erikvmSo here is the breakdown of this approach:
VeritasPrepKarishma wrote:
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
Talks about the concept the question is testing - successive % changes and tells you what the concept is. Uses a random example.
VeritasPrepKarishma wrote:
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.
Talks about a formula related to this concept. Uses the same example as above.
VeritasPrepKarishma wrote:
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, we come to the given question. Shows you why statement 2 is sufficient. You just use the formula on x and y and you can see that statement 2 is sufficient.
Statement 1 is not sufficient because it tells you that x - y is positive. It doesn't tell you whether x - y - xy/100 is positive.
Pick some numbers to see how statement 1 is not sufficient:
If x = 10 and y = 5,
Rent in 1997 is 100, rent in 1998 is 110 and rent in 1999 is 104.5.
Rent in 1997 < Rent in 1999
But if
If x = 10 and y = 9.99999999 (almost 10 but still x > y)
Rent in 1997 is 100, then rent in 1998 is 110 and rent in 1999 is very slightly more than 99.
Rent in 1997 > Rent in 1999
So the rent in 1997 may be more or less than rent in 1999 if x > y. Hence statement 1 alone is not sufficient.
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Karishma
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