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Is X greater than Y? Statement I: X is 20% more than Z. Statement II: Y is 30% more than Z.
Data in statement I alone is sufficient
Data in statement II alone is sufficient
Data in both statements together are sufficient
Data in both statements together are not sufficient
Data in both statements together are sufficient
Express both variables X and Y in terms of the common variable Z and compare the coefficients directly.
Express both variables X and Y in terms of the common variable Z and compare the coefficients directly.
Analyze Statement I
From statement I, X is 20% more than Z. Mathematically, X = Z + 0.20Z = 1.20Z.
Analyze Statement II
From statement II, Y is 30% more than Z. Mathematically, Y = Z + 0.30Z = 1.30Z.
Compare X and Y
Comparing 1.20Z and 1.30Z, we see that Y is clearly greater than X for any positive value of Z. Therefore, both statements are required to establish the relationship between X and Y.
A: Statement I only provides the value of X relative to Z, which is insufficient to determine X vs Y. B: Statement II only provides the value of Y relative to Z, which is insufficient to determine X vs Y. D: Both statements are sufficient because they allow us to define both variables as multiples of Z, enabling a direct comparison.
C is correct because combining both statements allows us to define X as 1.2Z and Y as 1.3Z, proving Y > X.
In Data Sufficiency involving variables, always look for a common variable to bridge the gap between statements; if one is missing, the relationship usually cannot be determined.
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