BTGmoderatorDC wrote: ↑Wed Feb 26, 2020 7:29 pm
If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it would if every boy in the class buys a juice box and every girl in the class buys a soda. If there are more boys than girls in the class, what is the difference between the number of boys and the number of girls in the class?
A. 1
B. 3
C. 4
D. 12
E. Cannot be uniquely determined
OA
A
Source: Veritas Prep
We can let b = the number of boys in the class, g = the number of girls in the class, s = price of a soda and j = price of a juice box. From the information given in the problem, we see that:
bs + gj = bj + gs - 1 and b > g
We need to determine the value of b - g.
Let’s look at the equation bs + gj = bj + gs - 1 and simplify
bj + gs - bs - gj = 1
bj - bs - gj + gs = 1
b(j - s) - g(j - s) = 1
(b - g)(j - s) = 1
Since b, g, j and s are integers and the only way two positive integers multiplied together yield a product of 1 is 1 x 1, we see that b - g = 1 and j - s = 1. Thus, we see that b - g = 1. (Note: We must assume that the cost of both soda and juice is in whole cents, not fractions of a cent. If this assumption were not made, then the correct answer would be E.)
Answer: A
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