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In an NGO, every worker is given a UID number. A worker is associated with the women wing if and only if UID is divisible by 10 whereas a worker is associated with the old age wing if and only if UID is divisible by 6. Every number from 100 to 200 is assigned as UID. A worker is male if and only if UID is divisible by 4 and rests are female. How many males are associated with the women wing?

In an NGO, every worker is given a UID number. A worker is associated with the women wing if and only if UID is divisible by 10 whereas a worker is associated with the old age wing if and only if UID is divisible by 6. Every number from 100 to 200 is assigned as UID. A worker is male if and only if UID is divisible by 4 and rests are female. How many males are associated with the women wing? Correct Answer 6

Given:

UID of women wing worker is divisible by 10

UID of old age wing worker is divisible by 6

UID of male is divisible by 4

Concept Used:

Multiples of a in 1, 2, 3, …, n = n/a (Consider integer value only)

Where n and a are natural numbers

Calculation:

UIDs of males associated with the women wing will be divisible by both 10 and 4.

⇒ Divisible by LCM of (10, 4)

⇒ Divisible by 20

Multiples of 20 in 1, …, 200 = 200/20 = 10

Multiples of 20 in 1, …, 100 = 100/20 = 5

Multiples of 20 in 100, …, 200 = 10 – 5 + 1 = 6

1 is added because 100 is also a multiple of 20.

∴ 6 males are associated with the women wing.

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