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Question

Consider three sets A,B,C such that set A contains all three digit numbers that are multiples of 4, set B contains all three digit even numbers that are multiples of 3 and set C contains all three digit numbers that are multiples of 5. Then the value of n[(AB)×(AC)]n[(BC)×(ABC)] is

A
152
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B
154
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C
15
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D
30
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Solution

The correct option is A 152
A={100,104,108,...,996}
B={102,108,114,...,996}
C={100,105,110,...,995}

AB= All 3 digit multiples of 12
{108,120,132,...,996}
99610812+1=75 elements.

BC= All 3 digit multiples of 30
{120,150,180,...,990}
99012030+1=30 elements.

CA= All 3 digit multiples of 20
{100,120,140,160,...,980}
98010020+1=45 elements.

ABC= All 3 digit multiples of 60
{120,180,...,960}
96012060+1=15 elements.

n[(AB)×(AC)]n[(BC)×(ABC)]
=n(AB)×n(AC)n(BC)×n(ABC)
=75×4530×15
=152

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