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E
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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.
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04 Jan 2025, 07:42
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edwin.que
Question: Is value of Machine 1 > value of Machine 2 in 10 years?
Value in 10 years depends on current value and the rate of depreciation. Depreciation is like negative compound interest.
(1) The current value of Machine 1 is twice the current value of Machine 2.
Current value of machine 1 is double of current value of machine 2. So we can easily visualize that after 10 years, value of machine 1 could be higher than that of machine 2 (say if their rate of depreciation is similar)
But what if rate of depreciation of machine 1 is 99% and that of machine 2 is 1%. Then after 10 years, value of machine 1 will be a fraction of the value of machine 2.
Hence not sufficient
(2) x = 2y
This tells us that rate of depreciation of machine 1 is twice that of machine 2. But what if current value of machine 1 is 1000 times higher than that of machine 2? Even with the faster rate of depreciation, after 10 years, value of machine 1 may remain higher.
Using both, now we know that current value of machine 1 is twice that of machine 2 and rate of dep of machine 1 is also twice that of machine 2.
Say if the rate is very small - say x = 1% and y = 0.5%, then both values will decrease by a small amount and value of machine 1 will stay higher.
But if the rate is large - say x = almost 100% and y = almost 50%, then value of machine 1 becomes negligible while machine 2 will still have some value.
Hence we can still not say which machine will have higher value after 10 years.
Answer (E)
General Discussion
01 Nov 2023, 23:49
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edwin.que
- 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
