If 2x + y = 7, what is the value of x ? (1) y = 3 (2) 3x + y = 9 GMAT data sufficiency

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

(1) y = 3
(2) 3x + y = 9

          A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
          B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
          C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
          D) EACH statement ALONE is sufficient.
          E) Statements (1) and (2) TOGETHER are not sufficient.

Approach Solution 1

Assumed: 2x + y = 7

What does x equal in terms of value?
First claim: y = 3.
Replace using the given equation to obtain: 2x + (3) = 7
To get x = 2, solve the problem.

Statement 1 is sufficient because we are confident in our ability to respond to the target question.
                 2. 3x plus y equals 9.
This equation can be rewritten as follows: x + (2x + y) = 9
We can use x + (2x + y) = 9 and substitute to get: x + 7 = 9 because the given information informs us that 2x + y = 7.

To get x = 2, solve the problem.
Statement 2 is sufficient since we are confident in our ability to respond to the target question.
Hence, D is the correct answer.

Approach Solution 2

To find the value of x, we can use the given equation 2x + y = 7 and the information provided in the statements.
Let's evaluate each statement:
(1) y = 3
If y = 3, we can substitute this value into the original equation:
2x + 3 = 7
Now, we can solve for x:
2x = 7 - 3
2x = 4
x = 4/2
x = 2
So, from statement (1), we find that x = 2.

Statement (2): 3x + y = 9
We are given that 2x + y = 7 from the original equation.
Now, we can rewrite the equation 3x + y = 9 as follows: x + (2x + y) = 9
Since we know that 2x + y = 7, we can substitute it into the equation: x + 7 = 9
Now, we can solve for x:
x = 9 - 7
x = 2
Thus, from statement (2), we find that x = 2.
D is the correct answer.

Approach Solution 3

We can use the equation 2x + y = 7 and the data in the statements to determine the value of x.
Let's assess each assertion:
(1) y = 3
If y = 3, we can enter this number in the original equation as follows:
2x + 3 = 7
We can now determine x:
2x = 7 - 3
2x = 4 x = 4/2 x = 2
So, x = 2 is what we deduce from claim (1).

Indication (2): 3x + y =
We can deduce from the original equation that 2x + y = 7.
Now, the formula 3x + y = 9 can be rewritten as follows: x + (2x + y) = 9
Given that 2x + y = 7, we can replace it in the equation by saying: x + 7 = 9
We can now determine x:
x = 9 - 7 x = 2
As a result, we discover that x = 2 from assertion (2).
The correct response is D.

“If 2x + y = 7, what is the value of x ? (1) y = 3 (2) 3x + y = 9" - is a topic of the GMAT data sufficiency section of the GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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