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Q.

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


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a

12

b

13

c

10

d

6

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