MathRevolution wrote:
[
Math Revolution GMAT math practice question]
If \(n\) is a positive integer, which of the following can’t be the value of \((n+1)^4-n^4\)?
A. 2465
B. 4641
C. 6096
D. 7825
E. 9855
KEY CONCEPTS:
#1) If n is an integer, then n and n+1 are consecutive integers
#2) If n and n+1 are consecutive integers, then one value is ODD and the other value is EVEN
#3) ODD^4 = (ODD)(ODD)(ODD)(ODD) = ODD
#4) EVEN^4 = (EVEN)(EVEN)(EVEN)(EVEN) = EVEN
#5) ODD - ODD = EVEN
#6) ODD - EVEN = ODD
#7) EVEN - ODD = ODD
#8) EVEN - EVEN = EVENFrom
#2, there are two possible cases to consider:
case 1: n is EVEN and n+1 is ODD
case 2: n is ODD and n+1 is EVEN
case 1: n is EVEN and n+1 is ODD
In this case, (n+1)^4 - n^4 = ODD^4 - EVEN^4
= ODD - EVEN (from
#3 and
#4)
= ODD (from
#6)
case 2: n is ODD and n+1 is EVEN
In this case, (n+1)^4 - n^4 = EVEN^4 - ODD^4
= EVEN - ODD (from
#3 and
#4)
= ODD (from
#7)
In both cases, (n+1)^4 - n^4 = some ODD integer.
Check the answer choices........
All of the answer choices are ODD, except for answer choice C
Since (n+1)^4 - n^4 can't be EVEN, the correct answer is C
Cheers,
Brent
_________________
Test confidently with gmatprepnow.com