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How many five digit multiples of 11 are there, if the five digits are 3, 4, 5, 6 and 7?

Repetition of digits is now allowed?

  • A.10
  • B.11
  • C.12
  • D.13

Answer: C

A number is divisible by 11, if the difference between the sum of digits at even places and odd places is either 0 or divisible by 11.

Numbers 5,3,6,4,7 is a multiple of 11

∵(5+6+7)−(3+4)=11, which is a multiple of 11

The number at odd places 5,6,7 can be arranged in 3! ways and 3,4 can be arranged in 2! ways.

Therefore, the total number of ways of such numbers =3!×2!=12

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