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09 Apr 2021, 10:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (01:52) correct
30%
(02:04)
wrong
based on 158
sessions
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When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 8. If 1 < m < 200, what is the greatest possible value of m?
A. 47
B. 65
C. 103
D. 117
E. 164
A. 47
B. 65
C. 103
D. 117
E. 164
16 Apr 2021, 10:15
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Bunuel
When m is divided by 9, the remainder is 2 --> \(m=9q+2\) --> m can be 2, 11, 20, 29, 38, 47, ...
When m is divided by 13, the remainder is 8 --> \(m=13p+8\) --> m can be 8, 21, 34, 47, 60, 73, ...
There is a way to derive general formula for m (of a type \(m=dx+r\), where d is divisor and r is a remainder) based on above two statements:
Divisor d would be the least common multiple of above two divisors 9 and 13, hence \(d=117\) and the remainder r would be the first common integer in above two patterns, hence \(r=47\).
Therefore general formula based on both statements is \(m=117x+47\) --> n can be 47, 164, 211, ... Since m must be less than 200, then the greatest possible value of m is 164.
Answer: E.
More about deriving general formula for such problems at: https://gmatclub.com/forum/manhattan-rem ... ml#p721341
Hope it helps.
General Discussion
ramlala
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09 Apr 2021, 11:45
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When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 8. If 1 < m < 200, what is the greatest possible value of m?
A. 47
B. 65
C. 103
D. 117
E. 164
We have to find greatest possible value of m, lets start with choice E
164 is divided by 13, 13*12=156+8=164
164 is divided by 9, 9*18=162+2=164
Both conditions are fulfilled.
Ans E
A. 47
B. 65
C. 103
D. 117
E. 164
We have to find greatest possible value of m, lets start with choice E
164 is divided by 13, 13*12=156+8=164
164 is divided by 9, 9*18=162+2=164
Both conditions are fulfilled.
Ans E
