The average of 11 results is 50. The average of the first six is 49 and of the last six is 52. What is the sixth result?
56. The first six and the last six together count the sixth result twice: 6 x 49 + 6 x 52 = 294 + 312 = 606, while all 11 total 550. The extra 56 is the sixth result.
Explain it simply
Picture 11 people in a line. "First six" are positions 1 to 6 and "last six" are positions 6 to 11. The person in position 6 is in both groups. If you add both group totals, you count everyone once except that person, who is counted twice. Subtract the overall total, and what remains is that person.
Example
Question: 11 results average 50. First 6 average 49, last 6 average 52. Find the 6th.
- Total of all 11 = 11 x 50 = 550.
- Total of first 6 = 6 x 49 = 294.
- Total of last 6 = 6 x 52 = 312.
- 294 + 312 = 606 counts the 6th result twice.
- 6th result = 606 - 550 = 56.
console.log(6 * 49 + 6 * 52 - 11 * 50); // Output: 56If the groups do not overlap (say the first five and the last six of 11), the totals simply add up to the overall total and there is no hidden value to find, which is a useful check on how you read the question.
What to say in the interview
"The two groups overlap at the sixth value, so adding their totals counts it twice. 294 plus 312 is 606, minus the full total of 550 leaves 56."
Common mistakes
- Averaging 49 and 52 and comparing with 50.
- Missing that the overlap is exactly one value; count positions carefully.