If 3x – 2y = 7, What is the Value of x? x and y are Positive Integer GMAT Data Sufficiency

Question: If 3x – 2y = 7, what is the value of x?

1. x and y are positive integers
2. x = y - 1

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.

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
The problem statement states that 3x – 2y = 7. It is asked to find the value of x.

(1) x and y are positive integers

3x = 7 + 2y
x=\(\frac{1}{3}(7+2y)\)

y = 1 —> \(x=\frac{1}{3}(9)\), x = 3

y = 4 —> \(x=\frac{1}{3}(15)\), x = 5

y = 10 —> \(x=\frac{1}{3}(27)\), x = 9

Not sufficient.

(2) x = y – 1
3(y – 1) – 2y = 7
3y – 3 – 2y = 7
y = 10
For y = 10 and x = 9
Sufficient.

Approach Solution 2:

The problem statement states that 3x – 2y = 7. It is asked to find the value of x.

Statement 1: x and y are positive integers.
The statement is not constricting enough, we have many combinations of x and y that can solve this.

x = 3 and y = 1, or x = 5 and y = 4

Hence, Insufficient

Statement 2: x = y - 1
We have two equations with two variables that are linear and independent. That allows us to solve a unique solution so this is sufficient.

Approach Solution 3:
The problem statement states that 3x – 2y = 7. It is asked to find the value of x.
Therefore, we have 2 variables (x and y) and 1 equation.

Statement 1: x and y are positive integers.
Possible pairs of (x,y) are x = 3, y = 1 and x = 5, y = 4.
Since statement 1 does not generate a unique answer, it is not sufficient

Statement 2: x = y - 1
We have y = x + 1
Further we know, 3x - 2y = 7
By pugging the value of y we get:
=>3x -2(x+1) = 7
=> x - 2 = 7
=> x = 9.

Therefore, Statement 2 generates a unique answer. Hence, statement 2 alone is sufficient.

“If 3x – 2y = 7, what is the value of x?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide”. 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 comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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