Problem:
The number halfway between 61 and 41 is
Answer Choices:
A. 101
B. 51
C. 245
D. 247
E. 125
Solution:
Since 61=122=244 and 41=123=246, it follows that the number halfway between 61 and 41 is 245.
OR
The number halfway between any two numbers is their arithmetic mean (average):
261+41=2244+6=22410=245
OR
Estimating each fraction to three decimal places and calculating the average yields
261+41≈20.167+0.250=20.417=0.2085
which is closest to 245≈0.2083.
Answer: C.
The problems on this page are the property of the MAA's American Mathematics Competitions