Subject: General Aptitude · Chapter: Number System · Exam: 2005 · Marks: · Difficulty:
The number formed from the last two digits (ones and tens) of the expression $2^{12 n}-6^{4 n}$, where $n$ is any positive integer is
(a)10
(b)00
(c)30
(d)02
Answer
Answer (as printed): B
Explanation
We have: $\left(2^{12 n}-6^{4 n}\right)=\left(2^{12 n}-2^{4 n} \times 3^{4 n}\right)=2^{4 n}\left(2^{8 n}-3^{4 n}\right)$. Putting $n=1$, we get the number $2^{4}\left(2^{8}-3^{4}\right)$ $=16(256-81)=(16 \times 175)=2800$ Hence, the number formed by last two digits is 00.
Explanation as extracted from the printed page; notation may be imperfect.