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

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

Say there are x no. of boys and y no. of girls, and say the price of one soda is s¢ and the price of one juice box is j¢.

Thus, the class spends (sx + jy)¢.

Had the boys and girls swapped soda and juice box, the class would have spent (jx + sy)¢

=> (jx + sy) – (sx + jy) = 1

(x – y)(j – s) = 1

Since x > y, we have (x – y) > 0. Moreover, we know that x and y are positive integers, thus, (x – y) is also an integer. The only possible value for (x – y) = 1.

The correct answer: A

Hope this helps!

-Jay
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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