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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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Since we have 2 variables (a and x) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) & 2) together give us:
From condition 1) we get:
3x - [7x - {2x - 4(5 - 6x)}] = -10x + 4
3x – 7x + (2x – 20 + 24x) = -10x + 4
3x - 7x + 26x – 20 = -10x + 4
22x – 20 = -10x + 4
32x = 24
x= 24/32 = ¾
From condition 2) we get:
–a + 5 = 11x
a = 5 – 11x
Thus, we have x = 3/4 and a = 5 – 11x. So, a = 5 – 11(3/4) = 5 – 33/4 = 20/4 - 33/4 = -13/4.
Since 'no' is also a unique answer, according to CMT (Common Mistake Type) 1, both conditions are sufficient.
The answer is unique, and conditions 1) and 2) together are sufficient according to Common Mistake Type 2, which states that the number of answers must be only one.
Both conditions 1) & 2) together are sufficient.
Therefore, C is the correct answer.
Answer: C
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations,” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C, or E.
