Hi J_Shreyan,

Please make sure that you post the questions in the correct thread.

P.S. YOU HAVE BEEN POSTING DATA SUFFICIENT QUESTIONS IN PROBLEM SOLVING THREAD
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by [email protected] » Sat Sep 06, 2014 11:34 am
Hi j_shreyans,

This question is perfect for TESTing Values.

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

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: B

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