The positive number a is q percent greater than the positive number b, which is p percent less than a itself. If a is increased by p percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a
Choose the correct choice from the following answers
A) I only	B) II only	C) III only	D) I and II only	E) II and III only
a = (1 + q%)b   b = (1-p%)a   a = (1 + q%)*(1-p%)a   So (1 + q%)(1 - p%) = 1 = No change   One easy solution to this would be q = 0 and p = 0. In that case, a = b = c. So statement II can hold.   Assuming p and q are not 0,   (1 + q%)(1 - p%) = 1 = No change   So if you increase something by q% (it becomes bigger) and then decrease it by p% (now you will need to decrease it by a lesser %), there is no change.   Such as, you increase 100 by 25% and it becomes 125. Then you decrease 125 by only 20% and it comes back to 100. (This should remind you of cost price, sale price, profit and margin). So q would be a higher percentage than p.   Now if you increase something by p% (the lower %) and then decrease by q% (the higher %), the value you will obtain will certainly be lower than original.   Say you increase a (100) by p% (20%) to get 120 and then decrease it by q% (25%), you will get c (90). Hence c &lt; a is possible too.   Answer (II and III only)
<result>E</result>
The positive number a is q percent greater than the positive number b, which is p percent less than a itself. If a is increased by p percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a