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Question

# If the sets A and B are defined as A={x:x=2n, n∈N, n<100}B={x :x=3n, n∈N, n<100} then, the number of elements in A∩B is

A
16
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B
198
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C
33
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D
59
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Solution

## The correct option is C 33A={x:x=2n, n∈N, n<100}={2,4,6,8,.....,198}B={x :x=3n, n∈N, n<100}={3,6,9,12,....,297}The elements in A∩B are the common multiples of 2 and 3 which are less than 199.Common multiples of 2 and 3 are multiple of 6. So A∩B will contain multiples of 6 less than 199.∴A∩B=(x: x=6n, n∈N, x<199}A∩B=(6, 12, 18, 24, ...., 198}n(A∩B)=33

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