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11 Jul 2019, 06:17
Kudos
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A
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Difficulty:
55%
(hard)
Question Stats:
59% (01:48) correct
41%
(02:14)
wrong
based on 153
sessions
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Time
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Not Attempted Yet
What is the remainder when \(7^m\)+2 is divided by 5?
(1) when m is divided by 4, the remainder is 1.
(2) when m is divided by 3, the remainder is 2.
(1) when m is divided by 4, the remainder is 1.
(2) when m is divided by 3, the remainder is 2.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
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KingAdam44
Joined: 21 Aug 2018
Last visit: 02 Oct 2020
Posts: 28
Given Kudos: 80
Location: Tunisia
Schools: Erasmus (S)
GMAT 1: 470 Q32 V23
GMAT 2: 550 Q32 V32
GPA: 3
WE:Analyst (Media/Entertainment)
11 Jul 2019, 07:17
Kudos
Bookmarks
Please give me further details regarding this question, I personally found it poorly written (replace m by n), and I cannot find the solution at all... I'm waiting for your solution and explanation! 
11 Jul 2019, 11:45
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Yup it must be \(7^m+2\).
Statement 1
m=4k+1
The unit digit of 7^{4k+1} is always 7.
Unit digit of \(7^m+2\) will be 7+2=9
\(7^m+2\)= 4 mod 7
Sufficient
Statement 2
m=3k+2
3k+2 when divided by 4 can leaves remainder 0,1, 2 or 3.
Hence unit digit of \(7^m+2\) can be 1, 3, 5 or 9
the remainder when \(7^m+2\) is divided by 5 can be 0,1,3 or 4
Insufficient
A
Statement 1
m=4k+1
The unit digit of 7^{4k+1} is always 7.
Unit digit of \(7^m+2\) will be 7+2=9
\(7^m+2\)= 4 mod 7
Sufficient
Statement 2
m=3k+2
3k+2 when divided by 4 can leaves remainder 0,1, 2 or 3.
Hence unit digit of \(7^m+2\) can be 1, 3, 5 or 9
the remainder when \(7^m+2\) is divided by 5 can be 0,1,3 or 4
Insufficient
A
KingAdam44
