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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
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B
3
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C
6
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D
12
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Solution

## The correct option is C 6To 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: →36=2×2×3×3 →42=2×3×7 →30=2×3×5 →24=2×2×2×3 The common factors among these are 2 and 3. ∴ GCD is 2×3=6. Hence, the maximum number of fruit baskets is 6. Each fruit basket would have 6 bananas, 7 apples, 5 oranges and 4 guavas.

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