Shamhoon wrote:The value of an investment increases by x% during January and decreases by y% during February. If the value of the investment is the same at the end of February as at the beginning of January, what is y in terms of x ?
200x
------
100 + 2x
x(2 + x)
--------
(1 + x)2
2x
---------
1 + 2x
x(200 + x)
-------------
10,000
10,000
100 - -------------
100 + x
Let investment = 100.
Let x=25.
Increase in January = 100 + 25% of 100 = 100+25 = 125.
To decrease back down to 100 in February, y=20:
125 - 20% of 125 = 125-25 = 100.
Since the question asks for the value of y, our target is y=20.
Now we plug x=25 into all the answers to see which yields our target of 20.
Only answer choice E works:
100 - 10,000/(100+x) = 100 - 10,000/(100+25) = 100-80 = 20.
The correct answer is
E.
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