Question: 2x+3y=?
- 2x+4y=3
- 4x+6y=6
(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.
Correct Answer: B
Solution and Explanation:
Approach Solution 1:
The question asks to find the value of 2x + 3y
Statement 1: 2x+4y=3
Here, we have 4y but no information is given on 3y.
Let us consider the value of x =10.
This can be further expanded as; 20+4y= 3,
This implies; y =-17/4.
Further, let’s consider the value of x to be 4,
Therefore; y = -5/4
We are getting two values of y. Hence, statement 1 alone is not sufficient.
Statement 2: 4x+6y=6
Thus, by dividing by 2 both the equations we get the answer 2x+3y=3, which is justified.
Hence, statement 2 alone is sufficient.
Approach Solution 2:
The second approach that can be adapted to solve this is equating the values of x and y by equating both equations in terms of LHS and RHS.
The above-mentioned question has two given equations: 2x+4y=3 and 4x+6y=6.
Equating both the equations in terms of LHS and RHS, we get:
2x+3y= (1÷2)(4x+6y)
Justifying the values and evaluating each equation on each side; LHS and RHS, we get the equation: 4x+6y=6.
Therefore, it is justified 4x+6y=6 and further is a unique value. 4x+6y=6 thus, it is sufficient for the above-mentioned equation.
The equation can be denoted in a graph as the above-mentioned pattern. The graph illustrates two axes; the x and y-axis. The left side depicts the negative side of the x-axis and the bottom side of the y-axis negative y-axis. The intersection in the graph that has been denoted in blue colour portrays the formula 4x+6y=6.
Hence, statement 2 alone is sufficient, but statement 1 alone is not sufficient.
Approach Solution 3:
The question asks to find the value of 2x + 3y
Statement 1: 2x+4y=3
This statement is insufficient since we do not know the value of x and y. Therefore, it cannot be possible to find the value of 2x+3y.
Statement 2: 4x+6y=6
Let’s divide both sides of the equation by 2.
(4x+6y)/2 = 6/2
=> 4x/2 + 6y/2 = 3
=> 2x + 3y = 3
Hence, statement 2 alone is sufficient to find the value of 2x + 3y.
“2x+3y=?”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This question has been taken from the book “Foundations of GMAT Math”. The GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions include a problem statement that is 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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