If a is the sum of m consecutive positive integers and b is the sum of n consecutive positive integers. For which of the following values of m and n is it impossible that a = b?  Pick one
A) m = 2; n = 6 B) m = 3; n = 6 C) m = 10; n = 4 D) m = 7; n = 9 E) m = 10; n = 7
I approached this in a different way, although may be longer but it's certainly more intuitive   It is impossible that a = b if one of them is necessarily even while the other is necessarily odd   for two consecutive integers the sum is necessarily odd   for six consecutive integers the sum is necessarily odd (sum of 3two consecutive integerswhich are all odd)   Thus A is incorrect.   The sum of 3 consecutive integers can be even or odd (an odd integer from the first 2 + an additional integer which can be even or odd). Thus B is incorrect. You can do a similar approach for D and E (it follows that the sum of a specified odd number of consecutive integers can be odd or even).   Leaving us with C to be the only not-wrong answer. To confirm, you can easily deduce that the sum of 4 consecutive integers (sum of 2 odd integers) is necessarily even while the sum of 10 consecutive integers (sum of 5 odd integers) is necessarily odd. Thus m = 10; n = 4 is the right answer.
<result>C</result>
If a is the sum of m consecutive positive integers and b is the sum of n consecutive positive integers. For which of the following values of m and n is it impossible that a = b?