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Question

If 74z5 is a multiple of 3, where z is a digit, then what are the possible values of z?

A
2
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B
5
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C
8
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D
All of these
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Solution

The correct option is D All of these
Since 74z5 is a multiple of 3.
Therefore according to the divisibility rule of 3, the sum of all the digits should be a multiple of 3.
Since, z is a digit.
7 + 4 + z + 5 = 16 + z
The first multiple of 3 which is greater than 16 is 18
16 + z = 18 z = 2
The next multiple of 3 which is greater than 16 is 21
16+z=21z=5
The next multiple of 3 which is greater than 16 is 24
16+z=24z=8
The next multiple of 3 which is greater than 16 is 27
16+z=24z=11
But z is a digit.
Therefore, z cannot be 11.
Hence 2, 5 and 8 are the possible values of z.

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