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 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
• 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:

Find the total for all 10 matches first (40 x 10), then see which statement lets you split off the last four matches cleanly.

Answer 1

The Correct Option is A

Step 1: Find the total runs scored in all 10 matches.
The batsman's average was 40 runs per match after 10 matches, so his total runs for the 10 matches is \(40 \times 10 = 400\) runs.
The last four matches are match numbers 7, 8, 9 and 10, since the season runs in order from match 1 to match 10.

Step 2: Check statement 1 alone.
Statement 1 says the average for the first 6 matches is 36, so the total runs in the first 6 matches is \(36 \times 6 = 216\).
Since the total for all 10 matches is 400, the runs scored in the remaining 4 matches (the last four) is \(400 - 216 = 184\).
The average for the last four matches is then \(184 \div 4 = 46\) runs. This is a single clean number, so statement 1 alone answers the question.

Step 3: Check statement 2 alone.
Statement 2 gives the average for all even numbered matches as 45 and for all odd numbered matches as 38.
There are 5 even numbered matches and 5 odd numbered matches in a set of 10, so the total runs by this statement would be \((5 \times 45) + (5 \times 38) = 225 + 190 = 415\) runs.
This directly clashes with the 400 total runs already fixed by the question (average 40 over 10 matches), so statement 2 cannot be reconciled with the given data to give one trustworthy value for the last four matches.
Statement 2 alone does not give a usable, consistent answer.

Final Answer:
Only statement 1 alone lets us pin down the average for the last four matches (46 runs), so statement (1) alone is sufficient. \[ \boxed{\text{a - Statement (1) alone is sufficient}} \]