Question:medium

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

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Find the total for all 10 matches first (40 x 10), then see which statement lets you split off the last four matches cleanly.
Updated On: Jul 21, 2026
  • If the data in statement (1) alone is sufficient to answer the question
  • If the data in statement (2) alone is sufficient to answer the question
  • If the data in both the statements together are needed to answer the question
  • If either statement (1) alone or statement (2) alone is sufficient to answer the question
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The Correct Option is A

Solution and Explanation

Step 1: Set the target.
Total runs over 10 matches = average x matches = \(40 \times 10 = 400\). The last four matches are the 7th, 8th, 9th and 10th games played, so we need the runs in just these four games.

Step 2: Use statement 1 by itself.
If the average of the first six games is 36, those six games add up to \(6 \times 36 = 216\) runs.
Whatever remains once we remove these 216 runs from the season total of 400 belongs to the last four games: \(400 - 216 = 184\) runs, giving an average of \(184/4 = 46\).
Since this is one exact figure, statement 1 by itself is enough.

Step 3: Use statement 2 by itself.
Among matches 7, 8, 9 and 10, matches 8 and 10 are even numbered and matches 7 and 9 are odd numbered, so this group has 2 even games and 2 odd games.
Using statement 2's averages, that gives \((2 \times 45) + (2 \times 38) = 90 + 76 = 166\), an average of \(166/4 = 41.5\) for the last four games.
But statement 2 also forces a season total of \((5 \times 45) + (5 \times 38) = 415\) runs, which does not match the 400 runs fixed by the question, so its numbers cannot be trusted on their own.
So statement 2 by itself fails to give a reliable value.

Step 4: Conclude.
Statement 1 alone works cleanly and statement 2 alone does not, so the answer is that statement (1) alone is sufficient. \[ \boxed{\text{a}} \]
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