What is the value of x? (1) x^(1/2) = x

‘What is the value of x? (1) x^(1/2) = x - 2 (2) x ≠ 1’ is a GMAT Quantitative Reasoning topic. GMAT quantitative reasoning section analyses the candidates' ability to solve mathematical, and quantitative problems and interpret graphic data. This section of the GMAT exam comprises 31 questions that need to be completed in 62 minutes. The question in this section has 5 options. Candidates need to solve the question and find out the correct answer. GMAT Quant syllabus has mainly the two categories-

Problem Solving: In this section, candidates indicate the best five answer choices. This question type in GMAT Quantitative analyses candidates logical and analytical reasoning skills.
Data Sufficiency: This question type in GMAT Quantitative analyses candidates’ quantitative problems and identifies relevance with the data given.

Topic: What is the value of x?
(1) \(\sqrt{x}\)=x−2
(2) x ≠ 1

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are not sufficient.

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Answer: C

Model Answer
This question has only one approach to solve
Explanation:
We will take each statement and try solve for it
From the 1st statement \(\sqrt{x}\)=x−2, we get
Squaring both sides, we have x=(x-2)^2
or say
Opening up the RHS and simplifying, we have
x^2-5x+4=0
so x= 4 or x = 1
Therefore, x has two values, 1 and 4. We need a unique value of x
Now, since LHS is +ve so 1 is not possible at square root value at RHS. The equation \(\sqrt{x}\)=x−2 does not fit by placing 1.
If we place 1 instead of x, we get √1=1-2, 1=-1
This is invalid
Now, if we place x=4,
√4=4-2, 2=2
This is valid. Hence, we will consider x=4
So the option 1 is sufficient.
From the 2nd statement, x ≠ 1, we have:
From statement II alone, x≠1. This is not sufficient to find the value of x.
Hence, the 2nd option is not sufficient at all.
Combining statements I and II, we have the following:
From statement I, x = 1 or 4. From statement II, x≠1.
This means, x = 4. The combination of statements is sufficient.
The correct answer is C.

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What is the value of x? (1) x^(1/2) = x - 2 (2) x ≠ 1

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