# CAT 2020 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Quants Questions | Question 20

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Question 20 : If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

1. 56
2. 49
3. 46
4. 59

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Since the product is involved, we will keep the numbers as close as possible
bc = 96 and c < 9
b c
12 × 8 = 96
16 × 6 = 96
24 × 4 = 96
ab = 432
a b
12 × 36 = 432
16 × 27 = 432
24 × 18 = 432

So possible values of a = 36, b = 12, c = 8 Sum = 58
a = 27, b = 16, c = 6 Sum = 49
a = 18, b = 24, c = 4 Sum = 46
Least possible value = 46

The question is "If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is"

##### Hence, the answer is, "46"

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