The table shows 5 people (Adam, Betty, Carol, David, and Eddy) and the difference between each weight and the average we

[Max@Math Revolution]

[GMAT math practice question]

The table shows 5 people (Adam, Betty, Carol, David, and Eddy) and the difference between each weight and the average weight of the 5 people. What is the weight of the lightest person among those five people?

1) If another person, Fred, who is 8 kg heavier than Adam, is included, the average is increased by 4%.
2) x is an even prime number.

[Max@Math Revolution]

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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.

Since the sum of all the differences between the weights and their average is zero, we have 4 + (-7) + 6 + (-5) + x = 0 or x = 2.
Thus, we don’t need condition 2), since the table already tells us that x = 2.

Let’s look at the condition 1).

Assume the new average, including Fred, is m’.
We have m’ = [5m + (m + 12)] / 6, m’ = (6m + 12) / 6, m’ = m + 2. We also m’ = 1.04m, since we are told the average increases by 4%.
Putting the 2 equations together gives us m + 2 = 1.04m.
Then we have 0.04m = 2 or m = 50.
Thus, the lightest weight is Betty’s weight m – 7 = 43.

The answer is unique, and the condition is sufficient according to Common Mistake Type 2, which states that the number of answers must be only one.

Condition 1) ALONE is sufficient.
Therefore, A is the answer.
Answer: A