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Question: Let y be an element of the set A = {1, 2, 3, 5, 6, 10, 15, 30} and x<sub>1</sub>, x<sub>2</sub>, x<s...

Let y be an element of the set A = {1, 2, 3, 5, 6, 10, 15, 30} and x1, x2, x3 be integers such that x1 x2 x3 = y, then the number of positive integral solutions of x1 x2 x3 = y is

A

64

B

27

C

81

D

None of these

Answer

64

Explanation

Solution

Let us consider a dummy variable x4

so that x1x2x3x4 = 30. If x1x2x3 = 15 x4 = 2

if x1x2x3 = 30 then x4 = 1 so on

also x1x2x3x4 = 2 × 3 × 5