GMAT Official Guide 2019 The research funds of a certain

[BTGmoderatorDC]

The research funds of a certain company were divided among three departments, X, Y, and Z. Which one of the three departments received the greatest proportion of the research funds?

(1) The research funds received by departments X and Y were in the ratio 3 to 5, respectively.
(2) The research funds received by departments X and Z were in the ratio 2 to 1, respectively.

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Hi All,

We're told that the research funds of a certain company were divided among three departments, X, Y, and Z. We're asked which one of the three departments received the greatest proportion of the research funds. This question can be solved in a number of different ways, including by TESTing VALUES.

1) The research funds received by departments X and Y were in the ratio 3 to 5, respectively.

Fact 1 gives us a ratio of X to Y (X:Y = 3:5), so we know that Y received a larger proportion of the funds than X did. But we don't know how much Z received.
IF...
X=3, Y=5, Z=1, then the answer to the question is Department Y.
X=3, Y=5, Z=10, then the answer to the question is Department Z.
Fact 1 is INSUFFICIENT

2) The research funds received by departments X and Z were in the ratio 2 to 1, respectively.

Fact 2 gives us a ratio of X to Z (X:Z = 2:1), so we know that X received a larger proportion of the funds than Z did. But we don't know how much Y received.
IF...
X=2, Y=1, Z=1, then the answer to the question is Department X.
X=2, Y=10, Z=1, then the answer to the question is Department Y.
Fact 2 is INSUFFICIENT

Combined, we have the following ratios:
X:Y = 3:5
X:Z = 2:1
We can 'combine' those ratios (multiply the first ratio by 2 and the second ratio by 3), which gives us:
X:Y = 6:10
X:Z = 6:3
X:Y:Z = 6:10:3
Thus, Department Y will ALWAYS get the most funding.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

The research funds of a certain company were divided among three departments, X, Y, and Z. Which one of the three departments received the greatest proportion of the research funds?

(1) The research funds received by departments X and Y were in the ratio 3 to 5, respectively.
(2) The research funds received by departments X and Z were in the ratio 2 to 1, respectively.

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