Two farmers agree that pigs are worth $300 and that goats are worth $

Question

Two farmers agree that pigs are worth $300 and that goats are worth $210. When one farmer owes the other money, he pays the debt in pigs or goats, with “change” received in the form of goats or pigs as necessary. (For example, a $390 debt could be paid with two pigs, with one goat received in change.) What is the amount of the smallest positive debt that can be resolved in this way?

(A) $5

(B) $10

(C) $30

(D) $90

(E) $210

(A) $5

(B) $10

(C) $30

(D) $90

(E) $210

Chethan92 · Answer

300*5 = 1500$ worth of pigs
210*7 = 1470$ worth of goats.

Smallest difference is 30$.

C is the answer.

GMATWhizTeam · Answer

Solution:  
Let  x  and  y  be the number of pigs and goat respectively.
 • x and y are positive integers because they are animals.
•  |300*x – 210*y|=D , Where  D  is the debt
• | 30(10*x-7*y)|=D 
•  30|10*x-7*y|=D 
 o The minimum possible value of  10*x – 7*y  is  1  at x =2 and y =3, because x and y both are positive integers. 
•  30*1 = D 
 o Minimum Debt that can be resolved is $  30   
Hence, the correct answer is  Option C.

fireagablast · Answer

I got 30, but how does the above solution account for cases that involve paying back debt by a combination of goats and pigs?
300x-210y=D only seems to relate paying back pigs with goats. Obviously goat - goat = 0, so that might be why it's not listed, but i would like to understand what the full equation would look like, including reducing down to 300x-210y = D.

my way was manual chug
Goats:
300
600
900
1200

Pigs:
210
420
630
840
960
1080
1300

Smallest difference is 630-600= 30, and no combinations of G's and P's get smaller.

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • Two farmers agree that pigs are worth $300 and that goats are worth $210
• When one farmer owes the other money, he pays the debt in pigs or goats, with “change” received in the form of goats or pigs as necessary. (For example, a $390 debt could be paid with two pigs, with one goat received in change.)

To find  
We need to determine
 • The smallest possible debt amount, that can be resolved in the mentioned way

Approach and Working out  
Assuming that for the smallest possible debt amount case, there are P pigs and G goats

The difference in their values = the minimum resolvable value = 300P – 210G or 210G – 300P = 30 (10P – 21G) or 30 (21G – 10P)
 • At minimum value, 10P must be equal to 21G
• Hence, minimum resolvable value = 30

Thus, option C is the correct answer.

Correct Answer: Option C

martinfzb · Answer

It seems that the solution is the LCM of 300 and 210, 30 for this case.

bumpbot · Answer

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Two farmers agree that pigs are worth $300 and that goats are worth $

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