The GATE Grind

GATE 2014 EC (EC4) – Question 10

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

A five-digit number is formed using 1,3,5,7,9 without repetition. Find the sum of all such five-digit numbers.

  1. 6666660
  2. 6666600
  3. 6666666
  4. 6666606

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 6666600

Explanation

There are5!=120numbers. Each digit appears4!=24times in each place, so each place has digit sum24(1+3+5+7+9)=600. Multiply by the place-value sum11111:total=600×11111=**6666600,B**. No leading-zero restriction is needed because all digits are nonzero.