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Collection of remainder problems in GMAT

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Re: Collection of remainder problems in GMAT [#permalink] New post 04 Dec 2010, 07:58
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Fijisurf wrote:
I guess I am still not sure why in the original post sandipchowdhury wrote:

sandipchowdhury wrote:
St 1: when n is divided by 21 ( 7 and 3) the remainder is an odd number.
But it cannot be 7, 3 or 9 . Hence the possibilities are : 1 and 5.


Why remainder cannot be 7, 3 or 9? (because in case of 28 divided by 21 remainder is 7)


OK. It's just not correct.

When n is divided by 21 the remainder is an odd number --> n=21q+odd=7*3q+odd. Now, this odd number can be ANY odd number from 1 to 19, inclusive.

As for r:
If n=22 then n divided by 21 gives remainder of 1 and n divded by 7 also gives remainder of 1;
If n=24 then n divided by 21 gives remainder of 3 and n divded by 7 also gives remainder of 3;
If n=26 then n divided by 21 gives remainder of 5 and n divded by 7 also gives remainder of 5;
If n=28 then n divided by 21 gives remainder of 7 and n divded by 7 gives remainder of 0.

So r can equal to 1, 3, 5 or 0.

Hope it helps.
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Re: Collection of remainder problems in GMAT [#permalink] New post 13 Dec 2010, 12:43
Sandipchowdhury, thanks for the collection
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Re: Collection of remainder problems in GMAT [#permalink] New post 13 Dec 2010, 19:55
Great thanks guys. Helps out a great deal however I am still a bit confused. Anyone have any suggestions on where to get more help with these types of problems? Thanks in advance.
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Re: Collection of remainder problems in GMAT [#permalink] New post 14 Dec 2010, 00:30
Expert's post
spyguy wrote:
Great thanks guys. Helps out a great deal however I am still a bit confused. Anyone have any suggestions on where to get more help with these types of problems? Thanks in advance.


Remainders:
Theory: compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html

PS questions:
remainder-101074.html
remainder-problem-92629.html
number-properties-question-from-qr-2nd-edition-ps-96030.html
remainder-when-k-96127.html
ps-0-to-50-inclusive-remainder-76984.html
good-problem-90442.html
remainder-of-89470.html
number-system-60282.html
remainder-problem-88102.html

All PS questions on remainders: search.php?search_id=tag&tag_id=199


DS questions:
remainder-problem-101740.html
remainder-101663.html
ds-gcd-of-numbers-101360.html
data-sufficiency-with-remainder-98529.html
sum-of-remainders-99943.html
ds8-93971.html
need-solution-98567.html
gmat-prep-ds-remainder-96366.html
gmat-prep-ds-93364.html
ds-from-gmatprep-96712.html
remainder-problem-divisible-by-86839.html
gmat-prep-2-remainder-86155.html
remainder-94472.html
remainder-problem-84967.html

All DS questions on remainders: search.php?search_id=tag&tag_id=198

Hope it helps.
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Re: Collection of remainder problems in GMAT [#permalink] New post 19 Dec 2010, 19:12
It was a pleasant surprise to see my one year old post still being discussed.
Currently I am studying at Stanford GSB.
If anyone has any question about Stanford GSB, you may contact me chowdhury_sandip@gsb.stanford.edu
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Re: Collection of remainder problems in GMAT [#permalink] New post 31 Dec 2010, 15:56
9.If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?

(1) n is not divisible by 2.

(2) n is not divisible by 3.

ST 1- if n is not divisible by 2, then n is odd, so both (n - 1) and (n + 1) are even. moreover, since every other even number is a multiple of 4, one of those two factors is a multiple of 4. so the product (n - 1)(n + 1) contains one multiple of 2 and one multiple of 4, so it contains at least 2 x 2 x 2 = three 2's in its prime factorization.
But this is not sufficient, because it can be (n-1)*(n+1) can be 2*4 where remainder is 8. it can be 4*6 where the remainder is 0.

ST 2- if n is not divisible by 3, then exactly one of (n - 1) and (n + 1) is divisible by 3, because every third integer is divisible by 3. therefore, the product (n - 1)(n + 1) contains a 3 in its prime factorization.
Just like st 1 this is not sufficient

the overall prime factorization of (n - 1)(n + 1) contains three 2's and a 3.
therefore, it is a multiple of 24.
sufficient

Answer C



What if N=1? 1 is not divisible by 2 or 3.
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Re: Collection of remainder problems in GMAT [#permalink] New post 01 Jan 2011, 02:21
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girishkakkar wrote:
9.If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?

(1) n is not divisible by 2.

(2) n is not divisible by 3.

ST 1- if n is not divisible by 2, then n is odd, so both (n - 1) and (n + 1) are even. moreover, since every other even number is a multiple of 4, one of those two factors is a multiple of 4. so the product (n - 1)(n + 1) contains one multiple of 2 and one multiple of 4, so it contains at least 2 x 2 x 2 = three 2's in its prime factorization.
But this is not sufficient, because it can be (n-1)*(n+1) can be 2*4 where remainder is 8. it can be 4*6 where the remainder is 0.

ST 2- if n is not divisible by 3, then exactly one of (n - 1) and (n + 1) is divisible by 3, because every third integer is divisible by 3. therefore, the product (n - 1)(n + 1) contains a 3 in its prime factorization.
Just like st 1 this is not sufficient

the overall prime factorization of (n - 1)(n + 1) contains three 2's and a 3.
therefore, it is a multiple of 24.
sufficient

Answer C



What if N=1? 1 is not divisible by 2 or 3.


Please discuss specific questions in PS or DS subforums.

This question is discussed here: ds-from-gmatprep-96712.html

As for your question: if n=1 then (n - 1)(n + 1) equals to zero and zero is divisible by every integer (except zero itself) so by 24 too.
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Re: Collection of remainder problems in GMAT [#permalink] New post 03 Jan 2011, 04:44
great collection. Thanks
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Re: Collection of remainder problems in GMAT [#permalink] New post 10 Apr 2011, 10:46
8.If n is a positive integer and r is the remainder when 4 + 7n is divided by 3, what is the value of r ?

(1) n + 1 is divisible by 3.

(2) n > 20

Answer A
st1... n+1 divisible by 3..so n=2,5,8,11......
this gives 4+7n=18,39,60....remainder 0 in each case......
st2) insufficient ....n can have any value

Another approach:
4 + 7n = 4 + 4n + 3n = 4(n+1) + 3n

From statement 1) we can see that 4(n+1) and 3n are divisible by 3 so the remainder is 0.
From statement 2) " insufficient ....n can have any value"
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Re: Collection of remainder problems in GMAT [#permalink] New post 02 Jul 2011, 05:33
awesome set of questions...VERY VERY helpful
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Re: Collection of remainder problems in GMAT [#permalink] New post 07 Aug 2011, 10:31
Quote:
st1. take multiples of 8....divide them by 4...remainder =1 in each case...


but how can it be so? multiples of 8 are also multiples of 4
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Re: Collection of remainder problems in GMAT [#permalink] New post 07 Aug 2011, 18:25
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st1. take multiples of 8....divide them by 4...remainder =1 in each case...


but how can it be so? multiples of 8 are also multiples of 4


hey :wink:

because P has a remainder of 5 after dividing by 8 , so P= (multiple of 8) + 5
take numbers ( 40 + 5 ) / 8 = 5 + ( 5/8 )
divide 45 by 4 the remainder is 1

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Re: Collection of remainder problems in GMAT [#permalink] New post 07 Aug 2011, 21:06
HI,Silver!)
yep, I missed it.
thanks a lot?
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Re: Collection of remainder problems in GMAT [#permalink] New post 07 Aug 2011, 21:15
Galiya wrote:
HI,Silver!)
yep, I missed it.
thanks a lot?
+1


you are welcome :)
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Re: Collection of remainder problems in GMAT [#permalink] New post 07 May 2012, 15:28
[quote="sandipchowdhury"]I have collected these problems on remainder. This type of problem is frequently asked in DS.
Answers are also given.

3.If p is a positive odd integer, what is the remainder when p is divided by 4 ?

(1) When p is divided by 8, the remainder is 5.

(2) p is the sum of the squares of two positive integers.


st1. take multiples of 8....divide them by 4...remainder =1 in each case...


st2. p is odd ,since p is square of 2 integers...one will be even and other odd....now when we divide any even square by 4 v ll gt 0 remainder..and when divide odd square vll get 1 as remainder......so intoatal remainder=1
Ans : D

i don t aggree in your approach it is clearly said that P is not a multiple of 8 Since it has a remainder of 5
So your ST 1 ?

FOR sT2 Why do you consider that the sum of 2 square one is even and one odd
do you considered that it is the sum of the Following square
I am very confused

please help

best regards
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Re: Collection of remainder problems in GMAT [#permalink] New post 07 Jul 2012, 09:52
good stuff, book making for future reference.

Thank you
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Re: Collection of remainder problems in GMAT [#permalink] New post 17 Feb 2014, 18:35
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Re: Collection of remainder problems in GMAT [#permalink] New post 18 Apr 2014, 02:01
8.If n is a positive integer and r is the remainder when 4 + 7n is divided by 3, what is the value of r ?

(1) n + 1 is divisible by 3.

(2) n > 20

My method -
1) n+1 is divisible by 3 =>
7n + 4 can be written as (4n+3n + 4)

now, check for divisibility
[4(n+1) + 3n]/3 => 4(something divisible by 3)/3 + 3n/3

hence, the expression is divisible by 3.

2) n > 20
not sufficient, as different values of r are possible.
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Re: Collection of remainder problems in GMAT [#permalink] New post 18 Apr 2014, 02:10
Expert's post
honey86 wrote:
8.If n is a positive integer and r is the remainder when 4 + 7n is divided by 3, what is the value of r ?

(1) n + 1 is divisible by 3.

(2) n > 20

My method -
1) n+1 is divisible by 3 =>
7n + 4 can be written as (4n+3n + 4)

now, check for divisibility
[4(n+1) + 3n]/3 => 4(something divisible by 3)/3 + 3n/3

hence, the expression is divisible by 3.

2) n > 20
not sufficient, as different values of r are possible.


OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-a-positive-integer-and-r-is-the-remainder-when-93364.html
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: Collection of remainder problems in GMAT   [#permalink] 18 Apr 2014, 02:10
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