The problem can be rephrased as follows:
Quote:
Is \(y^2-y^3<x^3-x^2\)?
(1) \(y^2-y < x-x^2\)
(2) \(y^2-y^4 < x^4-x^2\)
Let x=1.1.
Substituting x=1.1 into the rephrased problem, we get:
Quote:
Is \(y^2-y^3<0.121\)?
(1) \(y^2-y < -0.11\)
(2) \(y^2-y^4 < 0.2541\)
Case 1: \(y = 0.2\)
Statement 1: \(y^2-y=-0.16\), with the result that \(y^2-y<-0.11\)
Statement 2: \(y^2-y^4 = 0.0384\), with the result that \(y^2-y^4 < 0.2541\)
Is \(y^2-y^3<0.121\)?
In this case, \(y^2-y^3=0.032\), so the answer to the rephrased question stem is YES.
Case 2: \(y = 0.5\)
Statement 1: \(y^2-y=0.5^2-0.5 = -0.25\), with the result that \(y^2-y<-0.11\)
Statement 2: \(y^2-y^4 = 0.1875\), with the result that \(y^2-y^4 < 0.2541\)
Is \(y^2-y^3<0.121\)?
In this case, \(y^2-y^3=0.125\), so the answer to the rephrased question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.
This problem seems WAY beyond what the GMAT would expect of a test-taker -- even one performing at the very highest level.
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