ziyuenlau wrote:Is x^4 + y^4 > z^4 ?
1. x² + y² > z²
2. x + y > z
Target question: Is x^4 + y^4 > z^4 ?
Statement 1: x² + y² > z²
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 1, y = 1 and z = 1. This meets the condition that x² + y² > z². In this case,
x^4 + y^4 > z^4
Case b: x = 1/2, y = 1/2 and z = 2/3. This meets the condition that x² + y² > z². In this case,
x^4 + y^4 < z^4
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: x + y > z
This statement doesn't FEEL sufficient either, so I'll TEST some values.
There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 1, y = 1 and z = 1. This meets the condition that x² + y² > z². In this case,
x^4 + y^4 > z^4
Case b: x = 1/2, y = 1/2 and z = 2/3. This meets the condition that x² + y² > z². In this case,
x^4 + y^4 < z^4
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the
same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: x = 1, y = 1 and z = 1. This meets the condition that x² + y² > z². In this case,
x^4 + y^4 > z^4
Case b: x = 1/2, y = 1/2 and z = 2/3. This meets the condition that x² + y² > z². In this case,
x^4 + y^4 < z^4
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer:
E
Cheers,
Brent
