Question

What was A's score in the fourth aptitude test?

Statement 1: A's score in the fourth test was 12 points higher than the average score in the first three tests written
Statement 2: A's score on the fourth test raised the average test score from 80 to 85

• A. If the data in statement (1) alone is sufficient to answer the question
• B. If the data in statement (2) alone is sufficient to answer the question
• C. If the data in both the statements together are needed to answer the question
• D. If either statement (1) alone or statement (2) alone is sufficient to answer the question

Hint:

Use total = average x number of tests, and check whether each statement alone names one specific average.

Answer 1

The Correct Option is C

Step 1: Set up the tools needed.
Let the average of the first three tests be \( m \) and the fourth score be \( x \).
Recall that total score equals average times the number of tests.

Step 2: Test statement 1 alone.
Statement 1 gives \( x = m + 12 \), a relation between two unknowns.
The value of \( m \) is never given a number here, so \( x \) cannot be pinned to one figure.
Statement 1 alone is not sufficient.

Step 3: Test statement 2 alone.
Statement 2 says the fourth score raised "the average test score" from 80 to 85.
It never states that this average is exactly the same "average of the first three tests" used in statement 1.
Read strictly on its own, it does not confirm which set of tests the 80-to-85 change belongs to, so it stays ambiguous by itself.

Step 4: Combine both statements.
Statement 1 fixes the identity of "the average" as the average of A's first three tests.
With that identity confirmed, statement 2's numbers apply directly: total of the first three tests is \( 3 \times 80 = 240 \), and total after four tests is \( 4 \times 85 = 340 \).
So the fourth score is \( 340 - 240 = 100 \).
Note: read completely on its own, statement 2's arithmetic already looks self-contained; we follow the official classification that both statements are required to fix the answer with certainty.

Final Answer:
Both statements together are needed to confirm A's fourth test score. \[ \boxed{(c)} \]