Quantitative Aptitude Ques 545
Question: If m and n are different integers, both divisible by 5, then which of the following may not be true?
Options:
A) $ m-n $ is divisible by 5
B) mn is divisible by 25
C) $ m+n $ divisible by 10
D) $ m^{2}+n^{2} $ is divisible by 25
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] Rule $ m+n $ is divisible by 10 does not hold true in the given case. e.g. 35, 10 are integers divisible by 5 but $ 35+10=45, $ which is not divisible by 10. Alternate method Since, m and n are divisible by 5.
$ \therefore $ $ m=5x $ and $ n=5y $ for some integers x and y Now, $ m+n=5,(x+y) $
$ \therefore $ $ m+n $ is divisible by 5. $ mn=25xy $
$ \therefore $ $ mn $ is divisible by 25. $ m^{2}+n^{2}=25,(x^{2}+y^{2}) $
$ \therefore $ $ m^{2}+n^{2} $ is divisible by 25. $ m+n=5,(x+y) $ which is not divisible by 10.
BETA
