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
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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