Bunuel wrote:

Is it true that x rounded to the nearest tenth is equal to y rounded to the nearest tenth?

(1) (10x) rounded to the nearest unit is equal to (10y) rounded to the nearest unit.

(2) (x/10) rounded to the nearest hundredth is equal to (y/10) rounded to the nearest hundredth.

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, and then recheck the question.

Let's analyze how to get the nearest tenth. The nearest tenth of 1.345 is 1.3 and that of 1.456 is 1.5.

Thus we define the nearest tenth as follows.

If n - 1/2 ≤ 10x < n + 1/2 where n is an integer, n/10 is the nearest tenth.

10 * 1.345 = 13.45

13 - 1/2 = 12.5 ≤ 13.45 < 13.5 = 13 + 1/2

13/10 = 1.4 is the nearest tenth of 1.345.

10 * 1.456 = 14.56

15 - 0.5 = 14.5 ≤ 14.56 < 15.5 = 15 + 0.5

15/10 = 1.5 is the nearest tenth of 1.456.

Condition 1):

The definition of the nearest unit of 10x is as follows.

If n - 0.5 ≤ 10x < n + 0.5, n is the nearest unit of 10x and n/10 is the nearest tenth of x.

Thus condition 1) is same as the definition of nearest tenth of x.

The condition 1) is sufficient.

Condition 2):

If n - 0.5 ≤ 100 * (x/10) < n + 0.5, n/100 is the nearest hundredth of (x/10), which is equivalent to the definition of the nearest tenth that n/10 is the nearest tenth of x.

Thus condition 2) is same as the definition of nearest tenth of x.

The condition 2) is sufficient.

Therefore, D is the answer.

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