Question: If x + 2y – 3z = 5 and 2x + 2y + 3z = 8, then 9x + 12y = ?

(A) 15
(B) 23
(C) 31
(D) 39
(E) It cannot be determined.

Correct Answer: D
Solution and Explanation
Approach Solution 1:

To find the solution for 9x + 12y = 3 * (3x + 4y). We need to eliminate z from the equation:
Let, x + 2y – 3z = 5 ... (1)
Let, 2x + 2y + 3z = 8 ... (2)
Adding both the equations we get, 3x + 4y = 13
3 * (3x + 4y) = 13 * 3 = 39

Hence the correct answer is D.

Approach Solution 2:

Equation 1 is x + 2y − 3z = 5.
Equation 2 is 2x + 2y + 3z = 8.
Solving Equations 1 and 2,
x + 2y − 3z = 5..
2x + 2y + 3z = 8
----------------
3x + 4y + 0 = 13
Now multiplying the resultant equation by 3 to get
9x + 12y = 39

Therefore,
9x + 12y = 39

Hence the correct answer is D.

Approach Solution 3:

(x + 2y – 3z = 5) + (2x + 2y + 3z = 8) => 3x + 4y = 13
Thus,
9x + 12y = 39

Hence the correct answer is D.

“If x + 2y – 3z = 5 and 2x + 2y + 3z = 8, then 9x + 12y = ?” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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