Question

After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equally distributing. What is the smallest possible total number of sweets?

• A. 328
• B. 348
• C. 358
• D. Data inadequate

Hint:

Express the total as N = 25x + 8, then find the smallest x for which N - 22 is exactly divisible by 28.

Answer 1

The Correct Option is C

A more direct check-by-listing approach works well here since the numbers are small. We list numbers that leave remainder 8 when divided by 25, then check each one against the second condition (remainder 22 when divided by 28).

1. List candidates from the first condition: N = 25x + 8 gives the sequence 8, 33, 58, 83, 108, 133, 158, 183, 208, 233, 258, 283, 308, 333, 358, ...
2. Check each against the second condition: dividing each by 28 and checking the remainder, none of the values up to 333 leave remainder 22 (for example 333 / 28 = 11 remainder 25, and 308 / 28 = 11 remainder 0).
3. Test 358: 358 / 28 = 12 remainder 22, which is exactly the required remainder.

So the smallest total number of sweets satisfying both conditions is 358, confirming option C. Any smaller common solution would require going below the first term of the sequence, which isn't possible since sweets can't be negative.