Question : Which is the smallest three-digit number which when increased by 5 becomes divisible by both 2 and 3?
Option 1: 102
Option 2: 105
Option 3: 103
Option 4: 108
Correct Answer: 103
Solution :
Consider the numbers,
102, 103, 105, and 108
⇒ For 102,
When increased by 5, the number becomes 107 which is not divisible by 2.
Now, The number = 103
When increased by 5, the number = 108
⇒ $\frac{108}{2}=54$ and $\frac{108}{3}=36$
Number = 105, when increased by 5, it becomes 110, which is not divisible by 3.
Number = 108, when increased by 5, it becomes 113, which is not divisible by 2.
Hence, the correct answer is 103.
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