number of employees

[finance]

MegaTech and UltraCorp are considering a
merger to form the MegaUltraTech
Corporation. Does MegaTech have more
employees than UltraCorp?
(1) The average (arithmetic mean) age
of UltraCorp employees is 32.8, while the
average age of MegaTech employees
is 27.2.
(2) If the merger goes through and all
employees from both companies remain
employed, the average (arithmetic mean)
age of the MegaUltraTech employees will
be 31.4.

[kmittal82]

I think its (C) i.e. both statements combined

Let total number of employess in MegaTech = m (ages of each be m1, m2 , m3 .... )
Let total number of employess in UltraTech = u (ages of each be u1, u2 , u3 .... )

We need to find if m > u , or, is [m / u] > 1 (since m and u will always be positive)

(1)
[ m1 + m2 + ....] / m = 27.2
[ u1 + u2 + ....] / u = 32.8

This itself doesn't say anything about the numbers, so not sufficient

(2)
[m1 + m2 + ...u1 + u2 + ... ] / [m + n ] = 31.4

Again, not enough info to deduce the relationshup between m and n

combining:

Form (1), we get
m1 + m2 + .... = 27.2m
u1 + u2 + .... = 32.8u

Putting this in (2)

27.2m + 32.8u = 31.4m + 31.4u
1.4 u = 3.8m

This is enough to establish a relationship between m and u, hence sufficient.

[finance]

Thank you!

The only explanation provided in my book was that since the average age for Ultra Tech employees is closer to the average age of all employees taken together after the merger, then we could conclude that the number of employees in Ultra Tech is higher. Now that I read your solution, I see it makes sense to me.

[kmittal82]

The book's answer also makes sense, but its not all that obvious at first sight.

If in doubt, go the old fashioned way

[naveen451]

this problem can be solved easily by allegation method

[mirantdon]

+1 for C .
btw . lol naveen .. allegation method ?!!

you would get the proportion but not the number