Q39 / 60 · KVPY 2014 (SA) · Mathematics

The number of all 3 -digit numbers abc (in base10) for which $(a \times b \times c)+(a \times b) 6+(c \times a)+a+b+c=29$ is

  • A
    6
  • B
    10
  • Correct answer
    C
    14
  • D
    18

Solution

$\begin{array}{l} (a \times b \times c)+(a \times b)+(c \times a)+(a+b+c)=29 \\ (1+a)(1+b)(1+c)=30 \\ =2 \times 3 \times 5 \rightarrow(a, b, c) \Rightarrow(1,2,3) \Rightarrow 6 \\ =1 \times 6 \times 5 \rightarrow(a, b, c) \Rightarrow(0,5,4) \Rightarrow 4 \\ =1 \times 3 \times 10 \rightarrow(a, b, 1) \Rightarrow(0,2,9) \Rightarrow 4 \\ \quad \frac{14}{} &{ } \end{array}$

Hence, the correct answer is option: 'C'.

More Permutation Combination Questions