62 candies were equally distributed to a group of children. If the num

There's a nice rule that says, If N divided by D equals Q with remainder R, then N = DQ + R
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

Let n = number of children
Let c = number of candies that each child received.

So, we can rephrase the given information as: When 62 candies are divided among n children, each child receives c candies and there are (n-2) candies remaining.
In other words, 62 divided by n equals c with remainder (n-2)

Applying the above rule, we get: 62 = cn + n-2
Add 2 to both sides to get: 64 = cn + n
Factor out the n to get: 64 = n(c + 1)
Divide both sides by n to get: 64/n = c + 1
Subtract 1 from both sides to get: c = 64/n - 1

This tells us that c is 1 less than some divisor of 64 (64/n must be a divisor of 64)

Now check the answer choices.

a. 1. Since 2 is a divisor of 64, we can see that 1 is 1 less than some divisor of 64. ELIMINATE A
b. 3. Since 4 is a divisor of 64, we can see that 3 is 1 less than some divisor of 64. ELIMINATE B
c. 7. Since 8 is a divisor of 64, we can see that 7 is 1 less than some divisor of 64. ELIMINATE C
d. 9. 9 is NOT is 1 less than some divisor of 64. KEEP D
e. 15. Since 16 is a divisor of 64, we can see that 15 is 1 less than some divisor of 64. ELIMINATE E

Answer: D

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