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

Question

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. 122

A. 3
B. 5
C. 6
D. 10
E. 122

Nidzo · Answer

Let n = 24
Let m = 40

(24*40)/18
= 24/18 * 40/18

24/18 = 1 with a remainder of 6
40/18 = 2 with a remainder of 4

4*6 = 24 which means that that another 18 can go into that. 24-18 = 6
Remainder will be 6.

Answer C

Showmeyaa · Answer

Given:
 \frac{n}{9}, R = 6 
So, n can be 6, 15, 24......
Also given:
 \frac{m}{12}, R = 4 
m can be 4, 16, 28.....
Therefore, mn can be 24, 96...(you can pick any combination)
 \frac{mn}{18} 
 \frac{24}{18}, R = 6  - (C), IMO!

iamvishnu · Answer

Hi  Bunuel  can you please explain answer for this question

Posted from my mobile device

rightday1121 · Answer

I had a slight question on this explanation. You had stated that n can be " 6 , 15, 24, ..." and m can be " 4 , 16, 28.....".

Would it be technically not possible for n to be 6 or m to be 4 since we need a quotient of at least 1 for the problem to work? For example, a bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Okay, there, at least 1 smaller bag HAS to be an outcome, so n =6 cannot be a possibility as that leaves the quotient as 0  .

Similar line of reasoning for why m cannot be 4.

JeffTargetTestPrep · Answer

According to the information given, we have:

n = 9q + 6 where q is an integer.

m = 12p + 4 where p is an integer.

So,

nm = (9q + 6)(12p + 4) =

108pq + 72p + 36q + 24 =

108pq + 72p + 36q + 18 + 6 =

18(6pq + 4p + 2q +1) + 6

Thus, the remainder when nm is divided by 18 is 6.

Answer: C

Paras96 · Answer

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. 122

Let p & q be some positive integer, therefore according to the given scenario
=> n = 9p + 6
=> m = 12q + 4

=>nm=(9p + 6)(12q + 4)=108pq+36p+72q+24=  108pq+36p+72q+18 ] +6=18  +  6  = 18k+ 6

Therefore, the remainder when nm is divided by 18 = 6

Hence C

Aryan19852 · Answer

I solved the LCM method
9- 3*3
12-3*2*2
18-3*3*2
So, cancelling out 3*2 remains which is 6 the remainder

Posted from my mobile device

Abhishek009 · Answer

Min possible value of n = 15 when divided by 9 leaves remainer of 6
Min possible value of m = 16 when divided by 12 leaves remainer of 4

So,  \frac{mn}{18} = 16*\frac{15}{18}=  Rem  6 , Answer will be (C)

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

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

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