Problem Solving

What is the remainder when you divide 2^200 by 7?

A. 1
B. 2
C. 3
D. 4
E. 5

This mgmat Q.

Should be D

PGMAT wrote:What is the remainder when you divide 2^200 by 7?

A. 1
B. 2
C. 3
D. 4
E. 5

This mgmat Q.

I hope i can explain this....

Number remainder
2^3 1
2^4 2
2^5 4
2^6 1
2^7 2
2^8 4

So this 1,2,4 pattern repeats... and it repeats after every 3 numbers..means

Number remainder
2^3 1
2^6 1
2^9 1
2^12 1

Now lets find the biggest multiple of 3 below 200 its 198..so
2^198 1
2^199 2
2^200 4

Answer:D

Hope u understood...All the best..... It took some time for me to figure out but will not forget now this problem...thanks....