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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
(1) The current value of Machine 1 is twice the current value of Machine 2.
(2) x = 2y
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. Both statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. Both statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
01 Nov 2023, 23:49
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edwin.que
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
(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.
Combined
From Statement 1 and Statement 2 we know that -
- v_1 = 2v_1
- x = 2y
\(v_1*[1-\frac{x}{100}]^{10} > v_2*[1-\frac{y}{100}]^{10}\)
\(2v_2*[1-\frac{2y}{100}]^{10} > v_2*[1-\frac{y}{100}]^{10}\)
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
29 May 2024, 06:45
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For a value of Y between 6.28 and 65.91, the value of M1 will be less than M2. For any other value Y, the value of M1 is more than the value of M2.
Option E
Option E
