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good one

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by vaivish » Sat Jul 26, 2008 12:21 pm
There are 135 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14


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by acecoolan » Sat Jul 26, 2008 12:39 pm
I dont know if there is algebraic way of solving this faster but I just worked this out by substitution (speedy since the number of employees is small)

10 people in june - so even we assume 9 in all other months
10 + 9*11 = 109 (less than total employees)
similarly for 11 in june
11 + 10*11 = 121 less than total employees
for 12 in june
12 + 11 * 11 = 133 less than total employees

So 13 fits the bill and hence would be the least possible for June.

I would be interested to see other simpler and better solutions ..anybody?
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by AleksandrM » Sat Jul 26, 2008 1:30 pm
135/12 = 11 with remainder of 3. Therefore, you have 11 people who are born in each month with 3 to distribute to each month - attempting to minimize June but keep it as maximum, at the same time.

You can give 1 person to, say, September, which will make its output 12. You then must keep 2 for June, which will give it 13 people.

Hey, I was born in June, I guess my month wins.
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