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 B All of theseSince 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=21⇒z=5 The next multiple of 3 which is greater than 16 is 24 ⇒16+z=24⇒z=8 The next multiple of 3 which is greater than 16 is 27 ⇒16+z=24⇒z=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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