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

It is currently 23 Oct 2019, 08:37

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

A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58465
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 28 Apr 2016, 01:12
1
32
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (02:22) correct 31% (02:32) wrong based on 369 sessions

HideShow timer Statistics

Most Helpful Expert Reply
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8023
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 28 Apr 2016, 02:21
6
11
Bunuel wrote:
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when nm is divided by 18?

A. 3
B. 5
C. 6
D. 10
E. 12


A good Q..

the equation that can be formed for n peanuts = > n=9x+6..
the equation that can be formed for m peanuts = > m=12y+4..


so mn = (9x+6)(12y+4) where both x and y are integers..
\((9x+6)(12y+4) = 3(3x+2)*4(3y+1) = 12(9xy+6y+3x+2) = 12*3(3xy+2y+x) +12*2.\).
Now 12*3(3xy+2y+x) is Div by 18 hence remainder would be 24 div by 18..
so R =24-18 = 6
C
_________________
General Discussion
SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1873
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 29 Apr 2016, 00:48
10
Bunuel wrote:
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when nm is divided by 18?

A. 3
B. 5
C. 6
D. 10
E. 12


n = 9x + 6
m = 12y + 4

nm = (9x + 6)*(12y + 4) = 108xy + 36x + 72y + 24
Remainder of nm/18 = (108xy + 36x + 72y + 24)/18

Observe that the first three terms are a multiple of 18
24 when divided by 18 leaves remainder 6
Hence mn/18 will leave remainder 6

Correct Option: C
Manager
Manager
User avatar
B
Joined: 17 Nov 2014
Posts: 50
Location: India
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 29 Apr 2016, 08:17
1
n = 9x + 6
m = 12y + 4

nm = (9x + 6)*(12y + 4) = 108xy + 36x + 72y + 24
Remainder of nm/18 = (108xy + 36x + 72y + 24)/18
The first three terms are a multiple of 18
24 when divided by 18 leaves remainder 6
Hence, mn/18 will leave remainder 6

Option :C
Manager
Manager
avatar
B
Joined: 24 Jul 2016
Posts: 50
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 11 Jul 2017, 20:56
1
Bunuel wrote:
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when nm is divided by 18?

A. 3
B. 5
C. 6
D. 10
E. 12


i multiplied the 2 remainder 6 & 4 and divided the product by 18 (6x4/18). the remainder was 6.
Intern
Intern
avatar
B
Joined: 13 Jul 2017
Posts: 29
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 19 Jul 2017, 04:01
How I did that
9(x)+6=15
12(x)+4=16
Assume they are actually 15 and 16 take unit digit 5*6=30
30/8=24
remainder 6
Is it right approach
Expert opinion please
Manager
Manager
avatar
B
Joined: 04 May 2014
Posts: 151
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 20 Aug 2017, 23:28
1
Easy way
n=9q+6 or n can be 6, 15, 24....
m=12q+4 or n can be 4, 16, 28...
take any 2 nos from above series
NM=6X4=24
24/18=reminder=6.
Senior Manager
Senior Manager
User avatar
G
Status: love the club...
Joined: 24 Mar 2015
Posts: 269
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 17 Sep 2017, 04:25
gps5441 wrote:
Easy way
n=9q+6 or n can be 6, 15, 24....
m=12q+4 or n can be 4, 16, 28...
take any 2 nos from above series
NM=6X4=24
24/18=reminder=6.


hi

how can you say so ....?

take 15 and 16 for example ...
nm = 15 x 16

now (15 x 16)/18 leaves remainder 1
and yes, obviously, it will work with 6, and 4, as the numbers themselves can be 6, and 4 ...

if you have anything to say, please say to me ...

thanks in advance ..
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1224
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post Updated on: 01 Oct 2018, 21:19
1
Bunuel wrote:
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when nm is divided by 18?

A. 3
B. 5
C. 6
D. 10
E. 12


assuming one peanut per smaller bag,
least possible value of n=9+6=15
and least possible value of m=12+4=16
nm=15*16=240
240/18 leaves a remainder of 6
C

Originally posted by gracie on 17 Sep 2017, 11:46.
Last edited by gracie on 01 Oct 2018, 21:19, edited 1 time in total.
Manager
Manager
avatar
B
Joined: 04 May 2014
Posts: 151
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 21 Sep 2017, 18:49
gmatcracker2017 wrote:
gps5441 wrote:
Easy way
n=9q+6 or n can be 6, 15, 24....
m=12q+4 or n can be 4, 16, 28...
take any 2 nos from above series
NM=6X4=24
24/18=reminder=6.


hi

how can you say so ....?

take 15 and 16 for example ...
nm = 15 x 16

now (15 x 16)/18 leaves remainder 1
and yes, obviously, it will work with 6, and 4, as the numbers themselves can be 6, and 4 ...

if you have anything to say, please say to me ...

thanks in advance ..


15x16=240
240/18 leaves a reminder of 6.

Posted from my mobile device
IIMA, IIMC School Moderator
User avatar
V
Joined: 04 Sep 2016
Posts: 1366
Location: India
WE: Engineering (Other)
CAT Tests
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 25 Aug 2018, 21:23
1
chetan2u niks18 Bunuel VeritasKarishma GMATPrepNow gmatbusters

How about this approach?

Bag 1: 9k+ 6
Bag 2: 12m + 4

Multiplying peanuts of bag 1 and bag 2:
3(3K+2) * 4 (3m+1)
or
12 (3k+2) (3m+1) . . . . . (1)

Q asks: remainder when divisor is 18

can I use concept LCM of 12 and 18 is 36 beyond (1) ?
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8023
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 25 Aug 2018, 21:30
1
adkikani wrote:
chetan2u niks18 Bunuel VeritasKarishma GMATPrepNow gmatbusters

How about this approach?

Bag 1: 9k+ 6
Bag 2: 12m + 4

Multiplying peanuts of bag 1 and bag 2:
3(3K+2) * 4 (3m+1)
or
12 (3k+2) (3m+1) . . . . . (1)

Q asks: remainder when divisor is 18

can I use concept LCM of 12 and 18 is 36 beyond (1) ?


12(3k+1)(3m+2)..
Next step should be 12(9mk+3m+6k+2)=(12*9mk+12*3m+12*6k+12*2)
All terms except 12*2 are divisible by 18...
So 24 divided by 18 leaves a remainder of 6.
_________________
Manager
Manager
avatar
B
Joined: 29 May 2017
Posts: 126
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 30 Sep 2018, 20:43
chetan2u wrote:
Bunuel wrote:
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when nm is divided by 18?

A. 3
B. 5
C. 6
D. 10
E. 12


A good Q..

the equation that can be formed for n peanuts = > n=9x+6..
the equation that can be formed for m peanuts = > m=12y+4..


so mn = (9x+6)(12y+4) where both x and y are integers..
\((9x+6)(12y+4) = 3(3x+2)*4(3y+1) = 12(9xy+6y+3x+2) = 12*3(3xy+2y+x) +12*2.\).
Now 12*3(3xy+2y+x) is Div by 18 hence remainder would be 24 div by 18..
so R =24-18 = 6
C


picking numbers is so much easier for this.....any particular reason why we do the algebra?
Intern
Intern
avatar
B
Joined: 28 Sep 2018
Posts: 6
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 01 Oct 2018, 09:21
What I did is simply expressed the statement in the form of N = QK + R

n = 9x + 6
=> 2n = 18x + 12 (multiplying by 2 on both sides) -- i)

m = 12y + 4
(3/2)m = 18y +6 (multiplying by 3/2 on both sides) --ii)


we know if r1 and r2 are the two reminders of n and m when divided by a, then if mn is divided by a; the remainder will be r1*r2

Multiplying i) and ii)
(observing only the remainders)
3mn --Remainder--> (12*6)%18
=> mn --Remainder--> 24%18 = 6
Intern
Intern
User avatar
B
Joined: 19 Jul 2017
Posts: 40
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 17 Mar 2019, 09:48
testcracker wrote:
gps5441 wrote:
Easy way
n=9q+6 or n can be 6, 15, 24....
m=12q+4 or n can be 4, 16, 28...
take any 2 nos from above series
NM=6X4=24
24/18=reminder=6.


hi

how can you say so ....?

take 15 and 16 for example ...
nm = 15 x 16

now (15 x 16)/18 leaves remainder 1


and yes, obviously, it will work with 6, and 4, as the numbers themselves can be 6, and 4 ...

if you have anything to say, please say to me ...

thanks in advance ..

+ C
when you deal with REMINDERS take care AVOIDING to REDUCE any numbers

BEFORE

MULTIPLICATION
SO RIGHT TO REDUCE 15*16=240/18 SO REMINDER=6
AND WRONG TO REDUCE 40/3 to reach to 3
hope this help!
_________________
He gives power to the faint; and to them that have no might he increases strength. Isaiah 40:29


You never FAIL until you stop TRYING
Manager
Manager
User avatar
G
Joined: 31 Jan 2019
Posts: 172
Location: Switzerland
Concentration: General Management
GPA: 3.9
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

Show Tags

New post 10 Oct 2019, 12:22
Bunuel wrote:
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when nm is divided by 18?

A. 3
B. 5
C. 6
D. 10
E. 12


N=9x +6
N could be 6

M=12y + 4

M could be 4

N*M=6*4=24

Remainder when divided by 18=> 24-18=6

Option C
GMAT Club Bot
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts   [#permalink] 10 Oct 2019, 12:22
Display posts from previous: Sort by

A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts

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





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