Question

A certain number is not an integer. Is the number less than .4?
(1) The number rounded to the nearest tenth is .4.
(2) The number rounded to the nearest integer is 0.

• 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.

Hint:

For Data Sufficiency questions about rounding, always write out the full range of possible values. A statement is insufficient if you can find one example within the range that gives a "Yes" answer and another that gives a "No" answer.

Answer 1

Answer: (E)

Step 1: Understanding the Question
Let N be the number. We are given that N is not an integer. The question is a Yes/No question: Is N<0.4?
Step 2: Analysis of Statement (1)
Statement (1) says that when N is rounded to the nearest tenth, the result is 0.4. This means that N must be in the range: \[ 0.35 \leq N<0.45 \] Within this range, we can find numbers that are less than 0.4 and numbers that are not less than 0.4.
If N = 0.38, then N is less than 0.4. The answer is "Yes".
If N = 0.42, then N is not less than 0.4. The answer is "No".
Since we can get both a "Yes" and a "No" answer, Statement (1) ALONE is not sufficient.
Step 3: Analysis of Statement (2)
Statement (2) says that when N is rounded to the nearest integer, the result is 0. This means that N must be in the range: \[ -0.5 \leq N<0.5 \] (Note: We are given N is not an integer, so N \(\neq\) 0). Within this range, we can also find numbers that satisfy both conditions.
If N = 0.3, then N is less than 0.4. The answer is "Yes".
If N = 0.45, then N is not less than 0.4. The answer is "No".
Since we can get both a "Yes" and a "No" answer, Statement (2) ALONE is not sufficient.
Step 4: Analysis of Statements (1) and (2) Together
Now we combine the information from both statements. From (1): \( 0.35 \leq N<0.45 \) From (2): \( -0.5 \leq N<0.5 \) The intersection of these two ranges is still \( 0.35 \leq N<0.45 \). Even with both conditions, we can still pick numbers that give different answers to the question "Is N<0.4?".
If we pick N = 0.39, it satisfies both conditions (rounds to 0.4 and to 0), and N<0.4. (Answer: Yes)
If we pick N = 0.41, it satisfies both conditions (rounds to 0.4 and to 0), and N is not<0.4. (Answer: No)
Since we still cannot determine a definite answer, the statements together are not sufficient.
Step 5: Final Answer
Because we can't get a definitive Yes or No answer even with both statements, the correct answer is (E).