Question: If \(0 < x \leq1\), then which one of the following is the maximum value of \((x-1)^2+x\)?

1. -2
2. -1
3. 0
4. 1
5. 2

Answer:

Approach Solution (1):

If you cannot spot that maximum value of \((x-1)^2+x\) for \(0 < x \leq 1\) is when\( x = 1\rightarrow(x-1)^2+x=1\)you can do the following:

Since \(0 < x \leq 1\), then \((x-1)^2+x\) is positive \(\rightarrow\) discard A, B and C.

For the same reason: \((x-1)^2+x\)  is a non-negative fraction less than 1.

Thus \((x-1)^2+x\) = (non-negative fraction less than 1) + (\(0 < x \leq 1\)) < 2. Discard E

Only D is left

Correct option: D

Approach Solution (2):

Given that:\(0 < x \leq 1\)

Placing value of x = 1 in the above equation:

\((1-1)^2+1=1\)

Correct option: D

“If, then which one of the following is the maximum value of?”- 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. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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