(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)
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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.
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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!
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case 1: x:y = 3:5 -> x earns less than y, but they give no info about z, insufficient
case 2: x:z = 2:1 -> x earns more than z, but they give no info about y, insufficient

combining 1 and 2: y earns more than x and x earns more than z, so y earns the greatest proportion of the research funds, sufficient

(1) X/Y=3/5

5X=3Y Insufficient.

(2) X/Z=2/1

X=2Z; Insufficient.


Considering both:
5X=3Y
5*2Z=3Y
10Z=3Y

Thus, 3Y=5X=10Z Sufficient.

The answer is C
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(1) X:Y=3:5 No Informaiton about Z; Insufficient.

(2) X:Z= 2:1 No Informaiton about Y; Insufficient.

Considering Both:

Multiplying (1) by 2; X:Y=6:10

Multiplying (2) by 3; X:Z= 6:3

So, Y has the largest portion. Sufficient.

The answer is C.
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Answer: Option C

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Solution:

Question Stem Analysis:

We need to determine which department (X, Y, or Z) received the greatest proportion of research funds.

Statement One Alone:

We see that the ratio of research funds received by departments X and Y were in the ratio 3 to 5. In other words, department Y received a greater proportion of funds than department X. However, since we don't have any information about funds received by department Z, statement one alone is not sufficient.

Statement Two Alone:

We see that the ratio of research funds received by departments X and Z were in the ratio 2 to 1. In other words, department X received a greater proportion of funds than department Z. However, since we don't have any information about funds received by department Y, statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we see that department X received a greater proportion of funds than department Z and department Y received a greater proportion of funds than department X. Thus, department Y must have received the greatest proportion of funds. The two statements together are sufficient.

Answer: C

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