Question

If x=232∗254∗276∗298 and is a multiple of 26n, where n is a non-negative integer, then what is the value of n26−26n?

Answer 1

"So, we have that the units digit of of n26−26nn26−26n?
A. -26
B. -25
C. -1
D. 0
E. 1

232∗254∗276∗298=odd∗odd∗odd∗odd=odd232∗254∗276∗298=odd∗odd∗odd∗odd=oddso xx is an odd number. The only way it to be a multiple of 26n26n (even number in integer power) is when n=0n=0, in If x=232∗254∗276∗298x=232∗254∗276∗298 and is a multiple of 26n26n, where nn is a non-negative integer, then what is the value of n26−26nn26−26n?
A. -26
B. -25
C. -1
D. 0
E. 1

232∗254∗276∗298=odd∗odd∗odd∗odd=odd232∗254∗276∗298=odd∗odd∗odd∗odd=oddso xx is an odd number. The only way it to be a multiple of 26n26n (even number in integer power) is when n=0n=0, in this case 26n=260=126n=260=1 and 1 is a factor of every integer. Thus n=0n=0 --> n26−26n=026−260=0−1=−1n26−26n=026−260=0−1=−1. Must know for the GMAT: a0=1a0=1, for a≠0a≠0- any nonzero number to the power of 0 is 1. Important note: the case of 0^0 is not tested on the GMAT.

Answer: C.