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Kaushik786
Joined: 20 May 2018
Last visit: 13 Dec 2023
Posts: 71
Given Kudos: 71
Location: India
Schools: Booth '22 Anderson '22 CBS '22 Johnson '22
GMAT 1: 740 Q50 V41
12 Mar 2021, 21:57
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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:
65%
(hard)
Question Stats:
61% (02:24) correct
39%
(02:26)
wrong
based on 95
sessions
History
Date
Time
Result
Not Attempted Yet
If m is a positive integer greater than 1, is m-1 a factor of 297 ?
1. 28 is divisible by m
2. m is divisible by 4
1. 28 is divisible by m
2. m is divisible by 4
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
12 Mar 2021, 23:29
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Kaushik786
Is m-1 a factor of 297 ? MEANS Is (m-1)*x=297?
Now \(297 = 27*11=3*3*3*11=3^3*11\)
Number of factors are (3+1)(1+1)=8 => 1, 3, 9, 11, 27, 33, 99 and 297.
That is, we have to find if m is any of 2, 4, 10, 12, 28, 34, 100, 298.
1. 28 is divisible by m
\(28=2^2*7\)
So m can be 2, 4, 7, 14, 28.
If m is 2, 4 or 28, then yes.
If m is 7 and 14, then no.
2. m is divisible by 4
If m is 4, 12, 28, or 100 , then yes.
If m is 8, 16 etc, then no.
Combined.
m is divisible by 4 and one of 2, 4, 7, 14 or 28.
Only 4 and 28 satisfy both the conditions, and in each case answer is yes.
C
13 Mar 2021, 03:38
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Given: m is an integer and m > 1
Is m - 1 a factor of 297?
\(297 = 3^3 * 11\)
Statement 1:
28 = m * p, where p is any positive integer.
m can be 2, 4, 7, 14 and 28.
=>m - 1 can be 1, 3, 6, 13, 27.
1, 3 and 27 are factors of 297 but 6 and 13 are not.
Statement 1 is Not Sufficient.
Statement 2:
m = 4 * k, where k is any positive integer.
m can be 4, 8, 16 and so on.
=>m - 1 can be 3, 7, 15 and so on.
3 is a factor of 297 but 7 is not, and so on.
Statement 2 is also Not Sufficient.
Statement 1 and Statement 2 combined:
28 = m * p and m = 4 * k, where k and p are any positive integers.
m can be 4 and 28 only.
=> m - 1 can be 3 and 27 only.
3 and 27 are both factors of 297.
=> m - 1 is a factor of 297.
Statement 1 and Statement 2 together are Sufficient.
So, correct answer is option C.
Is m - 1 a factor of 297?
\(297 = 3^3 * 11\)
Statement 1:
28 = m * p, where p is any positive integer.
m can be 2, 4, 7, 14 and 28.
=>m - 1 can be 1, 3, 6, 13, 27.
1, 3 and 27 are factors of 297 but 6 and 13 are not.
Statement 1 is Not Sufficient.
Statement 2:
m = 4 * k, where k is any positive integer.
m can be 4, 8, 16 and so on.
=>m - 1 can be 3, 7, 15 and so on.
3 is a factor of 297 but 7 is not, and so on.
Statement 2 is also Not Sufficient.
Statement 1 and Statement 2 combined:
28 = m * p and m = 4 * k, where k and p are any positive integers.
m can be 4 and 28 only.
=> m - 1 can be 3 and 27 only.
3 and 27 are both factors of 297.
=> m - 1 is a factor of 297.
Statement 1 and Statement 2 together are Sufficient.
So, correct answer is option C.
