How much money does Steve have?

[topspin20]

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

[mgm]

I have s = m + 90 and m + 1/3 *s = 0.8 * 2/3 s ...

Solving you get the OA

[Brent@GMATPrepNow]

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

Steve has 90 dollars more than Mike.
Let M = the amount of money Mike originally has
So, M + 90 = the amount of money Steve originally has

If Steve gives Mike 1/3 of his money . . .
In other words, Mike adds 1/3 of Steve's money to his money, AND Steve is left with 2/3 of what he originally had.
So, Mike now has M + 1/3(M + 90) dollars
And Steve now has 2/3(M + 90) dollars

. . . Mike will have 20% less than what Steve has left.
In other words, Mike's amount is equal to 80% of Steve's amount.
Or we can say Mike's amount is equal to 4/5 of Steve's amount.
So, M + 1/3(M + 90) = 4/5[2/3(M + 90)]
Expand and simplify: (4/3)M + 30 = (8/15)M + 48
Multiply both sides by 15: 20M + 450 = 8M + 720
Rearrange: 12M = 270
Solve: M = $22.50

Since Steve has $90 more than Mike, Steve must have [spoiler]$112.50[/spoiler]
Answer = D

Cheers,
Brent

[GMATGuruNY]

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%.
Success!