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In an office, every employee is given a UID number. An employee is from the technical branch if and only if UID is divisible by 5 whereas an employee is from the adjudication branch if and only if UID is divisible by 7. Every number from 1 to 200 is assigned as UID. An employee is female if and only if UID is divisible by 6 and rests are male. How many females are in the adjudication branch?

In an office, every employee is given a UID number. An employee is from the technical branch if and only if UID is divisible by 5 whereas an employee is from the adjudication branch if and only if UID is divisible by 7. Every number from 1 to 200 is assigned as UID. An employee is female if and only if UID is divisible by 6 and rests are male. How many females are in the adjudication branch? Correct Answer 4

Given:

UID of technical branch employee is divisible by 5

UID of adjudication branch employee is divisible by 7

UID of female employee is divisible by 6

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 females in the adjudication branch will be divisible by 7 and 6

Divisible by LCM of (7, 6)

⇒ Divisible by 42

Multiples of 42 in 1, …, 200 = 200/42 = 4

Here we Consider integer value only and ignore the remainder.

∴ Four females are in the adjudication branch.

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