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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 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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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

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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?

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

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

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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.

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 Expert opinion please

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