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23 Mar 2005, 20:29
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easy one;)
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25 Mar 2005, 15:09
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Please note that while x applies on the initial amount, y applies on the increased amount (100+x)/100 times of the original. Therefore, even when they're equal, the final amount is less than initial.
In case x > y, we dont know the relative magnitudes. Suppose increase is by 10% and decrease by 5% then, on 100, increased to 110, and decreased to 104.5 - this was a net increase. But if increase is 50% - increased to 150 and then decrease by 40%, decreased to 90 - this is a net decrease. Hence insufficient.
In case x = 1.2y,
initial increase from 100 to 100 +x.
After decrease, amount is (100 - x/1.2)/100 * (100+x)
= (1-x/120)(100+x)
= 100 + x - x/1.2 - x^2/120
= 100 + (20x - x^2)/120
= 100 + x(20-x)/120
This would be > 100 for x < 20%, = 100 for x = 20% and < 100 for x > 20%.
Therefore this too is insufficient.
Therefore (E).
In case x > y, we dont know the relative magnitudes. Suppose increase is by 10% and decrease by 5% then, on 100, increased to 110, and decreased to 104.5 - this was a net increase. But if increase is 50% - increased to 150 and then decrease by 40%, decreased to 90 - this is a net decrease. Hence insufficient.
In case x = 1.2y,
initial increase from 100 to 100 +x.
After decrease, amount is (100 - x/1.2)/100 * (100+x)
= (1-x/120)(100+x)
= 100 + x - x/1.2 - x^2/120
= 100 + (20x - x^2)/120
= 100 + x(20-x)/120
This would be > 100 for x < 20%, = 100 for x = 20% and < 100 for x > 20%.
Therefore this too is insufficient.
Therefore (E).
