edwin.que wrote:
The value of Machine 1 depreciates x% per year and the value of Machine 2 depreciates y% each year. Will the value of Machine 1 be greater than the value of Machine 2 in 10 years?
(1) The current value of Machine 1 is twice the current value of Machine 2.
(2) x = 2y
- Value of Machine 1 = \(v_1\)
- Value of Machine 2 = \(v_2\)
- Rate of depreciation of Machine 1 = \(x%\)
- Rate of depriciation of Machine 2 = \(y%\)
- Value of depreciation of Machine 1 after 10 years = \(v_1*[1-\frac{x}{100}]^{10}\)
- Rate of depriciation of Machine 2 = \(v_2*[1-\frac{y}{100}]^{10}\)
Question \(v_1*[1-\frac{x}{100}]^{10} > v_2*[1-\frac{y}{100}]^{10}\)
Statement 1 and Statement 2 are not sufficient as both the statement gives us information of only one parameter. Statement 1 provides us with the information that \(v_1 = 2v_2\) and doesn't provide us with any relationship between \(x\) and \(y\). While Statement 2, provides us information between \(x\) and \(y\), it doesn't provide us information about \(v_1\) and \(v_2\). Hence, the statements individually are not sufficient and we can eliminate A, B, and D.
CombinedFrom Statement 1 and Statement 2 we know that -
\(v_1*[1-\frac{x}{100}]^{10} > v_2*[1-\frac{y}{100}]^{10}\)
\(2v_2*[1-\frac{2y}{100}]^{10} > v_2*[1-\frac{y}{100}]^{10}\)
Dividing both sides by \(v_2\) we get,
\(2*[1-\frac{2y}{100}]^{10} > [1-\frac{y}{100}]^{10}\)
Simplifying we get -
\((\frac{100-2y}{100-y})^{10} > \frac{1}{2}\)
Hence, we can conclude that the inequality holds true only for a certain value of \(y\).
As we have no information on the value of \(y\), the statements combined are not sufficient.
Option E