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Question

 The total number of positive integral solutions (x,y,z) such that xyz=24 is :


A
36
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B
45
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C
24
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D
30
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Solution

The correct option is B 30
x.y.z=24
x.y.z=23.31
x=2a13b1,   y=2a23b2,  z=2a33b3
a1,a2,a3{0,1,2,3}
b1,b2,b3{0,1}
Case: 1  a1+a2+a3=3
Non negative solution = 3+31C31=5C2=10
Case: 2  b1+b2+b3=1
Non negative solution = 1+31C31=3C2=3
Total solutions =10×3=30

Mathematics

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