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
07 Feb 2014, 10:49
Question Stats:
56% (01:57) correct 44% (01:50) wrong based on 344 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
Official Answer and Stats are available only to registered users. Register/ Login.




Director
Joined: 14 Dec 2012
Posts: 771
Location: India
Concentration: General Management, Operations
GPA: 3.6

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
07 Feb 2014, 11:04
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...
GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabularylistforgmatreadingcomprehension155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmatanalyticalwritingassessment : http://www.youtube.com/watch?v=APt9ITygGss




Math Expert
Joined: 02 Sep 2009
Posts: 49911

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
07 Feb 2014, 11:01



Manager
Joined: 14 Jan 2013
Posts: 145
Concentration: Strategy, Technology
GMAT Date: 08012013
GPA: 3.7
WE: Consulting (Consulting)

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
08 Feb 2014, 02:49
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?
_________________
"Where are my Kudos" ............ Good Question = kudos
"Start enjoying all phases" & all Sections
__________________________________________________________________ http://gmatclub.com/forum/collectionofarticlesoncriticalreasoning159959.html
http://gmatclub.com/forum/percentages700800levelquestions130588.html
http://gmatclub.com/forum/700to800levelquantquestionwithdetailsoluition143321.html



Director
Joined: 14 Dec 2012
Posts: 771
Location: India
Concentration: General Management, Operations
GPA: 3.6

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
08 Feb 2014, 02:53
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...
GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabularylistforgmatreadingcomprehension155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmatanalyticalwritingassessment : http://www.youtube.com/watch?v=APt9ITygGss



Intern
Joined: 21 Jan 2012
Posts: 4

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
03 Apr 2014, 23:30
I have a doubt. 1275 is divisible by 3, cannot we reduce question to 1271*405*1277*1285 divided by 4 ?



Math Expert
Joined: 02 Sep 2009
Posts: 49911

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
04 Apr 2014, 01:38



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
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
04 Apr 2014, 03:24
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: 14
Location: India

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
04 Apr 2014, 05:52
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: 226

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
01 May 2014, 00:09
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
Joined: 02 Sep 2009
Posts: 49911

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
01 May 2014, 00:18
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 22 Aug 2013
Posts: 80

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
01 May 2014, 22:08
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. Answer: D. 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)
Please help the community by giving Kudos.



Math Expert
Joined: 02 Sep 2009
Posts: 49911

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
02 May 2014, 02:14
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. Answer: D. 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: when5125isdividedby13theremainderobtainedis130220.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 26 Feb 2014
Posts: 2

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
09 May 2014, 10:01
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
Status: DONE!
Joined: 05 Sep 2016
Posts: 384

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
17 Nov 2016, 12:41
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
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
18 Nov 2016, 01:42
\(1271*1275*1277*1285\)
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
Joined: 17 Jul 2014
Posts: 2653
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
21 Nov 2016, 09:36
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. answer is D, 9.



Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 629

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
21 Nov 2016, 18:08
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).
_________________



NonHuman User
Joined: 09 Sep 2013
Posts: 8410

Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid
[#permalink]
Show Tags
24 Sep 2018, 02:12
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: What is the remainder when 1271 * 1275 * 1277 *1285 is divid &nbs
[#permalink]
24 Sep 2018, 02:12






