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12 Days of Christmas GMAT Competition with Lots of Fun
If m and n are positive integers, do they yield the same remainder when divided by 24?
(1) m and n yield the same remainder when divided by 8.
(2) |m - n| is a multiple of 9
M36-93
If m and n are positive integers, do they yield the same remainder when divided by 24?
(1) m and n yield the same remainder when divided by 8.
(2) |m - n| is a multiple of 9
M36-93
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22 Dec 2020, 21:17
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If m and n are positive integers, do they yield the same remainder when divided by 24?
(1) m and n yield the same remainder when divided by 8.
(2) |m - n| is a multiple of 9
Solution :
answer is c)
lets analyze stem first
lets assume both m and n leave same remainder when divided by 24
so we can write m= 24 X + r and n as 24y + r where r >=0 and < 24
now |m -n | = 24 |X- Y| so basically question is asking if |m-n| = multiple of 24
statement 1 : gives us that |m-n|= 8k
so obviously we can have yes when when k is multiple of 3 and no if its not a multiple of 3 for the q , so insufficient
statement 2: we are given that |m-n|= 9K
so obviously we can have yes when k = multiple of 8 and no if k is not a multiple of 8 so insufficient
when we combine statement 1 and statement 2 we get |m-n| = 72 K
So that's perefect if |m-n| is multiple of 72 , it will definitely be a multiple of 24
so answer goes with c) Both statements combined together are sufficient but neither statement alone is sufficient
(1) m and n yield the same remainder when divided by 8.
(2) |m - n| is a multiple of 9
Solution :
answer is c)
lets analyze stem first
lets assume both m and n leave same remainder when divided by 24
so we can write m= 24 X + r and n as 24y + r where r >=0 and < 24
now |m -n | = 24 |X- Y| so basically question is asking if |m-n| = multiple of 24
statement 1 : gives us that |m-n|= 8k
so obviously we can have yes when when k is multiple of 3 and no if its not a multiple of 3 for the q , so insufficient
statement 2: we are given that |m-n|= 9K
so obviously we can have yes when k = multiple of 8 and no if k is not a multiple of 8 so insufficient
when we combine statement 1 and statement 2 we get |m-n| = 72 K
So that's perefect if |m-n| is multiple of 72 , it will definitely be a multiple of 24
so answer goes with c) Both statements combined together are sufficient but neither statement alone is sufficient
12 Nov 2021, 08:05
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Bunuel
Official Solution:
If \(m\) and \(n\) are positive integers, do they yield the same remainder when divided by 24?
If the remainders were the same then we'd be able to write \(m=24p+r\) and \(n=24q+r\).
Subtract one from another \(m-n=24(p-q)\). So, when \(m\) and \(n\) yield the same remainder when divided by 24, their difference is a multiple of 24.
(1) \(m\) and \(n\) yield the same remainder when divided by 8.
The same way as above, we can deduce that this statement implies that \(m-n\) is a multiple of 8. So, \(m-n\) may or may not be a multiple of 24. Not sufficient.
(2) \(|m - n|\) is a multiple of 9.
This means that \(m-n\) is a multiple of 3 but we don't know whether it is also a multiple of 8. Not sufficient.
(1)+(2) From (1) \(m-n\) is a multiple of 8 and from (2) it's is a multiple of 3, thus \(m-n\) is a multiple of 24. Sufficient.
Answer: C
