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 the 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 fixed total from the question stem first, then check whether each statement's information is even consistent with that total before using it.
Updated On: Jul 20, 2026
  • If the data in statement (1) alone is sufficient to answer the question, but the data in statement (2) alone is not sufficient.
  • If the data in statement (2) alone is sufficient to answer the question, but the data in statement (1) alone is not sufficient.
  • 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.
  • If the data in neither statement (1) nor statement (2) is sufficient to answer the question, and more data is needed.
Show Solution

The Correct Option is A

Solution and Explanation

First, see what statement (2) alone would seem to give. The last four matches are numbered 7, 8, 9 and 10, which are odd, even, odd, even respectively. Using the averages from statement (2), that would be $38, 45, 38, 45$, giving an average of $(38+45+38+45)/4 = 166/4 = 41.5$.
But check this against the question stem: the batsman's average over all 10 matches is fixed at 40, so the total runs must be $400$. Statement (2) implies odd matches total $5 \times 38 = 190$ and even matches total $5 \times 45 = 225$, adding to $415$, not $400$. Since this contradicts the given total, the figure of 41.5 cannot be trusted, and statement (2) alone fails to give a reliable answer.
Now use statement (1): first 6 matches average 36, so they total $216$ runs, leaving $400 - 216 = 184$ runs for the last 4 matches, an average of $184/4 = 46$. This total is fully consistent with the given data, so statement (1) alone is enough.
The correct choice is that statement (1) alone is sufficient, but statement (2) alone is not, option (a).
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