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Difficulty:
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Question Stats:
57% (02:44) correct
43%
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based on 5306
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The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?
(1) \(x > y\)
(2) \(\frac{xy}{100} < x-y\)
(1) \(x > y\)
(2) \(\frac{xy}{100} < x-y\)
02 Jan 2010, 15:16
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The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?
Given:
Question:
(1) \(x>y\),
(2) \(\frac{xy}{100} < x -y\).
Answer: B.
Given:
- Rent in 1997 - \(r\);
Rent in 1998 - \(r*(1+\frac{x}{100})\);
Rent in 1999 - \(r*(1+\frac{x}{100})*(1-\frac{y}{100})\).
Question:
- Is \(r<r*(1+\frac{x}{100})*(1-\frac{y}{100})\)?
Is \(1<1-\frac{y}{100}+\frac{x}{100}-\frac{xy}{10000}\)?
Is \(x-y>\frac{xy}{100}\) ?
(1) \(x>y\),
- Based on this information we cannot conclude whether \(x-y>\frac{xy}{100}\). Not sufficient.
(2) \(\frac{xy}{100} < x -y\).
- This, directly gives an YES answer to the question. Sufficient.
Answer: B.
This is a question based on successive percentage changes i.e. a number changes by a certain factor, then it changes again by some other factor and so on. Take 100 for example. I first increase it by 10% so it becomes 110. I then decrease 110 by 20% so it becomes 88.
I personally favor multiplying the factor of change together e.g.
\(100 * (1 + \frac{10}{100}) * (1 - \frac{20}{100})\) = 88
but a lot of my students like to use the simple formula of two successive percentage changes which is: \(a + b + \frac{ab}{100}\)
(You can derive it very easily. Let me know if you face a problem)
If a number is changed by a% and then by b%, its overall percentage change is as given by the formula.
Using it in the example above, a = 10, b = -20 (since it is a decrease)
\(a + b + \frac{ab}{100}\) = \(10 - 20 - \frac{10*20}{100}\) = -12%
So overall change will be of -12%. 100 becomes 88.
In our question above, since we have two successive percentage changes of x% and y% (which is a decrease) so the formula gives us \(x - y - \frac{xy}{100}\) is the overall change. The question is, whether this change is positive i.e. whether \(x - y - \frac{xy}{100}\) > 0 or
\(x - y > \frac{xy}{100}\)?
Since statement 2 tells us that \(x - y > \frac{xy}{100}\), it is sufficient.
And yes, it helps to be clear about exactly what is asked before you move on to the statements.
Here is a post on successive percentage changes: https://anaprep.com/arithmetic-successi ... e-changes/
I personally favor multiplying the factor of change together e.g.
\(100 * (1 + \frac{10}{100}) * (1 - \frac{20}{100})\) = 88
but a lot of my students like to use the simple formula of two successive percentage changes which is: \(a + b + \frac{ab}{100}\)
(You can derive it very easily. Let me know if you face a problem)
If a number is changed by a% and then by b%, its overall percentage change is as given by the formula.
Using it in the example above, a = 10, b = -20 (since it is a decrease)
\(a + b + \frac{ab}{100}\) = \(10 - 20 - \frac{10*20}{100}\) = -12%
So overall change will be of -12%. 100 becomes 88.
In our question above, since we have two successive percentage changes of x% and y% (which is a decrease) so the formula gives us \(x - y - \frac{xy}{100}\) is the overall change. The question is, whether this change is positive i.e. whether \(x - y - \frac{xy}{100}\) > 0 or
\(x - y > \frac{xy}{100}\)?
Since statement 2 tells us that \(x - y > \frac{xy}{100}\), it is sufficient.
And yes, it helps to be clear about exactly what is asked before you move on to the statements.
Here is a post on successive percentage changes: https://anaprep.com/arithmetic-successi ... e-changes/
. 
