Question

What was A's score in 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 raise the average test score from 80 to 85

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question.

Answer 1

The Correct Option is C

To determine A's score in the fourth aptitude test, we need to examine both statements provided.

1. From Statement 1:
   "A's score in the fourth test was 12 points higher than the average score in the first three tests written."
   • Let the average score of the first three tests be \( x \).
   • Then, A's score in the fourth test is \( x + 12 \).
   • However, without knowing the value of \( x \), we cannot determine the exact score.
2. From Statement 2:
   "A's score on the fourth test raised the average test score from 80 to 85."
   • Let the total score for the first three tests = \( 3 \times 80 = 240 \).
   • Total score after the fourth test = \( 4 \times 85 = 340 \).
   • So, A's score in the fourth test added to 240 should equal 340, giving: \(x = 340 - 240 = 100\).
   • This calculation accurately determines the score as 100.

Now, combining both statements:

1. From Statement 1, A's fourth test score is \( x + 12 \).
2. From Statement 2, the fourth test raised the average score from 80 to 85, concluding the score must be 100.
3. Both statements complement each other but aren't logically interdependent for finding \( x\).

Conclusion: Statement 2 alone gives the fourth test score as 100.

Therefore, the correct interpretation of the provided options is that both statements together can provide further reasoning, but Statement 2 alone suffices to derive the exact score, making the best choice:

Correct Answer: Statement (2) alone is sufficient to answer the question.