What number was removed?
2012-02-01
A Basic GRE/GMAT Word problem:
The average of 8 numbers is 20. If after one number is removed, the average of the remaining 7 numbers is 16. What number was removed?
[Spoiler Below]
Remembering that the mean is the sum divided by the number of numbers:
1: `"Average"_8 = 20 = "Sum"_8/8`
2: `"Average"_7 = 16 = "Sum"_7/7`
so:
3: `160 = "Sum"_8`
and:
4: `112 = "Sum"_7`
noting that: `"Sum"_8 = "Sum"_7 + RemovedNumber`,
5: `"Sum"_8 = 160 = "Sum"_7 + RemovedNumber`
Subtracting (4) from (5), we get: `48 = RemovedNumber`
Video:
The average of 8 numbers is 20. If after one number is removed, the average of the remaining 7 numbers is 16. What number was removed?
[Spoiler Below]
Remembering that the mean is the sum divided by the number of numbers:
1: `"Average"_8 = 20 = "Sum"_8/8`
2: `"Average"_7 = 16 = "Sum"_7/7`
so:
3: `160 = "Sum"_8`
and:
4: `112 = "Sum"_7`
noting that: `"Sum"_8 = "Sum"_7 + RemovedNumber`,
5: `"Sum"_8 = 160 = "Sum"_7 + RemovedNumber`
Subtracting (4) from (5), we get: `48 = RemovedNumber`
Video: