prashantbacchewar 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 ?
A. (200x)\(100 + 2x)
B. x(2 + x)\(1 + x)^2
C. 2x\1 + 2x
D. x(200 + x)\10,000
E. 100 – (10,000 \ 100 + x)
Multiplying by 5/4 = a 25% increase
Multiplying by 4/5 = a 20% decrease
Multiplying by 2/1 = a 100% increase
Multiplying by 1/2 = a 50% decrease
Multiplying by 4/1 = a 300% increase
Multiplying by 1/4 = a 75% decrease
For the investment to be same at the end of February, it must be multiplied by RECIPROCALS -- the equivalent of multiplying by a FACTOR OF 1 -- so that the value of the investment does not change.
Case 1: 5/4 * 4/5 --> a 25% increase followed by a 20% decrease --> x=25, y=20
Case 2: 2/1 * 1/2 --> a 100% increase followed by a 50% decrease --> x=100, y=50
Case 3: 4/1 * 1/4 --> a 300% increase followed by a 75% decrease --> x=300, y=75
What is the value of y in terms of x?Any of the cases above can be used to determine the correct answer.
In Case 1, plugging x=25 into the correct answer will yield 20 (the value of y).
In Case 2, plugging x=100 into the correct answer will yield 50 (the value of y).
In Case 3, plugging x=300 into the correct answer will yield 75 (the value of y).
Only E is viable.
If we consider Case 3 and plug x=300 into E, we get:
\(100 - \frac{10000}{400} = 100 - \frac{100}{4} = 100 - 25 = 75\)
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