Thousandths Digit

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If l denotes the thousandths digit in the decimal representation of n above, what digit is l?

(1) If n were rounded to the nearest hundredth, the result would be 9.95.

(2) If n were rounded to the nearest thousandth, the result would be 9.946.

Review: Thousandths Digit




Explanation

We read the question. Evidently l will be an integer between 0 and 9, but we don't know otherwise what to expect. On to the statements, first separately.

Statement (1) indicates that l is 5 or greater. That's required for the number n to round up 9.95. That leaves a number of possible cases, so Statement (1) is insufficient.

Statement (2) indicates that l is 5. This is the only possible case, because the 6 that comes after l in the original number means that when we round, l will increment by one. That's the only possible case, so Statement (2) is sufficient.

The correct answer is (B).


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