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The positive number a is q percent greater than the positive number b,
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11 May 2015, 07:18
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Re: The positive number a is q percent greater than the positive number b,
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12 May 2015, 23:29
Bunuel wrote: 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
A) I only B) II only C) III only D) I and II only E) II and III only
Kudos for a correct solution. a = (1 + q%)b b = (1p%)a a = (1 + q%)*(1p%)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 < a is possible too. Answer (E)
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Re: The positive number a is q percent greater than the positive number b,
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11 May 2015, 07:55
Let q = 10% then p = 100/11 % let b = 100 then a = 110 after increasing a by p and decreasing by q we get c = 108 therefore c<a C it is



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Re: The positive number a is q percent greater than the positive number b,
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11 May 2015, 21:50
Quote: The positive number a is q percent greater than the positive number b, which is p percent less than a itself. I assume this means that a > b, and thus q and p are positive. Because b is positive, p < 100. 1) a = (1+q)b = b+bq 2) b = (1p)a = a  ap plug 2 into 1: a = a  ap + (a  ap)q = a  ap + aq  apq subtract a from both sides and rearrange the right side: 0 = aq  ap  apq Quote: 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? Because c is a positive number, q < 100. a*(1+p)*(1q)=c (a+ap)*(1q)=c a+apaqapq=c subtract a from both sides (because we want to see if c  a > 0, = 0 or < 0): ap  aq  apq = c  a from above: 0 = aq  ap  apq or ap = aq  apq plug that in: aq  apq aq  apq = ca aq  aq = 0 apq  apq = 2apq so c  a = 2apq, because a, p and q are all positive, c  a = 2 * positive number, which is < 0. This is C. NOTE: if p and q are allowed to be 0 or negative, then the answer changes. If p and q are allowed to be 0, so a = b, then II can be correct. For example, a = 10, b = 10, p = 0, q = 0.



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Re: The positive number a is q percent greater than the positive number b,
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11 May 2015, 22:03
darthsaini wrote: Let q = 10% then p = 100/11 % let b = 100 then a = 110 after increasing a by p and decreasing by q we get c = 108 therefore c<a C it is A hint here: the question is  "could be true" Plugging in values gave you that one of the three statements (c < a) could be true. But what can you say about the other two statements? By taking a single set of values, how can you prove that they cannot be true? Suggest you to think logically.
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Re: The positive number a is q percent greater than the positive number b,
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27 May 2016, 19:24
VeritasPrepKarishma wrote: Bunuel wrote: 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
A) I only B) II only C) III only D) I and II only E) II and III only
Kudos for a correct solution. a = (1 + q%)b b = (1p%)a a = (1 + q%)*(1p%)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 < a is possible too. Answer (E) completely stumped could not think of p=q=0 could be one of solution. question should mention either of p or q is also positive number.then the ans will be C otherwise its E thanks karishma..



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Re: The positive number a is q percent greater than the positive number b,
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28 Jan 2017, 08:18
VeritasPrepKarishma wrote: Bunuel wrote: 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
A) I only B) II only C) III only D) I and II only E) II and III only
Kudos for a correct solution. a = (1 + q%)b b = (1p%)a a = (1 + q%)*(1p%)aSo (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 < a is possible too. Answer (E) Would you please explain how did you get this ' a = (1 + q%)*(1p%)a' ? I am in trouble to understand this.
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Re: The positive number a is q percent greater than the positive number b,
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29 Jan 2017, 04:49
Hi Bunuel,
Correct answer in the question is C; however the explanation given by VeritasPrepKarishma says that the answer is E. Please clarify which one is correct. If it is C then why we neglected the case when p=0, q=0



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Re: The positive number a is q percent greater than the positive number b,
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27 Jul 2018, 19:20
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