Data Sufficiency

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

Hi ziyuenlau,

This question can be solved by TESTing VALUES. When a DS prompt involves lots of exponents, it's likely that you'll have to consider values OTHER than positive integers though (including 0, negatives, fractions, etc.).

We're asked if X^4 + Y^4 > Z^4. This is a YES/NO question.

Since Fact 2 is easier to deal with than Fact 1, I'm going to start there (we might also be able to use our work on Fact 2 to more easily deal with Fact 1)....

2) X + Y > Z

IF....
X = 1, Y = 0 and Z = 0, then the answer to the question is YES.
X = 1/2, Y = 1/2 and Z = .7, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

1) X^2 + Y^2 > Z^2

The TESTs that we used in Fact 2 also "fit" the information in Fact 1...

IF....
X = 1, Y = 0 and Z = 0, then the answer to the question is YES.
X = 1/2, Y = 1/2 and Z = .7, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

Combined, we have two sets of numbers that fit both Facts and produce different answers to the given question (one YES and one NO).
Combined, INSUFFICIENT.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich