Question

The average score of a batsman was 40 runs per match after 10 matches. What was his average score for the last four matches?

Statement (1): Average for the first 6 matches is 36.
Statement (2): Average for all even numbered matches is 45 and for odd numbered matches is 38.

• A. If the data in statement (1) alone is sufficient to answer the question, but the data in statement (2) alone is not sufficient.
• B. If the data in statement (2) alone is sufficient to answer the question, but the data in statement (1) alone is not sufficient.
• 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.
• E. If the data in neither statement (1) nor statement (2) is sufficient to answer the question, and more data is needed.

Hint:

Find the fixed total from the question stem first, then check whether each statement's information is even consistent with that total before using it.

Answer 1

The Correct Option is A

From the question, total runs scored in 10 matches = \(40 \times 10 = 400\).

Statement (1): Average of the first 6 matches is 36, so runs in the first 6 matches = \(36 \times 6 = 216\). Runs in the last 4 matches = \(400 - 216 = 184\), so average for the last 4 matches = \(184/4 = 46\). This is a single, consistent value, so statement (1) alone is sufficient.

Statement (2): This says the average of the 5 even numbered matches (2, 4, 6, 8, 10) is 45 and the average of the 5 odd numbered matches (1, 3, 5, 7, 9) is 38. If this were true, the total for all 10 matches would be \(5 \times 45 + 5 \times 38 = 225 + 190 = 415\), but the question already fixes the total at 400 runs. Since 415 does not match 400, statement (2) is not consistent with the information already given in the question, so it cannot be relied on to give a dependable value for the last four matches. Statement (2) alone is not sufficient.

Since statement (1) alone answers the question but statement (2) alone does not, the correct choice is (a).