Question: If n > 0, which of the following must be true?

1. \(n^2>1\)
2. \(n-n^2<0\)
3. \(2n-1>1\)

1. I only
2. II only
3. III only
4. I and II only
5. None

Correct Answer: E

Approach Solution (1):

(1) True for all values of n except 1
When n = 1; \(n^2>1\)

(2) True for all values of n except 1
When n = 1; \(n-n^2<0\)

(3) True for all values of n

Correct Answer: E

Approach Solution (2):

Note: n is positive but we don’t know whether it is an integer or fraction.

(1)\(n^2>1\). Not necessarily, let x be \(\frac{1}{2}\)

(2)\(n-n^2<0\). Let x be \(\frac{1}{2}\). False

(3) 2n – 1 > 0. Let be \(\frac{1}{2}\). 2 * \(\frac{1}{2}\)- 1 = 0. False

Thus, none of these options are correct. This question is designed to test fractional case.

Correct Answer: E

“If n > 0, which of the following must be true?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills.

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