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18 Apr 2022, 00:29
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:28) correct
34%
(01:40)
wrong
based on 182
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(|x-2|>5\)?
(1) \(x^2>49\)
(2) \(x<-2\)
(1) \(x^2>49\)
(2) \(x<-2\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
18 Apr 2022, 01:27
Kudos
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GMATNinja
given \(|x-2|>5\)
we get x>7 and x<-3
#1
\(x^2>49\)
x has to be least -8 or +8
we get yes for target sufficient
#2
x<-2
we get yes and no to target ; as its not mentioned that x is an integer
insufficient
option A
18 Apr 2022, 08:58
Kudos
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Step 1: Analyse Question Stem
|x – a| represents the distance of the number x from a, on the number line.
Therefore, question stem can be rephrased as,
“Is the distance of x from 2 > 5?”
This is possible if x > 7 or x < -3.
Therefore, the question to be answered is “Is x > 7 or x< -3?”
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: \(x^2\) > 49
Transferring 49 to the LHS and factoring using standard algebraic identities, we have,
\(x^2 – 49\) > 0
\(x^2 – 7^2\) > 0
(x + 7) (x – 7) > 0
Therefore, x > 7 or x < -7.
This helps us to answer the question with a definite YES since x < - 7 means x is definitely less than -3.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: x<−2
If x = -2.5, |x – 2| < 5
If x = -5, |x – 2| > 5
Statement 2 alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
|x – a| represents the distance of the number x from a, on the number line.
Therefore, question stem can be rephrased as,
“Is the distance of x from 2 > 5?”
This is possible if x > 7 or x < -3.
Therefore, the question to be answered is “Is x > 7 or x< -3?”
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: \(x^2\) > 49
Transferring 49 to the LHS and factoring using standard algebraic identities, we have,
\(x^2 – 49\) > 0
\(x^2 – 7^2\) > 0
(x + 7) (x – 7) > 0
Therefore, x > 7 or x < -7.
This helps us to answer the question with a definite YES since x < - 7 means x is definitely less than -3.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: x<−2
If x = -2.5, |x – 2| < 5
If x = -5, |x – 2| > 5
Statement 2 alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
