GMAT Official Guide 2019 The research funds of a certain

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

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