hutch27 wrote:at ABC academy, the ratio of the number of girls to the number of boys is 5 to 3. if 20 boys and 20 girls were to leave, the ratio of the number of boys to the number of girls would be 2 to 5. How many children are at ABC academy?
A 56
B 60
C 72
D 84
E 96
An alternate -- and perhaps the fastest -- approach is to plug in the answer choices, which represent the total number of children.
G:B = 5:3, implying that there are 5 girls for every 3 boys.
Since = 5+3 = 8, the total number of children must be a multiple of 8.
Eliminate B and D.
After 40 children leave, G:B = 5:2, implying that there are 5 girls for every 2 boys.
Since 5+2 = 7, the resulting number of children must be a multiple of 7.
Thus, when 40 is subtracted from the correct answer choice, the result must be a multiple of 7:
A: 56-40 = 16.
C: 72-40 = 32.
E: 96-40 = 56.
Only the result in red is a multiple of 7.
The correct answer is
E.
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