CAT 1997 — QA Question 20
DivisibilityEasy
If m and n are integers divisible by 5, which of the following is not necessarily true?
Answer & solution
Correct answer: m + n is divisible by 10
- A
m – n is divisible by 5
- B
m2 – n2 is divisible by 25
m + n is divisible by 10
- D
None of these
Solution
The best way to solve this is the method of simulation, e.g. let m = 10 and n = 5. Therefore m – n = 5, which is divisible by 5.
m2 – n2 = 100 – 25 = 75, divisible by 25. m + n = 10 + 5 = 15 is not divisible by 10.
Hence, the answer is (c).
Note that for the sum of two multiples of 5 to be divisible by 10, either both of them should be odd (i.e. ending in 5) or both of them should be even (i.e. ending in 0).