In a certain mixed-gender school, the number of boys exceeds the number of girls. After 3 boys depart and 4 girls join the school, the number of boys still outnumbers the girls. What is the minimum number of boys that could have been initially enrolled in the school, given that there was at least one girl to start with?
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Love how you solved this
Can someone explain it other way?
Thanks! This one was tricky to wrap my head around at first. The "minimum" part tripped me up.
Same here! I kept thinking there must be some algebraic equation to solve, but it's more about testing the smallest possible numbers.
Wait, how do we use the "at least one girl" condition? I assumed girls could be zero, so I got a different answer. Can someone explain?
If there were zero girls initially, then after 4 girls join, there'd be 4 girls. The boys after 3 depart must still outnumber them. So boys initially would need to be at least 8? But that's not the minimum if we allow zero girls. The condition says at least one girl, so we have to start with at least 1 girl. That changes the minimum.
This was medium difficulty for me. The key is to set up the inequality and test the smallest integer values. I initially forgot that girls must be at least 1, so I almost picked 8. Good question!
What it tests
Your ability to convert between fractions, ratios, and decimals and to reason proportionally.
Common trap
Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.