Is |x−6|>5 ?
(1) x is an integer
(2) x^2<1
OAB
|x-6|>5
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|a-b| = the DISTANCE between a and b on the number line.j_shreyans wrote:Is |x−6|>5 ?
(1) x is an integer
(2) x^2<1
OAB
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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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.
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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When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:j_shreyans wrote:Is |x−6| > 5 ?
(1) x is an integer
(2) x² < 1
OAB
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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This looks good, except it's unclear what role your calculations are playing.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.
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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Question : Is |x−6|>5 ?j_shreyans wrote:Is |x−6|>5 ?
(1) x is an integer
(2) x^2<1
OAB
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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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
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
"GMATinsight"Bhoopendra Singh & Sushma Jha
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Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich