If x is a positive integer, what is the value of x?

Question: If x is a positive integer, what is the value of x?

1. \(x^2-5x+5=1-x\)
2. \(x^2=4\)
    

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

“If x is a positive integer, what is the value of x?"- is the topic of GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Prep Plus 2021”. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprise 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer:

Firstly, consider the statement (1),

It is given that \(x^2-5x+5=1-x\)

This statement is sufficient in itself because it can be solved as:

\(x^2-5x+5=1-x\)

\(x^2-4x+4=0\)

\(x^2-2x-2x+4=0\)

\(x(x-2)-2(x-2)=0\)

\((x-2)(x-2)=0\)

Therefore, value of x = 2

Now, we will take statement (2),

It is given that \(x^2=4 \)

From here, we will get: x = \(\pm\) 2

But it is said that x is a positive integer, so the value of x can be only 2.

Hence, we can say that this statement is also sufficient in itself.

Correct Answer: D

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