Question

A fruit vendor has $36$ bananas, $42$ apples, $30$ oranges and $24$ guavas. The fruit vendor decides to make identical fruit baskets. He wants at least one banana, apple, orange and guava in each basket. Find the maximum number of fruit baskets that can be made.

• A. 2
• B. 3
• C. 6
• D. 12

Answer 1

The correct option is C 6

To find the maximum number of fruit baskets, having at least one banana, apple, orange and guava in each basket, we need to evaluate GCD of the 4 numbers.

The factor trees of $36,42,30$ and $24$ are as follows:

$\to 36=2\times 2\times 3\times 3$
$\to 42=2\times 3\times 7$
$\to 30=2\times 3\times 5$
$\to 24=2\times 2\times 2\times 3$

The common factors among these are $2$ and $3.$
$\therefore$ GCD is $2\times 3=6.$

Hence, the maximum number of fruit baskets is $6.$

Each fruit basket would have 6 bananas, 7 apples, 5 oranges and 4 guavas.