It is currently 21 Oct 2017, 03:37

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Moderator
Joined: 01 Sep 2010
Posts: 3356

Kudos [?]: 9068 [1], given: 1154

What is the remainder when you divide 2^200 by 7? [#permalink]

### Show Tags

02 Oct 2011, 11:50
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

54% (00:44) correct 46% (01:04) wrong based on 166 sessions

### HideShow timer Statistics

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

2 divided by 7 leaves remainder 2................

From Gmatclub test

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

_________________

Kudos [?]: 9068 [1], given: 1154

Manager
Joined: 03 Mar 2011
Posts: 88

Kudos [?]: 163 [6], given: 12

Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Re: how deal with this problem ??? [#permalink]

### Show Tags

02 Oct 2011, 12:11
6
KUDOS
1
This post was
BOOKMARKED
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.
_________________

If my post is useful for you not be ashamed to KUDO me!
Let kudo each other!

Kudos [?]: 163 [6], given: 12

Manager
Joined: 08 Sep 2011
Posts: 68

Kudos [?]: 5 [0], given: 5

Concentration: Finance, Strategy
Re: how deal with this problem ??? [#permalink]

### Show Tags

16 Nov 2011, 15:17
answer is D. this is very similar to the 32^32^32 divided by 7 question.

Kudos [?]: 5 [0], given: 5

Manager
Joined: 29 Oct 2011
Posts: 180

Kudos [?]: 158 [0], given: 19

Concentration: General Management, Technology
Schools: Sloan '16 (D)
GMAT 1: 760 Q49 V44
GPA: 3.76
Re: how deal with this problem ??? [#permalink]

### Show Tags

17 Nov 2011, 07:07
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,....)

Kudos [?]: 158 [0], given: 19

Intern
Status: Stay Hungry, Stay Foolish.
Joined: 05 Sep 2011
Posts: 40

Kudos [?]: 9 [0], given: 6

Location: India
Concentration: Marketing, Social Entrepreneurship
Re: how deal with this problem ??? [#permalink]

### Show Tags

17 Nov 2011, 09:46
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.

Kudos [?]: 9 [0], given: 6

Director
Joined: 03 Aug 2012
Posts: 899

Kudos [?]: 887 [0], given: 322

Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Re: how deal with this problem ??? [#permalink]

### Show Tags

09 Aug 2013, 04:55
Question without an OA:

REM(2^200/7)

By using binomial thrm:

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

REM [ (7+1)^66 * 4] /7

REM[ (1*4)/7]

Hence , 4
_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Kudos [?]: 887 [0], given: 322

Senior Manager
Joined: 10 Jul 2013
Posts: 330

Kudos [?]: 419 [0], given: 102

Re: how deal with this problem ??? [#permalink]

### Show Tags

09 Aug 2013, 05:39
carcass wrote:
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

2 divided by 7 leaves remainder 2................

From Gmatclub test

..............
..............
(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.
_________________

Asif vai.....

Kudos [?]: 419 [0], given: 102

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129078 [0], given: 12194

Re: What is the remainder when you divide 2^200 by 7? [#permalink]

### Show Tags

09 Aug 2013, 11:22
OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-remainder-when-you-divide-2-200-by-140821.html
_________________

Kudos [?]: 129078 [0], given: 12194

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16609

Kudos [?]: 273 [0], given: 0

Re: What is the remainder when you divide 2^200 by 7? [#permalink]

### Show Tags

08 Dec 2015, 12:16
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Re: What is the remainder when you divide 2^200 by 7?   [#permalink] 08 Dec 2015, 12:16
Display posts from previous: Sort by