What digit does X represent if each of X and Y are single digits in the decimal 7.5XY9 ?

1. If the decimal is rounded to the nearest hundredth, the result is 7.55

2. If the decimal is rounded to the nearest tenth, the result is 7.5

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer

Statement 1 says that the result of rounding the decimal to the nearest hundredth is 7.55. No information is given about the thousandths place so it is impossible to determine if the last digit of 7.55 was originally 5 or 4.

Statement 1 alone is insufficient to answer the question.

Statement 2 says that the result of rounding the decimal to the nearest tenth is 7.5. Notice that according to our rounding rules, this statement implies that the digit in the hundredths spot in the original decimal, was less than 5. There are 5 different digits less than 5 (including 0), and Statement 2 alone gives us no way to determine which of those is the actual value of the hundredths digit.

Statement 2 alone is also NOT sufficient to answer the question. Since the digit represented by the "X must be 4, the statements together are sufficient to answer the question.

Correct Answer - Choice C

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