Question

The no. of positive integral soln's of xyz = 30 is

• A. 28
• B. 27
• C. 30
• D. 24

Answer 1

Answer: (B)

27

Answer 2

xyz = 2 x 3 x 5 (2, 3, 5) → ∠3

= 1 x 6 x 5 (1, 6, 5) → ∠3

= 1 x 15 x 2 (1, 15, 2) → ∠3

= 10 x 3 x 1 (10, 3, 1) → ∠3

= 30 x 1 x 1 (30, 1, 1) → $\frac{\angle 3}{\angle 2}$

No. of solutions = 4 x ∠3 + $\frac{\angle 3}{2}$ = 24 + 3 = 27.

Method: xyz = 2 x 3 x 5

No. of solutions = 3³ = 27.