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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.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer.

Condition 1)

Since the median is 51, x could be any value greater than or equal to 51.

This is NOT sufficient.

Condition 2)

Since the range is 29=65-36, x could be any value between 36 and 65, inclusive.

This is NOT sufficient.

Conditions 1) and 2)

Condition 1) tells us that x could be any value greater than or equal to 51, while condition 2) tells us that x could be any value between 36 and 65, inclusive. Combining these ranges tells us that x could be any value between 51 and 65, inclusive.

Therefore, the two conditions are NOT sufficient, when considered together.

The answer is E.

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.

Answer: E

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