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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
20% (02:18) correct
80%
(02:22)
wrong
based on 241
sessions
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Is \(x^3+y^3>x^2 +y^2\)?
(1) \(x+y > x^2+y^2\)
(2) \(x^4 + y^4 > x^2+y^2\)
(1) \(x+y > x^2+y^2\)
(2) \(x^4 + y^4 > x^2+y^2\)
30 Sep 2021, 04:28
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The problem can be rephrased as follows:
Let x=1.1.
Substituting x=1.1 into the rephrased problem, we get:
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.
Quote:
Let x=1.1.
Substituting x=1.1 into the rephrased problem, we get:
Quote:
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.
13 Oct 2021, 23:44
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