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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.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Let the integers be x – 1, x and x + 1 where x is a positive integer. Since their sum, x – 1 + x + x + 1 = 3x is a multiple of 10, x must be a multiple of 10.
Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
Condition 1)
The median, x, of the three integers is a multiple of 9 and a multiple of 10.
Since x < 100, we must have x = 90.
Therefore, the smallest of the integers is x – 1 = 89.
Thus, condition 1) is sufficient.
Condition 2)
If x = 30, the integers are 29, 30, 31 and the smallest integer is 29.
If x = 90, the integers are 89, 90, 91 and the smallest integer is 89.
Since we do not obtain a unique answer, condition 2) is not sufficient.
Therefore, the answer is A.
Answer: A
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