If g is an Integer and x is a Prime Number, Which of the Following Must be an Integer? GMAT Data Sufficiency

Question: If g is an integer and x is a prime number, which of the following must be an integer?

1.  (\(g^2\)x+5gx) / x
2. \(g^2\) - \(x^2\)/3
3. 6 (g/2) - 100 (g/2)2

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 g is an integer and x is a prime number, which of the following must be an integer?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Reviews". 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 sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Approach Solution 1:

There is only one approach to solve the problem statement.

Given:

• g is an integer and x is a prime number

Find out:

• Which of these are an integer:
• (\(g^2\)x+5gx) / x
• \(g^2\) - \(x^2\)/3
• 6 (g/2) - 100 \((g/2)^2\)

We will take each statement separately and check if they are an integer.

Let us see the Statement 1:

=>(\(g^2\)x+5gx) / x
We can cancel the x as it cannot be 0.

Hence, this simplifies to \(g^2\)+5g which has to be an integer.

From the above, we get that statement 1 is always an integer.
Let us see the Statement 2:

=>\(g^2\) - \(x^2\)/3

The \(g^2\)part must be an integer, so we check \(x^2\)/3 and see if that part is an integer.

If we have x = 3 then \(x^2\)/3 is an integer, but any other prime would make it not an integer.
From the above, we get that the statement 2 isn't always an integer.

Let us see the Statement 3:

=>6 (g/2) - 100 \((g/2)^2\)

This simplifies to 3g−25\(g^2\).

All components multiplied are integers so the result is an integer.

From the above, we get that the statement 3 is always an integer.

1 and 3 are always an integer.

Correct Answer: D

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