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

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answer is A.

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Detailed Solution

Concept- 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.
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

Hence, option 1 is correct.

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