GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Sep 2018, 19:48

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

When positive integer k is divided by 1869, the remainder is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
avatar
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 277
When positive integer k is divided by 1869, the remainder is  [#permalink]

Show Tags

New post Updated on: 24 Sep 2013, 14:57
4
8
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

82% (01:03) correct 18% (01:52) wrong based on 250 sessions

HideShow timer Statistics

When positive integer k is divided by 1869, the remainder is 102. What is the remainder when k is divided by 89?

A. 0
B. 1
C. 13
D. 23
E. 51

_________________

I'm the Dumbest of All !!


Originally posted by shrive555 on 10 Dec 2010, 11:20.
Last edited by Bunuel on 24 Sep 2013, 14:57, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: remainder  [#permalink]

Show Tags

New post 10 Dec 2010, 11:54
5
3
shrive555 wrote:
When positive integer k is divided by 1869, the remainder is 102. What is the remainder when k is divided by 89?

0
1
13
23
51

How to approach remainder question ?
THanks


Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, positive integer k is divided by 1869, the remainder is 102 --> \(k=1,869q+102\). Now, 1,869 itself is divisible by 89: 1,869=89*21, so \(k=1,869q+102=89*21q+89+13=89(21q+1)+13\) --> first term (89(21q+1)) is clearly divisible by 89 and the second term 13 divided by 89 yields remainder of 13.

Answer: C.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Manager
Manager
avatar
Joined: 17 Sep 2010
Posts: 185
Concentration: General Management, Finance
GPA: 3.59
WE: Corporate Finance (Entertainment and Sports)
Re: remainder  [#permalink]

Show Tags

New post 10 Dec 2010, 12:10
I did it in a more rudimentary fashion, but bunuel's explanation is outstanding.

Bunuel wrote:
shrive555 wrote:
When positive integer k is divided by 1869, the remainder is 102. What is the remainder when k is divided by 89?

0
1
13
23
51

How to approach remainder question ?
THanks


Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, positive integer k is divided by 1869, the remainder is 102 --> \(k=1,869q+102\). Now, 1,869 itself is divisible by 89: 1,869=89*21, so \(k=1,869q+102=89*21q+89+13=89(21q+1)+13\) --> first term (89(21q+1)) is clearly divisible by 89 and the second term 13 divided by 89 yields remainder of 13.

Answer: C.
Senior Manager
Senior Manager
User avatar
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 357
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross) - Class of 2014
GMAT 1: 730 Q49 V39
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)
Re: remainder  [#permalink]

Show Tags

New post 10 Dec 2010, 12:18
Bunuel wrote:
shrive555 wrote:
When positive integer k is divided by 1869, the remainder is 102. What is the remainder when k is divided by 89?

0
1
13
23
51

How to approach remainder question ?
THanks


Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, positive integer k is divided by 1869, the remainder is 102 --> \(k=1,869q+102\). Now, 1,869 itself is divisible by 89: 1,869=89*21, so \(k=1,869q+102=89*21q+89+13=89(21q+1)+13\) --> first term (89(21q+1)) is clearly divisible by 89 and the second term 13 divided by 89 yields remainder of 13.

Answer: C.



This is a great explanation.

Thanks
_________________

Go Blue!

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
avatar
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 277
Re: remainder  [#permalink]

Show Tags

New post 10 Dec 2010, 12:38
Thanks B.
one more question, If remainder is Zero or if we have any algebraic expression. The concept would be the same ?
For example :
If x is a positive integer and x+2 is divisible by 10, what is the remainder when x2+4x+9 is divided by 10?
_________________

I'm the Dumbest of All !!

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
Re: remainder  [#permalink]

Show Tags

New post 10 Dec 2010, 13:26
2
3
shrive555 wrote:
Thanks B.
one more question, If remainder is Zero or if we have any algebraic expression. The concept would be the same ?
For example :
If x is a positive integer and x+2 is divisible by 10, what is the remainder when x2+4x+9 is divided by 10?


x+2 is divisible by 10 --> \(x+2=10n\) for some positive integer \(n\)

\(x^2+4x+9=(x+2)^2+5=(10n)^2+5\) so this expression divided by 10 yields remainder of 5.

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

PS:
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

DS:
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

Hope 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?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
avatar
Joined: 03 Aug 2012
Posts: 807
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Premium Member
Re: remainder  [#permalink]

Show Tags

New post 24 Sep 2013, 09:01
2
K= 1869A +102

K/89 => {1869A + 102}/89

Since 1869 is perfectly divisible by 89

REM(K/89) = REM (102/89) = 13
_________________

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

Manager
Manager
avatar
Joined: 01 Feb 2012
Posts: 86
Re: When positive integer k is divided by 1869, the remainder is  [#permalink]

Show Tags

New post 01 Jan 2015, 11:06
Bunuel wrote:
shrive555 wrote:
When positive integer k is divided by 1869, the remainder is 102. What is the remainder when k is divided by 89?

0
1
13
23
51

How to approach remainder question ?
THanks


Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, positive integer k is divided by 1869, the remainder is 102 --> \(k=1,869q+102\). Now, 1,869 itself is divisible by 89: 1,869=89*21, so \(k=1,869q+102=89*21q+89+13=89(21q+1)+13\) --> first term (89(21q+1)) is clearly divisible by 89 and the second term 13 divided by 89 yields remainder of 13.

Answer: C.



Hi Bunuel,

Thanks for the wonderful solution to the problem however how to find out that 89 will go into 1869 at 21 times......I mean while trying to solve this question I thought if 1869 is divisible by 89 however after trying 4-5 multiples of 89 I gave up....is there a way to be able to see that? Thanks in advance.


Regards
Manager
Manager
User avatar
S
Joined: 13 Oct 2013
Posts: 131
Concentration: Strategy, Entrepreneurship
GMAT ToolKit User Premium Member CAT Tests
Re: When positive integer k is divided by 1869, the remainder is  [#permalink]

Show Tags

New post 01 Jan 2015, 12:12
1
how to find out that 89 will go into 1869 at 21 times


if you just divide 1869 with 89 , you will get 21



tirbah wrote:
Bunuel wrote:
shrive555 wrote:
When positive integer k is divided by 1869, the remainder is 102. What is the remainder when k is divided by 89?

0
1
13
23
51

How to approach remainder question ?
THanks


Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, positive integer k is divided by 1869, the remainder is 102 --> \(k=1,869q+102\). Now, 1,869 itself is divisible by 89: 1,869=89*21, so \(k=1,869q+102=89*21q+89+13=89(21q+1)+13\) --> first term (89(21q+1)) is clearly divisible by 89 and the second term 13 divided by 89 yields remainder of 13.

Answer: C.



Hi Bunuel,

Thanks for the wonderful solution to the problem however how to find out that 89 will go into 1869 at 21 times......I mean while trying to solve this question I thought if 1869 is divisible by 89 however after trying 4-5 multiples of 89 I gave up....is there a way to be able to see that? Thanks in advance.


Regards

_________________

---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way :)

Manager
Manager
avatar
Joined: 01 Feb 2012
Posts: 86
Re: When positive integer k is divided by 1869, the remainder is  [#permalink]

Show Tags

New post 01 Jan 2015, 23:15
Hi Sunita123,
Thanks for replying. Actually I have come across such situations many a times when I am not able to figure out that a particular no. is a factor of a another particular number. In order to find factors of a particular number I first try to see if it is divisible by 2,3,5,6,7 etc as checking divisibility with them is easier and once a number is not divisible by any of these I do not know what to do.
for example there is another question -

Question: If K is a positive integer, is (2^k) - 1 a prime number?
Statement 1: K is a prime number
Statement 2: K has exactly two positive divisors.

Here basically both statements convey the same thing so answer is either E or D.

I tried some prime number values for K to see if (2^k) - 1 is prime or not.....all values 3,5,7 gives the value of (2^k) - 1 as prime no. and when I checked with K=11 then -

2^11 - 1 = 2047....

I checked the divisibility of 2047 with all the numbers e.g. 2,3,5,7,13,19 etc and thought that it must be a prime number and as all the prime values of K resulted in prime number for the value of (2^k) - 1 I thought that answer should be D but the correct answer is E and it came out that 2047 is not a prime number and is divisible by 23 in 89 times. (2047 = 23*89)

So what I was trying to ask is - and now in the below question I missed to see that 1869 is 21*89. So I am not sure if something is wrong with my approach or if I am doing something wrong somewhere?

Please let me know if you have another perspective to deal with such questions. Many thanks.


Regards



sunita123 wrote:
how to find out that 89 will go into 1869 at 21 times


if you just divide 1869 with 89 , you will get 21



tirbah wrote:
Bunuel wrote:

Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, positive integer k is divided by 1869, the remainder is 102 --> \(k=1,869q+102\). Now, 1,869 itself is divisible by 89: 1,869=89*21, so \(k=1,869q+102=89*21q+89+13=89(21q+1)+13\) --> first term (89(21q+1)) is clearly divisible by 89 and the second term 13 divided by 89 yields remainder of 13.

Answer: C.



Hi Bunuel,

Thanks for the wonderful solution to the problem however how to find out that 89 will go into 1869 at 21 times......I mean while trying to solve this question I thought if 1869 is divisible by 89 however after trying 4-5 multiples of 89 I gave up....is there a way to be able to see that? Thanks in advance.


Regards
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India
Re: When positive integer k is divided by 1869, the remainder is  [#permalink]

Show Tags

New post 02 Jan 2015, 00:31
1
tirbah wrote:
Hi Sunita123,
Thanks for replying. Actually I have come across such situations many a times when I am not able to figure out that a particular no. is a factor of a another particular number. In order to find factors of a particular number I first try to see if it is divisible by 2,3,5,6,7 etc as checking divisibility with them is easier and once a number is not divisible by any of these I do not know what to do.
for example there is another question -

So what I was trying to ask is - and now in the below question I missed to see that 1869 is 21*89. So I am not sure if something is wrong with my approach or if I am doing something wrong somewhere?

Please let me know if you have another perspective to deal with such questions. Many thanks.



Right! So use the same approach:

1869
Not divisible by 2.
Divisible by 3 since 1+8+6+9 = 24 which is divisible by 3.
Divide by 3: 1869 = 3*623
Now 623 is not divisible by 2, 3 and 5. Try dividing by 7.
623 = 7*89

So 1869 = 3*7*89
89 is a prime number so no more factors are possible
1869 = 21*89

Also, another way - faster I might add - would be to start with 89 and see if it is a factor. Your approach depends on whether 89 is a factor of 1869 or not.
Divide 1869 by 89. You get 21.
So you know 1869 = 21*89
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8150
Premium Member
Re: When positive integer k is divided by 1869, the remainder is  [#permalink]

Show Tags

New post 24 Aug 2018, 00:34
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

GMAT Club Bot
Re: When positive integer k is divided by 1869, the remainder is &nbs [#permalink] 24 Aug 2018, 00:34
Display posts from previous: Sort by

When positive integer k is divided by 1869, the remainder is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.