(1) The research funds received by departments X and Y were in the ratio 3 to 5, respectively.
X : Y = 3 : 5 | For every $3x received by department X, department Y receives $5x. Since we
have no information about the funds received by department Z, we can't say for sure which of
the three departments gets the maximum funds Insufficient

(2) The research funds received by departments X and Z were in the ratio 2 to 1, respectively.
X : Z = 2 : 1 | For every $2y received by department X, department Z receives $y. Since we
have no information about the funds received by department Y, we can't say for sure which of
the three departments gets the maximum funds Insufficient

When we combine the information present in both the statements,
X:Y = 3:5 and X:Z = 2:1 -> X:Y:Z = 6:10:3. We can clearly see that
the department Y gets the maximum funds (Sufficient - Option C)
_________________

We'll translate the words into equations to make them easier to understand.
This is a Precise approach.

(1) gives us x:y = 3:5. Without information on z, we don't know which is largest.
Insufficient.

(2) so x:z = 2:1 Without information on y, this is insufficient.
Insufficient.

Combined: Even without explicitly calculating, we now know the ratio between x to both y and z and can therefore calculate which is largest.
Sufficient.

(C) is our answer.
_________________

IMO C
Y has greatest proportion
3 to 5 to 1.5

I will solve this with imaginary number to make is easy

We are asked to find who got the highest are?

Statement 1: X/Y = 3/5, we don't know the value of Z. i.e. not sufficient

Statement 2 X/Z = 2/1, this statement does not have any information for Y i.e. not sufficient

Statement (1)+(2):

X/y = 3/5 = 30/50

X/Z = 2/1. If X=30, then x/z = 30/15

Which means, X= 30, Y = 50 and Z = 15.

Y got the highest. Answer C.

hello pushpitkc hope you are having a cool summer weekend

have some questions

\(\frac{3x}{5y}\) \(\frac{2x}{1y}\)

so here i see a common value - i mean X so i mupltiply 3x by 2x and 5y by 2x so i get \(\frac{6x}{10y}\) after this i got confused i bit

two questions how did you get 3 here 6:10:3

and how did you assign values X:Y:Z = 6:10:3 respectively ?

thanks

Hey dave13

You seemed to have missed something here:
Statement 1 - X:Y is 3:5(3x:5x) | Statement 2 - X:Z is 2:1(2y:y)

To make the ratios equal, we multiply the first ratio by 2 making X:Y (6:10) - (if x = 2)
Similarly, we multiply the ratio obtained in the 2nd statement by 3, X:Z (6:3) - (if y = 3)
Now, the common ratio [X : Y : Z] - 6:10:3 on combining both the statements

Hope it clears your confusion!
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________