2ax - 3b = a - bx is an equation in terms of x. What is its

[Max@Math Revolution]

[GMAT math practice question]

2ax - 3b = a - bx is an equation in terms of x. What is its solution?

1) -3/2 is a solution of (b-a)x - (2a-3b) = 0
2) a = 3b

[deloitte247]

2ax - 3b - a + bx = 0
2ax + bx - 3b - a = 0
x(2a + b) - (a + 3b) = 0
So, let find the unknown variables;
Statement 1: -3/2 is a solution of (b-a)x - (2a-3b) = 0
One of the unknown variables in this expression is given but the remaining 2 variables are not given. Thus, -3/2 could be a solution of either variable a, b or x.
So, statement 1 is NOT SUFFICIENT

Statement 2: a = 3b
Express from the question stem x(2a + b) - (a + 3b) = 0
Substitute a=3b; we have,
x(2(3b) + b) - ((3b) + 3b) = 0
x(6b + b) - 6b = 0
7bx - 6b = 0
Variable x and b has no definite solution, hence, statement 2 is NOT SUFFICIENT.

Combining both statement together:
Statement 1: (b-a)x - (2a-3b) = 0
Statement 2: a = 3b
So, (b-3b)x - (2(3b) - 3b) = 0
(-2b)x - (6b - 3b) = 0
-2bx - 3b = 0
-2bx = 3b
Divide through by x
-2x = 3
x = -3/2
The solution for variable 'a' and 'b' is still unknown, hence, both statements combined together are NOT SUFFICIENT.

ANSWER = OPTION E

[Max@Math Revolution]

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
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The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
The question asks the value of (a+3b)/(2a+b) for the following reason.
2ax - 3b = a - bx
=> 2ax + bx = a + 3b
=> x(2a+b) = a+3b
=> x = (a+3b)/(2a+b)

Since we have a = 3b from condition 2), we have x = (a+3b)/(2a+b) = (3b+3b)/(6b+b) = (6b)/(7b) = 6/7.
Thus, condition 2) is sufficient.

Condition 1)
When we substitute -3/2 for x, we have (b-a)(-3/2) - (2a-3b) = 0 or (-3)(b-a) = 2(2a-3b). We have -3b+3a = 4a-6b or a = 3b.
Condition 1) is equivalent to condition 2), and it is also sufficient.

Therefore, D is the answer.

When a question asks for a ratio, if one condition includes a ratio and the other condition just gives a number, the condition including the ratio is most likely to be sufficient. This tells us that D is most likely to be the answer to this question, since each condition includes a ratio.

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).

This question is a CMT4(B) question: condition 2) is easy to work with, and condition 1) is difficult to work with. For CMT4(B) questions, D is most likely to be the answer.