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

Question

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

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

I saw the explanation but I can't how to figure out with this problem in a straightforward manner.....

And in this part I was really confused

The answers follow this pattern:
2 divided by 7 leaves remainder 2................

From Gmatclub test

bagrettin · Accepted Answer

Usually all problems which deal with big numbers and their divisibility involve some type of sequences.
See:
 2^1=2  The remainder is 2
 2^2=4  The remainder is 4
 2^3=8  The remainder is 1
 2^4=16  The remainder is 2
 2^5=32  The remainder is 4
 2^6=64  The remainder is 1
 2^7=128  The remainder is 2
...
If you could see, divisibility by 7 is connected with divisibility of the power by 3. If the power of 2 has the remainder 2 when it is divided by 3, then the remainder from division  2^x  by 7 is 4.

Since 200 has the remainder of 2 after division by 3, the answer is (D)

If you are frustrated about the remainder of the number which is fewer than 7, remember that the remainder is an integer r, where x=7*n+r, and n is also integer.
So, for example 2=0*7+2, so the remainder of 2 when it is divided by 7 is 2.

Bowtie · Answer

answer is D. this is very similar to the 32^32^32 divided by 7 question.

kostyan5 · Answer

You just follow the pattern in remainders as increasing powers of 2 are divided by 7.

In this case it's (2,4,1,2,4,1,....)

HD05 · Answer

The pattern of such questions is rather easy.
There is a whole lot more to these remainder type of questions. Format of such basic questions follow,
are a cyclical pattern.

For example in this question.
2^1 = 2
2^2 = 4
2^3 = 8
2^4 =16
2^5 =32

For such questions,remember one thing,try to get a difference of 1 between numerator and the denominator.

Here the answer is a clear 2.

TGC · Answer

Question without an OA:

REM(2^200/7)

By using binomial thrm:

REM ( 2^198 *2^2)/7

REM   /7

REM

Hence , 4

Asifpirlo · Answer

..............
..............
(2^200)/7
make closest to the denominator. the closest value of 2^something = 8
so, (2^3)66 . 2^2 (bring cube then balancing it, because 200 is not divided by 3)
8^66 . 2^2
= (7+1)^66 . 2^2
just consider the last number of the entire sequence that is (1)^66 . 2^2 = 4 , this is the remainder ,you don't have to divide it by 7. but if you have any negative value then plus that with the divisor.
suppose you got (7-1)^66 . 2^2 = (-1)^66 . 2^2 = -4. Then add it with the divisor you have. -4+7 = 3 is the remainder.

Bunuel · Answer

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-remainder-when-you-divide-2-200-by-140821.html

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards