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

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Math Expert
Joined: 02 Sep 2009
Posts: 47112
A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

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28 Apr 2016, 01:12
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12
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Difficulty:

45% (medium)

Question Stats:

71% (02:00) correct 29% (02:07) wrong based on 226 sessions

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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

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Joined: 02 Aug 2009
Posts: 6257
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

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28 Apr 2016, 02:21
2
3
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
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##### General Discussion
SVP
Joined: 06 Nov 2014
Posts: 1888
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

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29 Apr 2016, 00:48
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

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
Joined: 17 Nov 2014
Posts: 51
Location: India
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

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29 Apr 2016, 08:17
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
Joined: 24 Jul 2016
Posts: 54
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

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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
Joined: 13 Jul 2017
Posts: 29
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

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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
Manager
Joined: 04 May 2014
Posts: 162
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]

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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
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Posts: 278
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

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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 ...

VP
Joined: 07 Dec 2014
Posts: 1036
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts  [#permalink]

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17 Sep 2017, 11:46
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

least value of n=15
least value of m=16
nm=240
240/18 leaves a remainder of 6
C
Manager
Joined: 04 May 2014
Posts: 162
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]

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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 ...

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

Posted from my mobile device
Re: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts &nbs [#permalink] 21 Sep 2017, 18:49
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