# CAT 2020 Question Paper | Quants Slot 1

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

This question is from Number Theory. In CAT exam one can expect 1 to 2 questions from Number Theory. This question is about the products of two digits. Given the products of two digits, we need to find the smallest possible value of the sum of the three digits. Dealing with digits a number is a vital component in CAT Preparation. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

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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### Explanatory Answer

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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