Question

Josh had collection of $3489$ playing cards. He kept $9$ with him and distributed rest of them among his $12$ friends. He kept remaining cards with him. State wheather each friend got equal cards or not. How many cards did Josh had after distribution?

• A. Each have equal cards
• B. Some have more cards than others
• C. Josh had 9 cards with him.
• D. Josh had 10 cards with him

Answer 1

Answer: (A), (C)

Josh had 9 cards with him.

Total number of cards Josh had $=3489$

Cards left after he kept $9$ of them with himself $=3480$

$3480$ cards are distributed among $12$ friends.
Now, we need to check wheather 3480 is completely divisible by 12 or not.

Concept: If a number is divisible by both 4 and 3 then, the number is also divisible by 12.

$3480\to 3+4+8+0=15$, we know that 15 is a multiple of 3, hence 3480 is completely divisible by 3.
Last two digits of 3480 is divisible by 4, hence 3480 is divisible by 4.

Therefore, 3480 is divisible by 12 evenly.
Each friend got equal number of cards.

As there was no remaining card after distributing 3480 cards among 12 friends, hence Josh had same 9 cards with himself that he kept before distribution.