topspin20 wrote:Steve has 90 dollars more than Mike. If Steve gives mike 1/3 of his money, Mike will have 20% less than what Steve has left. How much money does Steve have?
A) $92.50
B) $100.00
C) $102.25
D) $112.50
E) $120.00
Answer: D
We can plug in the answers, which represent Steve's amount.
Since Steve relinquishes 1/3 of his money, the correct answer choice must be a value that can divided by 3.
A value is divisible by 3 if the sum of its digits is a multiple of 3.
Only D (1+1+2+5+0 = 9) and E (1+2+0+0+0 = 3) are viable.
Eliminate A, B and C.
Of the two remaining answer choices, the value in E is easier to plug in.
When the correct value is plugged in, Mike must have -- after receiving 1/3 of Steve's money -- 20% less money than Steve.
In other words, Mike's new amount must be 80% of Steve's new amount.
Answer choice E: 120
Since Steve has $90 more than Mike, Mike's amount = 120-90 = 30.
Amount Steve gives Mike = (1/3) * 120 = 40.
Steve's new amount = 120-40 = 80.
Mike's new amount = 30+40 = 70.
Mike's new amount/Steve's new amount = 70/80 = 7/8.
Since Mike's new amount is not 80% of Steve's new amount, eliminate E.
The correct answer is
D.
Answer choice D: 112.50
Since Steve has $90 more than Mike, Mike's amount = 112.50 - 90 = 22.50.
Amount Steve gives Mike = (1/3) * 112.50 = 37.50.
Steve's new amount = 112.50 - 37.50 = 75.
Mike's new amount = 22.50 + 37.50 = 60.
Mike's new amount/Steve's new amount = 60/75 = 4/5 = 80%.
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