Question

There is a five digit number. The fourth digit is $4$ greater than second digit, while third digit is $3$ less than second digit. The first digit is thrice the last digit.These are three pairs whose sum is $11$. Find the number.

• A. $35291$
• B. $65292$
• C. $63072$
• D. $95293$

Answer 1

The correct option is B $65292$

As per given conditions, there are three possible combinations for 2nd, 3rd and 4th digits. They are $(3,0,7),(4,1,8),(5,2,9)$

It is given that there are 3 pairs whose sum is $11$. All possible pairs are $(2,9),(3,8),(4,7),(5,6)$. Now required number is $5$ digit number and it contains $3$ pairs of $11$. So it must not be having $0$ and $1$ in it. Hence, the only possible combination for 2nd, 3rd and 4th digits is

$(5,2,9)$.

Also, 1st digit is thrice the last digit. The possible combinations are $(3,1),(6,2)$ and $(9,3)$, out of which only $(6,2)$ with $(5,2,9)$ gives 3 pairs of $11$.

Hence, the number is $65292$.