Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43916

What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
16 Apr 2015, 04:03
Question Stats:
58% (01:37) correct 42% (01:19) wrong based on 256 sessions
HideShow timer Statistics



Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 359

Re: What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
16 Apr 2015, 04:24
5
This post received KUDOS
5
This post was BOOKMARKED
Bunuel wrote: What is the remainder when 1555 * 1557 * 1559 is divided by 13?
(A) 0 (B) 2 (C) 4 (D) 9 (E) 11
Kudos for a correct solution. 1555/13>Remainder=8 1557/13>Remainder=10 1559/13>Remainder=12 8*10*12=960/13>Remainder=11 Answer: E



Manager
Joined: 15 May 2014
Posts: 65

What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
18 Apr 2015, 02:18
2
This post received KUDOS
1
This post was BOOKMARKED
\(\frac {1555\,*\,1557\,*\,1559}{13} = \frac {(15605) *(15603)*(15601)}{13}\) \(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\) \(=\) \((multiples\,of\,13\)) + \((5*3*1)\) \(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\) \(=\) \((multiples\,of\,13\))  \(15\)
here the last term \(15\) is a negative number \(\frac{15}{13}\,=\,quotient\,*13\,+\,remainder\) here remainder should be \(0\,\leq\,remainder\,<\,13\) So \(15\,=\,13\,(2)\,+\,11\) Remainder \(= 11\)
Answer E
Last edited by sudh on 18 Apr 2015, 20:07, edited 3 times in total.



Senior Manager
Joined: 27 Dec 2013
Posts: 298

Re: What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
18 Apr 2015, 07:38
I liked the way you solved the question. I did the same except that I elaborated the solution and ended up with some big numbers +960. Reached the same place and had the same answer 11. Everyday is learning . Nice work. AmoyV wrote: Bunuel wrote: What is the remainder when 1555 * 1557 * 1559 is divided by 13?
(A) 0 (B) 2 (C) 4 (D) 9 (E) 11
Kudos for a correct solution. 1555/13>Remainder=8 1557/13>Remainder=10 1559/13>Remainder=12 8*10*12=960/13>Remainder=11 Answer: E
_________________
Kudos to you, for helping me with some KUDOS.



Manager
Joined: 17 Mar 2015
Posts: 121

What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
18 Apr 2015, 09:36
sudh wrote: \(\frac {1555\,*\,1557\,*\,1559}{13} = \frac {(15605) *(15603)*(15601)}{13}\) \(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\) \(=\) \((multiples\,of\,13\)) + \((5*3*1)\) \(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\) \(=\) \((multiples\,of\,13\))  \(15\)
here the last term \(15\) is a negative number So \(13 \,\geq remainder \,\leq 26\) Since remainder should be a positive less than divisor \(26\,+\,11\,=\,15\) Remainder \(= 11\)
Answer E I am abit confused with the way you found an answer, maybe I'm not good at remainders but imo you can transform your expression like this to make it "easier", I guess: \((multiples\,of\,13\))  \(15\) = \((multiples\,of\,13\))  \(13\)  \(2\) = \((multiples\,of\,13\))  \(13\)  \(13\) + \(11\), which lets us explicitly figure out that the ending result of division is \("integer"  2 + 11/13\) which pretty much tells us that the remainder is 11. Ty for the solution though, pretty neat.



Manager
Joined: 15 May 2014
Posts: 65

What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
18 Apr 2015, 19:04
Zhenek wrote: sudh wrote: \(\frac {1555\,*\,1557\,*\,1559}{13} = \frac {(15605) *(15603)*(15601)}{13}\) \(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\) \(=\) \((multiples\,of\,13\)) + \((5*3*1)\) \(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\) \(=\) \((multiples\,of\,13\))  \(15\)
here the last term \(15\) is a negative number So \(13 \,\leq remainder \,\leq 26\) Since remainder should be a positive less than divisor \(26\,+\,11\,=\,15\) Remainder \(= 11\)
Answer E I am abit confused with the way you found an answer, maybe I'm not good at remainders but imo you can transform your expression like this to make it "easier", I guess: \((multiples\,of\,13\))  \(15\) = \((multiples\,of\,13\))  \(13\)  \(2\) = \((multiples\,of\,13\))  \(13\)  \(13\) + \(11\), which lets us explicitly figure out that the ending result of division is \("integer"  2 + 11/13\) which pretty much tells us that the remainder is 11. Ty for the solution though, pretty neat. Sorry for the confusion \(\frac{15}{13}\,=\,quotient\,*13\,+remainder\) here remainder should be \(0\,\leq\,remainder\,<\,13\) So \(15\,=\,13\,(2)\,+\,11\) Or we could just borrow \((2*13)\,=\,26\) from the \((multiples\,of\,13\)) and add them with \(15\), giving us the remainder \(11\)



Math Expert
Joined: 02 Sep 2009
Posts: 43916

Re: What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
20 Apr 2015, 04:30
2
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
Bunuel wrote: What is the remainder when 1555 * 1557 * 1559 is divided by 13?
(A) 0 (B) 2 (C) 4 (D) 9 (E) 11
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTIONSince it is a GMAT question (a question for which we will have no calculator), multiplying the 3 numbers and then dividing by 13 is absolutely out of question! There has to be another method. Say n = 1555 * 1557 * 1559 When we divide 1555 by 13, we get a quotient of 119 (irrelevant to our question) and remainder of 8. So the remainder when we divide 1557 by 13 will be 8+2 = 10 (since 1557 is 2 more than 1555) and when we divide 1559 by 13, the remainder will be 10+2 = 12 (since 1559 is 2 more than 1557). So n = (13*119 + 8)*(13*119 + 10)*(13*119 + 12) (you can choose to ignore the quotient and just write it as ‘a’ since it is irrelevant to our discussion) So we need to find the remainder when n is divided by 13. Note that when we multiply these factors, all terms we obtain will have 13 in them except the last term which is obtained by multiplying the constants together i.e. 8*10*12. Since all other terms are multiples of 13, we can say that n is 8*10*12 (= 960) more than a multiple of 13. There are many more groups of 13 balls that we can form out of 960. 960 divided by 13 gives a remainder of 11. Hence n is actually 11 more than a multiple of 13. We did not use the negative remainders concept here. Let’s see how using negative remainders makes our calculations easier here. The remainder of 8, 10 and 12 imply that the negative remainders are 5, 3 and 1 respectively. Now n = (13a – 5) * (13a – 3) * (13a – 1) The last term in this case is 5*3*1 = 15 This means that n is 15 less than a multiple of 13 i.e. actually 2 less than a multiple of 13 because when you go back 13 steps, you get another multiple of 13. This gives us a negative remainder of 2 which means the positive remainder in this case will be 11.
_________________
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: 18 Aug 2015
Posts: 8

Re: What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
25 Oct 2015, 09:57
Find out the remainders for individual terms: 8*10*12/13 = 80*12/13 = 2*12/13 = 24/13 = 11



Board of Directors
Joined: 17 Jul 2014
Posts: 2736
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
05 Oct 2016, 06:43
Bunuel wrote: What is the remainder when 1555 * 1557 * 1559 is divided by 13?
(A) 0 (B) 2 (C) 4 (D) 9 (E) 11
Kudos for a correct solution. i tried to figure out which option is the fastest... then came up with this one... 13 => 1300 is divisible by 13 1430 is divisible by 3 1560 is divisible by 3. 1555 = 15605, which means, if divided by 13, we'll have a remainder of 8 1557 = 15603, meaning that if divided by 13, we'll have a remainder of 10 1559 = 15601, meaning that if divided by 13, we'll have a remainder of 12. now..8*10*12 = or 80*(10+2) = 800+160=960. 960/13 = 73, with a remainder of 11. answer is E.



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3326
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
25 Jan 2018, 07:11
Bunuel wrote: What is the remainder when 1555 * 1557 * 1559 is divided by 13?
(A) 0 (B) 2 (C) 4 (D) 9 (E) 11
Kudos for a correct solution. \(\frac{1555}{13}\) = Remainder \(8\) \(\frac{1557}{13}\) = Remainder \(10\) \(\frac{1559}{13}\) = Remainder \(12\) Finally we have \(\frac{8*10*12}{13}\) = Remainder 11, Answer will be (E)
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Senior Manager
Joined: 31 Jul 2017
Posts: 305
Location: Malaysia
WE: Consulting (Energy and Utilities)

Re: What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
26 Jan 2018, 21:52
Bunuel wrote: What is the remainder when 1555 * 1557 * 1559 is divided by 13?
(A) 0 (B) 2 (C) 4 (D) 9 (E) 11
Kudos for a correct solution. Solved it this way  Divide each of the number by 13.. You will get 8,10,12 as remainder. Now, multiply the remainders and again Divide by 13.You will get 11 as remainder.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



SVP
Joined: 08 Jul 2010
Posts: 1960
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
27 Jan 2018, 00:43
Bunuel wrote: What is the remainder when 1555 * 1557 * 1559 is divided by 13?
(A) 0 (B) 2 (C) 4 (D) 9 (E) 11
Kudos for a correct solution. R(1555 * 1557 * 1559/3) Remainder when 1555 is divided by 13 = 8 Remainder when 1557 is divided by 13 = 10 (or 3) Remainder when 1559 is divided by 13 = 12 (or 1) Remainder [8*(3)*(1)/13] = R (24/13) = 11 Answer: Option E
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016

Re: What is the remainder when 1555 * 1557 * 1559 is divided by 13? [#permalink]
Show Tags
29 Jan 2018, 09:39
Bunuel wrote: What is the remainder when 1555 * 1557 * 1559 is divided by 13?
(A) 0 (B) 2 (C) 4 (D) 9 (E) 11 We don’t have to multiply the numbers and then divide the product by 13. We can divide each factor by 13 first. Notice that when 1555 is divided by 13, the remainder is 8 (with quotient = 119). Thus, the remainders are 10 and 12 when 1557 and 1559 are divided by 13, respectively. Now we multiply these remainders and divide the product by 13. Since 8 x 10 x 12 = 960 and when 960 is divided by 13, the remainder is 11 (with quotient = 73). Thus, the remainder, when 1555 x 1557 x 1559 is divided by 13, must also be 11. Answer: E
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: What is the remainder when 1555 * 1557 * 1559 is divided by 13?
[#permalink]
29 Jan 2018, 09:39






