Data Sufficiency

Can this be solved in two minutes.. spent a lot of time on this problem

Well here is my approach,

The question says that all of the employees either belong to Div X or Div Y.

(1) gives the required answer.SUFFICIENT.

(2) says that more than half of full time employees of X belong to Div X and more than half of part time emplyees of X belong to Div Y. This gives us the exact information we are looking for.

To understand this better lets take an example

Lets assume company X has 100 full time and 100 part time exployees.So the ration of company X is 1:1. According to (2) lets say 60 FT emplyees belong to X and 60 PT employees belong to Y.The question says that all employees either belong to X or Y.So if there are 60 FT emps in X, there would be 40 FT emps in Y.Similarly, if there are 60 PT emps in Y then there would be 40 PT emps in X.This way we can find out the ratio for Division X.Hence SUFFICIENT.


Do you get me??

I found this problem solved on a website (I don't remember what website though) some time ago....I think it's a very straightforward approach. Here it goes:

Let denote:
f1 = number of FT employee for div X
p1 = number of PT employee for div X
f2 = number of FT employee for div Y
p2 = number of PT employee for div Y
Then: f=f1+f2 and p=p1+p2

We are asked to show that:
f1/p1 > (f1+ f2)/(p1 + p2)
develop this inequation and we get:
f1p2 > f2p1

Stat.1 says: f2/p2 less then (f1+f2) divided by (p1+p2), develop it and we get f1p2 > f2p1 => stat.1 sufficient

stat.2 says: f1>f2 & p2>p1, multiply these two inequalities and you'll get:
f1p2 > f2p1 => stat.2 is sufficient

Ans. is D

Is that simple, or what??

thanks silivest60!

silivest60 wrote: stat.2 says: f1>f2 & p2>p1, multiply these two inequalities and you'll get:
f1p2 > f2p1 => stat.2 is sufficient

Can anybody elaborate?

ANYBODY?

4meonly wrote:ANYBODY?

In this equation,

since we know all the numbers are positive...
since employees are offcourse in positive.
let's say
3>2 and 5>4
offcourse 15>8 that's what is done here.

Hope it clears the confusion. Also, it can't be fractions.... only positive integers....

one more thing to add.....
as long as the variables on both sides in inequalities are positive, we can treat them same as equations.