SATHEE: Quantitative Aptitude Ques 545

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.

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