Each employee of company Z is employed in either Division X or Division Y, but not both. If each division has some part time employees, is the ratio of the number of full-time employees to number of part-time employees greater for Division X than for Company Z?
a. Ratio of number of full time employees to part-time employees is less for division Y than for company Z
b. More than ½ of full-time employees of company Z are employees of div X, and more than ½ of part-time employees of company Z are employees of div Y
imo : D
company Z
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 424
- Joined: Sun Dec 07, 2008 5:15 pm
- Location: Sydney
- Thanked: 12 times
- DanaJ
- Site Admin
- Posts: 2567
- Joined: Thu Jan 01, 2009 10:05 am
- Thanked: 712 times
- Followed by:550 members
- GMAT Score:770
Let's make some notations:
a = full time employees of company Z
b =part time employees of company Z
m = full time employees of division X
n =part time employees of division X
p = full time employees of division Y
q =part time employees of division Y
I'd say start with a bit of back solving. You're supposed to prove or disprove that:
m/n > (m + p)/(n + q)
mn + mq > mn + np
mq > np ----- divide by n
(m/n)*q > p ------ divide by q
m/n > p/q.
This means that what you're ultimately up against is proving that the ratio for division X is greater than the ratio for division Y.
1. tells you that (m + p)/(n + q) > p/q
mq + pq > np + pq
mq > np ---- divide by n
(m/n)*q > p ----- divide by q
m/n > p/q - what you were supposed to prove. So 1 is sufficient.
2. More than ½ of full-time employees of company Z are employees of div X translates to m > p. In the same time, more than ½ of part-time employees of company Z are employees of div Y means that q > n. This will obviously mean that m/n > p/q (since on the one side you're dividing the greater of m and p by the smaller of n and q). Again, this is sufficient.
There is an alternative way of looking at this: the ratio for the entire company will be something of a weighted average of the two division ratios. This means that it's somewhere between the two. However, you don't know if it's:
ratio division X < ratio total < ratio division Y
or
ratio division Y < ratio total < ratio division X.
Once you've established the relative position of any two elements (i.e. finding out that ratio X > ratio Y), you can pretty much answer the question (in my example, it's obviously the second case).
a = full time employees of company Z
b =part time employees of company Z
m = full time employees of division X
n =part time employees of division X
p = full time employees of division Y
q =part time employees of division Y
I'd say start with a bit of back solving. You're supposed to prove or disprove that:
m/n > (m + p)/(n + q)
mn + mq > mn + np
mq > np ----- divide by n
(m/n)*q > p ------ divide by q
m/n > p/q.
This means that what you're ultimately up against is proving that the ratio for division X is greater than the ratio for division Y.
1. tells you that (m + p)/(n + q) > p/q
mq + pq > np + pq
mq > np ---- divide by n
(m/n)*q > p ----- divide by q
m/n > p/q - what you were supposed to prove. So 1 is sufficient.
2. More than ½ of full-time employees of company Z are employees of div X translates to m > p. In the same time, more than ½ of part-time employees of company Z are employees of div Y means that q > n. This will obviously mean that m/n > p/q (since on the one side you're dividing the greater of m and p by the smaller of n and q). Again, this is sufficient.
There is an alternative way of looking at this: the ratio for the entire company will be something of a weighted average of the two division ratios. This means that it's somewhere between the two. However, you don't know if it's:
ratio division X < ratio total < ratio division Y
or
ratio division Y < ratio total < ratio division X.
Once you've established the relative position of any two elements (i.e. finding out that ratio X > ratio Y), you can pretty much answer the question (in my example, it's obviously the second case).