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# If a, b, and c are positive numbers such that a is b percent

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If a, b, and c are positive numbers such that a is b percent [#permalink]

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20 Jul 2013, 07:08
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If a, b, and c are positive numbers such that a is b percent of c, what is the value of c?

(1) a is c percent of b.

(2) b is c percent of a.

Took me a while. Will post OE later.
[Reveal] Spoiler: OA
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Re: If a, b, and c are positive numbers such that a is b percent [#permalink]

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20 Jul 2013, 07:15
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If a, b, and c are positive numbers such that a is b percent of c, what is the value of c?

a is b percent of c --> $$a=c*\frac{b}{100}$$.

(1) a is c percent of b --> $$a=b*\frac{c}{100}$$. The same info. Not sufficient.

(2) b is c percent of a --> $$b=a*\frac{c}{100}$$ --> $$a=\frac{100b}{c}$$ --> $$\frac{100b}{c}=c*\frac{b}{100}$$ --> $$b$$ reduces and we get: $$c^2=100^2$$ --> $$c=100$$ (discard c=-100 because we are told that c is positive). Sufficient.

Answer: B.
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Re: If a, b, and c are positive numbers such that a is b percent [#permalink]

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06 Oct 2014, 12:24
Hello from the GMAT Club BumpBot!

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Re: If a, b, and c are positive numbers such that a is b percent [#permalink]

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18 Aug 2015, 16:30
Bunuel wrote:
If a, b, and c are positive numbers such that a is b percent of c, what is the value of c?

a is b percent of c --> $$a=c*\frac{b}{100}$$.

(1) a is c percent of b --> $$a=b*\frac{c}{100}$$. The same info. Not sufficient.

(2) b is c percent of a --> $$b=a*\frac{c}{100}$$ --> $$a=\frac{100b}{c}$$ --> $$\frac{100b}{c}=c*\frac{b}{100}$$ --> $$b$$ reduces and we get: $$c^2=100^2$$ --> $$c=100$$ (discard c=-100 because we are told that c is positive). Sufficient.

Answer: B.

Hi Bunuel,

I understand why B is sufficient (as you have clearly shown) but I always thought that you need at least three equations to solve a system of equation with three variables involved (a, b, and c in this case). But it seems that we only needed two equations in this case (the one in QS and (2)) to solve for c. So does the rule about needing three equations for three variables not always hold?
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If a, b, and c are positive numbers such that a is b percent [#permalink]

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18 Aug 2015, 18:00
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torontoclub15 wrote:

Hi Bunuel,

I understand why B is sufficient (as you have clearly shown) but I always thought that you need at least three equations to solve a system of equation with three variables involved (a, b, and c in this case). But it seems that we only needed two equations in this case (the one in QS and (2)) to solve for c. So does the rule about needing three equations for three variables not always hold?

Let me try to answer your question.

You are correct to say that you need 'n' equations to solve for 'n' variables, but sometimes you might be able to solve for a particular variable by manipulating the given equations (when the number of equations < number of variables).

Example, Lets say the questions asks to find the value of 'a' and you are given the following equations:

a+b+c=100
200+b=a-c

On the first glance, you will mark that the statements are not sufficient as number of equations (=2) < number of variables (=3) but look carefully,

a+b+c=100...(1)
200+b = a-c ---> a-b-c=200....(2), adding equations (1) and (2) you get,

a=150 and hence the statements are sufficient.

Thus, in a DS question, you need to be absolutely sure that given a system of linear equations, you will not be able to eliminate n-1 variables in order to mark E. Otherwise, you will end up marking anything but E (i.e. you will be able to eliminate n-1 variables!).

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
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GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

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Re: If a, b, and c are positive numbers such that a is b percent [#permalink]

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18 Aug 2015, 19:03
Engr2012 wrote:
torontoclub15 wrote:

Hi Bunuel,

I understand why B is sufficient (as you have clearly shown) but I always thought that you need at least three equations to solve a system of equation with three variables involved (a, b, and c in this case). But it seems that we only needed two equations in this case (the one in QS and (2)) to solve for c. So does the rule about needing three equations for three variables not always hold?

Let me try to answer your question.

You are correct to say that you need 'n' equations to solve for 'n' variables, but sometimes you might be able to solve for a particular variable by manipulating the given equations (when the number of equations < number of variables).

Example, Lets say the questions asks to find the value of 'a' and you are given the following equations:

a+b+c=100
200+b=a-c

On the first glance, you will mark that the statements are not sufficient as number of equations (=2) < number of variables (=3) but look carefully,

a+b+c=100...(1)
200+b = a-c ---> a-b-c=200....(2), adding equations (1) and (2) you get,

a=300 and hence the statements are sufficient.

Thus, in a DS question, you need to be absolutely sure that given a system of linear equations, you will not be able to eliminate n-1 variables in order to mark E. Otherwise, you will end up marking anything but E (i.e. you will be able to eliminate n-1 variables!).

Hope this helps.

Excellent. Thanks for clearing that up. I had been blindly following that rule for DS questions without any further work.
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Kudos [?]: 1473 [1] , given: 789

If a, b, and c are positive numbers such that a is b percent [#permalink]

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19 Aug 2015, 04:16
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torontoclub15 wrote:
Engr2012 wrote:
torontoclub15 wrote:

Hi Bunuel,

I understand why B is sufficient (as you have clearly shown) but I always thought that you need at least three equations to solve a system of equation with three variables involved (a, b, and c in this case). But it seems that we only needed two equations in this case (the one in QS and (2)) to solve for c. So does the rule about needing three equations for three variables not always hold?

Let me try to answer your question.

You are correct to say that you need 'n' equations to solve for 'n' variables, but sometimes you might be able to solve for a particular variable by manipulating the given equations (when the number of equations < number of variables).

Example, Lets say the questions asks to find the value of 'a' and you are given the following equations:

a+b+c=100
200+b=a-c

On the first glance, you will mark that the statements are not sufficient as number of equations (=2) < number of variables (=3) but look carefully,

a+b+c=100...(1)
200+b = a-c ---> a-b-c=200....(2), adding equations (1) and (2) you get,

a=300 and hence the statements are sufficient.

Thus, in a DS question, you need to be absolutely sure that given a system of linear equations, you will not be able to eliminate n-1 variables in order to mark E. Otherwise, you will end up marking anything but E (i.e. you will be able to eliminate n-1 variables!).

Hope this helps.

Excellent. Thanks for clearing that up. I had been blindly following that rule for DS questions without any further work.

I forgot to mention one additional corollary of the above discussion. Is DS questions, just because you are given n equations for n variabels DOES NOT mean that you will be able to find a unique solution. Case in point:

Let the 3 equations be:

a+b+c =100
2a+2b+2c=200
3a+3b+3c=300

Thus although you are given 3 equations in 3 variables, these 3 equations are essentially the same. Thus, you can not solve this system of equations for a unique solution. Although superficially you had the sufficient number of equations, the answer will be E.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

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Re: If a, b, and c are positive numbers such that a is b percent [#permalink]

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02 Oct 2015, 07:53
kingflo wrote:
If a, b, and c are positive numbers such that a is b percent of c, what is the value of c?

(1) a is c percent of b.

(2) b is c percent of a.

Took me a while. Will post OE later.

If a, b, and c are positive numbers such that a is b percent of c, what is the value of c?
for statement 2) we get c^2 = 10000
Because c is positive , c=100
but if it were given as c is INTEGER then can we can say c = +100 or -100 and statment is insufficient.
I remember Bunuel's post, where he mentioned if GMAT has given even-root then it is always positive.
But if we are taking even-root of both sides then we need to consider both +ve and -ve
when it is odd root then it is always visible. whereas for even roots sign is hidden
Thanks
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Re: If a, b, and c are positive numbers such that a is b percent [#permalink]

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13 May 2017, 11:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a, b, and c are positive numbers such that a is b percent   [#permalink] 13 May 2017, 11:40
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# If a, b, and c are positive numbers such that a is b percent

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