After a certain project was completed and the team was paid for its work, Aris received 40% less money than each of the other team members. If the amount paid to the team had been divided evenly among all the team members, Aris would have received 60% more than he actually received. What fraction of the total amount paid to the team did Aris receive?
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This one took me way longer than it should have. I kept trying to set Aris's pay equal to some variable and then got lost in the "40% less than each other member" wording. For anyone stuck: the key is realizing every OTHER member got the same amount. Once I saw that, the rest fell into place. Tough but fair for 705+.
Same, the phrasing "each of the other team members" is what tripped me up. I initially read it as 40% less than the total the others got combined lol.
Can someone explain step by step how to set this up? I get that Aris = 0.6x if each other member is x, but then I don't know where to put the 60% part. Is the even split amount = 1.6 times Aris's actual? That's what I did but I want to confirm.
Yes, that's exactly it. The even-split amount is 60% MORE than what he actually got, so even split = 1.6 × Aris's actual pay. From there it's just a ratio setup.
Love this question. The trap answer is 1/12 if you misread which direction the 60% goes. Super clean once you write it as a ratio. Definitely on the harder end of percentage problems, maybe a 5/5 difficulty for me.
What it tests
Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.
Common trap
Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.