Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 17:39 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # What is the remainder when 1271 * 1275 * 1277 *1285 is divid

Author Message
TAGS:

### Hide Tags

Intern  Joined: 01 Aug 2006
Posts: 33
What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

2
12 00:00

Difficulty:   65% (hard)

Question Stats: 57% (01:56) correct 43% (01:51) wrong based on 364 sessions

### HideShow timer Statistics What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?

(A) 0
(B) 1
(C) 11
(D) 9
(E) 7
Director  Joined: 14 Dec 2012
Posts: 736
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34 GPA: 3.6
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

4
4
shreyas wrote:
What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?
(A) 0
(B) 1
(C) 11
(D) 9
(E) 7

OA should be D

In this type of questions we can separately divide each number with 12 and get remainder and then multiply remainder then divide by 12 ...the remainder which comes now will be the answer.
1271 div by 12==>remainder = 11
1275 div by 12 ==>rema = 3
1285 div by 12 ==> remain = 1
1277 div by 12 ==> rema = 5

now multiply the remainder = 165
165 div by 12 rem = 9

hence D
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 56304
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

3
1
shreyas wrote:
What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?
(A) 0
(B) 1
(C) 11
(D) 9
(E) 7

1271*1275*1277*1285 = (1272 - 1)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)

Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-1)(3)(-7)(1) = 21. Thus the question becomes: what is the remainder upon division of 21 by 12? The answer to this question is 9.

_________________
Manager  B
Joined: 14 Jan 2013
Posts: 133
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

blueseas wrote:
shreyas wrote:
What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?
(A) 0
(B) 1
(C) 11
(D) 9
(E) 7

OA should be D

In this type of questions we can separately divide each number with 12 and get remainder and then multiply remainder then divide by 12 ...the remainder which comes now will be the answer.
1271 div by 12==>remainder = 11
1275 div by 12 ==>rema = 3
1285 div by 12 ==> remain = 1
1277 div by 12 ==> rema = 5

now multiply the remainder = 165
165 div by 12 rem = 9

hence D

This is nice solution.... Does it hold true for all cases?
Director  Joined: 14 Dec 2012
Posts: 736
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34 GPA: 3.6
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

Mountain14 wrote:
blueseas wrote:
shreyas wrote:
What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?
(A) 0
(B) 1
(C) 11
(D) 9
(E) 7

OA should be D

In this type of questions we can separately divide each number with 12 and get remainder and then multiply remainder then divide by 12 ...the remainder which comes now will be the answer.
1271 div by 12==>remainder = 11
1275 div by 12 ==>rema = 3
1285 div by 12 ==> remain = 1
1277 div by 12 ==> rema = 5

now multiply the remainder = 165
165 div by 12 rem = 9

hence D

This is nice solution.... Does it hold true for all cases?

Yes this will hold true always.
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment
Intern  Joined: 21 Jan 2012
Posts: 4
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

I have a doubt. 1275 is divisible by 3, cannot we reduce question to 1271*405*1277*1285 divided by 4 ?
Math Expert V
Joined: 02 Sep 2009
Posts: 56304
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

singage wrote:
I have a doubt. 1275 is divisible by 3, cannot we reduce question to 1271*405*1277*1285 divided by 4 ?

No, we cannot do that. For example, 6 divided by 15 yields the remainder of 6 but if you reduce by 3, then the remainder of 2 divided by 5 yields the remainder of 2. As you can see the remainders are not the same.
_________________
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1787
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

1
blueseas wrote:
shreyas wrote:
What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?
(A) 0
(B) 1
(C) 11
(D) 9
(E) 7

OA should be D

In this type of questions we can separately divide each number with 12 and get remainder and then multiply remainder then divide by 12 ...the remainder which comes now will be the answer.
1271 div by 12==>remainder = 11
1275 div by 12 ==>rema = 3
1285 div by 12 ==> remain = 1
1277 div by 12 ==> rema = 5

now multiply the remainder = 165
165 div by 12 rem = 9

hence D

Did in the same way, with slight difference:

1271 = 1200 + 71 ; similar for other numbers as well

So just ignored 1200 as its divisible by 12 & worked upon only the last 2 digits

71
75
77
85

Result obtained is the same
_________________
Kindly press "+1 Kudos" to appreciate Intern  Affiliations: ScoreBoost
Joined: 07 Sep 2012
Posts: 13
Location: India
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

1
When a number is expressed as a product of numbers, the remainder is the product of remainders.

Lets say : $$N = a * b * c$$

Then $$R (\frac{N}{D})$$ = $$R (\frac{a}{D}) * R (\frac{b}{D}) * R (\frac{c}{D})$$

where : $$R (\frac{N}{D})$$ represents remainder N leaves when divided by D and so on.

Eg : Lets say 500 is expressed as the product of 3 numbers i.e 500 = 5*10*10 , and we are looking for the remainder when divided by 3.

$$R (\frac{500}{3}) = 2$$
$$R (\frac{5}{3}) = 2$$
$$R (\frac{10}{3}) = 1$$
$$R (\frac{10}{3}) = 1$$

We can clearly see that : $$R = R_1 * R_2 * R_3$$

Also when a number is expressed as the sum of numbers, the remainder is the sum of individual remainders:

If $$N = a + b + c$$, then

$$R (\frac{N}{D})$$ = $$R (\frac{a}{D}) + R (\frac{b}{D}) + R (\frac{c}{D})$$

Eg : Let 100 be expressed as the sum of numbers i.e 100 = 25 + 25 + 50

$$R (\frac{100}{3}) = 2$$
$$R (\frac{25}{3}) = 1$$
$$R (\frac{25}{3}) = 1$$
$$R (\frac{50}{3}) = 2$$

In this case the sum of remainders is equal to 4. Since we are looking for remainder when divided by 3, remainder of 4 means remainder of 1.

Cheers       Hope this helps .
_________________
Quant Instructor
ScoreBoost
Bangalore, India
Manager  Joined: 28 Apr 2014
Posts: 205
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

Bunuel wrote:
singage wrote:
I have a doubt. 1275 is divisible by 3, cannot we reduce question to 1271*405*1277*1285 divided by 4 ?

No, we cannot do that. For example, 6 divided by 15 yields the remainder of 6 but if you reduce by 3, then the remainder of 2 divided by 5 yields the remainder of 2. As you can see the remainders are not the same.

Not clear on this point Bunuel. I think the OP is saying that the question can be reduced to finding the Nr when 1271*405*1277*1285 / 4.

Ok I get it . So if we know that there is going to be a remainder , we can not reduce it like this. Would this be a correct understanding ?
Math Expert V
Joined: 02 Sep 2009
Posts: 56304
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

himanshujovi wrote:
Bunuel wrote:
singage wrote:
I have a doubt. 1275 is divisible by 3, cannot we reduce question to 1271*405*1277*1285 divided by 4 ?

No, we cannot do that. For example, 6 divided by 15 yields the remainder of 6 but if you reduce by 3, then the remainder of 2 divided by 5 yields the remainder of 2. As you can see the remainders are not the same.

Not clear on this point Bunuel. I think the OP is saying that the question can be reduced to finding the Nr when 1271*405*1277*1285 / 4.

Ok I get it . So if we know that there is going to be a remainder , we can not reduce it like this. Would this be a correct understanding ?

What I meant is the remainder of 21 divided by 15, won't be the same as the remainder of 21/3=7 divided by 15/3=5.
_________________
Manager  Joined: 22 Aug 2013
Posts: 76
Schools: ISB '15
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

Bunuel wrote:
shreyas wrote:
What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?
(A) 0
(B) 1
(C) 11
(D) 9
(E) 7

1271*1275*1277*1285 = (1272 - 1)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)

Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-1)(3)(-7)(1) = 21. Thus the question becomes: what is the remainder upon division of 21 by 12? The answer to this question is 9.

Hi Bunuel,
Any specific rule when doing this. (1272 - 1)(1272 + 3)(1284 - 7)(1284 + 1)
Because I can also write it as
(1272 - 1)(1272 + 3)(1272 + 5)(1284 + 1) which leads to incorrect answer.

Or do we need to make sure that product is +.
_________________
Veritas Prep - 650
MGMAT 1 590
MGMAT 2 640 (V48/Q31)

Math Expert V
Joined: 02 Sep 2009
Posts: 56304
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

seabhi wrote:
Bunuel wrote:
shreyas wrote:
What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?
(A) 0
(B) 1
(C) 11
(D) 9
(E) 7

1271*1275*1277*1285 = (1272 - 1)(1272 + 3)(1284 - 7)(1284 + 1) = (multiple of 12 - 1)(multiple of 12 + 3)(multiple of 12 - 7)(multiple of 12 + 1)

Now, if we expand this expression all terms but the last one will have a multiple of 12 in them, thus will leave no remainder upon division by 12, the last term will be (-1)(3)(-7)(1) = 21. Thus the question becomes: what is the remainder upon division of 21 by 12? The answer to this question is 9.

Hi Bunuel,
Any specific rule when doing this. (1272 - 1)(1272 + 3)(1284 - 7)(1284 + 1)
Because I can also write it as
(1272 - 1)(1272 + 3)(1272 + 5)(1284 + 1) which leads to incorrect answer.

Or do we need to make sure that product is +.

It would be easier if the last term is positive, though this approach would also give you the correct answer: the remainder when dividing -15 by 12 is also 9: -15=-2*12+9.

Check similar question here: when-51-25-is-divided-by-13-the-remainder-obtained-is-130220.html

Hope it helps.
_________________
Intern  Joined: 26 Feb 2014
Posts: 2
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

I tried doing this exercise the following way but it seems I do not get the same result.. So obviously I am doing something wrong. Could somebody possible tell me why this is not correct?

I just used the last 2 digits of each number as these would be the most important

So: 71*75*77*85.

The last 2 digits are 25, this means that 12 still goes twice into this number. With 1 remaining.
Is this exercise simply not solved by doing this or am I doing it completely wrong?
Current Student B
Status: DONE!
Joined: 05 Sep 2016
Posts: 368
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

Fair question. Tedious, but fair.

You'll need to divide each number separately by 12 and then multiply the remainders together and divide by 12 again.

1271/12 = 105 R 11
1275/12 = 106 R 3
1277/12 = 106 R 5
1285/12 = 107 R 1

(11x15)/12 = 13 R 9

Thus D is the correct answer.
Senior Manager  B
Joined: 13 Oct 2016
Posts: 363
GPA: 3.98
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

1
$$1271*1275*1277*1285$$

Because hundreds and thousands digits (12) bring no remainder upon division by 12 we need only to pay attention to

$$71*75*77*85$$

$$71 = -1(mod 12), 75 = 3 (mod 12), 77 = 5 mod (12), 85 = 1 (mod 12)$$

And we have:

$$(-1)*3*5*1 = -15 = -3 (mod 12) = 9 (mod 12)$$

Remainder is 9.
Board of Directors P
Joined: 17 Jul 2014
Posts: 2539
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

1
shreyas wrote:
What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?

(A) 0
(B) 1
(C) 11
(D) 9
(E) 7

my approach:
(1260 + 11) * (1272 +3) * (1272 + 5) * (1284 +1)
11*3*5*1 = 165
165/12 = quotient is 13, and remainder 9.
_________________
Manhattan Prep Instructor G
Joined: 04 Dec 2015
Posts: 756
GMAT 1: 790 Q51 V49 GRE 1: Q170 V170 Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

1
shreyas wrote:
What is the remainder when 1271 * 1275 * 1277 *1285 is divided by 12?

(A) 0
(B) 1
(C) 11
(D) 9
(E) 7

Here's a sneaky approach.

The product isn't even. So, when you divide it by 12, it can't have an even remainder (because 12 is even, so something with an even remainder would have to have been even to begin with.)

The product is a multiple of 3, because 1275 is a multiple of 3. So, when you divide it by 12, the remainder will be a multiple of 3. (That's because 12 is a multiple of 3. In order for a number to be divisible by 3, and also be of the form 12x + remainder, the remainder also has to be divisible by 3. If it wasn't, then the whole thing wouldn't be divisible by 3, either.)

The only possible remainders, then, are 3 and 9.

Only one of those - 9 - is in the answer choices. The answer is (D).
_________________ Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!
Non-Human User Joined: 09 Sep 2013
Posts: 11719
Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid  [#permalink]

### Show Tags

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.
_________________ Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid   [#permalink] 24 Sep 2018, 02:12
Display posts from previous: Sort by

# What is the remainder when 1271 * 1275 * 1277 *1285 is divid  