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13 Feb 2023, 00:19
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
47% (01:42) correct
53%
(01:48)
wrong
based on 133
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of m?
(1) \(|1-x| = m-3\); x is an integer.
(2) \(|2-m❘ = 7\)
(1) \(|1-x| = m-3\); x is an integer.
(2) \(|2-m❘ = 7\)
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
13 Feb 2023, 00:33
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What is the value of m?
(1) \(|1-x| = m-3\); x is an integer.
(2) \(|2-m❘ = 7\):
Two values. Not sufficient.
(1)+(2) Since from (1) we got that \(m \geq 3\), then from (2) \(m = 9\). Sufficient.
Answer: C.
(1) \(|1-x| = m-3\); x is an integer.
- Different values of x will give different values of m, so this statement is clearly insufficient.
We can derive an important info from this statement though: since the left hand side is nonnegative (it's an absolute value), then the right hand side must also be nonnegative, which would mean that \(m \geq 3\).
(2) \(|2-m❘ = 7\):
- \(2-m = 7\) or \(2-m = -7\);
\(m = -5\) or \(m = 9\).
Two values. Not sufficient.
(1)+(2) Since from (1) we got that \(m \geq 3\), then from (2) \(m = 9\). Sufficient.
Answer: C.
06 Mar 2023, 04:54
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TBT
Solution:
Pre Analysis:
- We are asked the exact value of m
Statement 1: \(|1-x| = m-3\); x is an integer.
- There is no need to even solve this further
- Because this equation has a variable x and will not get us an exact value of m
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: \(|2-m❘ = 7\)
- Either \(2-m=7\) or \(2-m=-7\)
\(⇒m=-5\) or \(m=9\) - We are getting two values of m
- Thus, statement 2 alone is also not sufficient and we can eliminate option B
Combining:
- When \(m=-5\)
- Then \(|1-x| = m-3=-5-3=-8\) which is not possible because the LHS is \(|1-x|\) which cannot be negative
- When \(m=9\)
- Then \(|1-x| = m-3=9-3=6\) which is possible
Hence the right answer is Option C
