Question:
The average of 11 numbers is 50. If the average of the first six numbers is 49 and that of the last six numbers is 52, then the sixth number is
The average of 11 numbers is 50. If the average of the first six numbers is 49 and that of the last six numbers is 52, then the sixth number is
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The first-six and last-six groups both include the sixth number, so it is the excess over the total.
Updated On: Jul 8, 2026
- 54
- 56
- 58
- 52
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The Correct Option is B
Solution and Explanation
Step 1: Total of all eleven.
Sum \(=11\times50=550\).
Step 2: Sums of the two overlapping groups.
First six \(=6\times49=294\); last six \(=6\times52=312\).
Step 3: The sixth number is counted twice.
\(294+312=606\), which exceeds \(550\) by the sixth number.
Step 4: Isolate it.
Sixth \(=606-550=56\).
\[\boxed{56}\]
Sum \(=11\times50=550\).
Step 2: Sums of the two overlapping groups.
First six \(=6\times49=294\); last six \(=6\times52=312\).
Step 3: The sixth number is counted twice.
\(294+312=606\), which exceeds \(550\) by the sixth number.
Step 4: Isolate it.
Sixth \(=606-550=56\).
\[\boxed{56}\]
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