BTGModeratorVI wrote: ↑

Sat Mar 14, 2020 6:47 am

If x > 0, which of the following must be true?

A. 1 < x
B. 0 < x < 2
C. -1 < x < 1
D. -10 < x
E. 1/100 < x


Answer: D
Source: Economist GMAT

All we know is that \(x\) is some positive number. Right away we can see that D must be true: if \(x\) is positive then it MUST be true that it's greater than \(-10\). Still let's check each option.

A. \(1 < x\). We don't know whether the number is greater than \(1\), it could be a positive number less than or equal to \(1\). Discard. \(\Large{\color{red}\chi}\)

B.\( 0 < x < 2\). The same here: we don't know whether the number is less than \(2\), it could be more than or equal to 2. Discard. \(\Large{\color{red}\chi}\)

C. \(-1 < x < 1\). The same as A. Discard. \(\Large{\color{red}\chi}\)

E. \(\dfrac{1}{100} < x\). We don't know whether the number is greater than \(\dfrac{1}{100}\), it could be a positive number less than or equal to \(\dfrac{1}{100}\). Discard. \(\Large{\color{red}\chi}\)

Therefore, the correct answer is D.