If a, b, and c are positive numbers such that a is b percent : GMAT Data Sufficiency (DS)
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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, 06:08
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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, 06:15
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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.

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06 Oct 2014, 11:24
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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, 15:30
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.

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, 17:00
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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?

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.
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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, 18:03
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?

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

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19 Aug 2015, 03:16
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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?

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.
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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, 06:53
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
Re: If a, b, and c are positive numbers such that a is b percent   [#permalink] 02 Oct 2015, 06:53
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