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Is x < 5?
(1) x^2 > 5
(2) x^2 + x < 5
Official Guide question
Answer: B
(1) x^2 > 5
(2) x^2 + x < 5
Official Guide question
Answer: B
Target question: Is x < 5?jjjinapinch wrote:Is x < 5?
(1) x² > 5
(2) x² + x < 5
Official Guide question
Answer: B
Statement 1: x² > 5
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 3 is a possible value since 3² > 5. In this case, x < 5
Case b: x = 6 is a possible value since 6² > 5. In this case, x > 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: x² + x < 5
IMPORTANT: x² is greater than or equal to 0 for ALL values of x.
So, let's let 0+ represent the value of x². This notation reminds us that x² equals some value that's greater than or equal to 0
Our inequality becomes: (0+) + x < 5
In order for the left side to be less than 5, x CANNOT be greater than or equal to 5
In other words, it MUST be the case that x < 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
