frankiegar wrote:
When the positive number a is rounded to the nearest tenth, the result is the number b. What is the tenths digit of a?
(1) When a is rounded to the nearest integer, the result is less than a.
(2) When b is rounded to the nearest integer, the result is greater than b.
Any suggestions?
Best,
(1) INSUFFICIENT: According to this statement, a must be rounded down to the nearest integer. The tenths digit of a could thus be any of 0, 1, 2, 3, or 4. Since there are five possibilities for the tenths digit, this statement is insufficient.
Test numbers if you're not sure: if a is 14.0, it will round down to 14. If a is 14.4, it will also round down to 14. If a is 14.5, it will round up to 15, so 5 cannot be the tenths digit of a, nor can digits larger than 5.
(2) INSUFFICIENT: According to this statement, b, which is the result of rounding a to the nearest tenth, must be rounded up to the nearest integer. Therefore, the tenths digit of b could be any of 5, 6, 7, 8, or 9. Test numbers if you're not sure: if b is 11.9, it will round up to 12. If b is 11.5, it will round up to 12. If b is 11.4, however, it will round down to 11, so 4 cannot be the tenths digit of b, nor can anything smaller than 4.
Recall that the problem asks about a, not b; therefore, we need to figure out which possible values for a will then round to one of the tenths digits 5, 6, 7, 8, or 9. The lowest such value of a is xxx.45 (where xxx could be any value). This number will round to xxx.5, so a tenths digit of 4 for the number a can produce a tenths digit of 5 for the number b. At the other end, the highest such value is xxx.949999, which will round to xxx.9. Therefore, according to this statement, the tenths digit of a could be 4, 5, 6, 7, 8, or 9. There are six possibilities, so the statement is insufficient.
Test numbers if you're not sure or if the above method is too abstract. First, the question stem tells us that when a is rounded to the nearest tenth, the result is b. If a is 14.45, that will round to 14.5 (remember, a is allowed to round up here because we're ignoring statement 1). As a result, b = 14.5. If b is then rounded, it will round up, which is what statement 2 tells us, so the smallest possible value for the tenths digit of a is 4. At the opposite end, if a is 14.94, it will round to 14.9, which represents b. If b is rounded, it will also round up, so the largest possible value for the tenths digit of a is 9.
(1) AND (2) SUFFICIENT: According to statement (1) the tenths digit of a could be 0, 1, 2, 3, or 4. According to statement (2), the tenths digit of a could be 4, 5, 6, 7, 8, or 9. The only value common to the two statements is 4, so, taking both statements together guarantees that the tenths digit of a is 4.
The correct answer is C.