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Three containers A, B and C have wine concentrations a, b and c, respe

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Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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New post 05 Jul 2017, 00:26
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Three containers A, B and C have wine concentrations a, b and c, respectively, such that a > b > c. If quantities p, q and r, of wine are taken from the three containers A, B and C, respectively, and mixed, is the concentration of the resulting mixture greater than b?

(1) a − b = b − c
(2) p > q > r

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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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New post 05 Jul 2017, 01:16
Bunuel wrote:
Three containers A, B and C have wine concentrations a, b and c, respectively, such that a > b > c. If quantities p, q and r , of wine are taken from the three containers A, B and
C, respectively, and mixed, is the concentration of the resulting mixture greater than b?

(1) a − b = b − c
(2) p > q > r


In question we are asked if (pa+qb+rc)/3 > b
Please note that all p,q,r,a,b,c are positive

(1) says b is (a+c)/2 but we do not know about p,q,r hence not sufficient

(2) says p>q>r

but we do not know about distance between a & b & c (What if a-b is far less than b-c) hence not sufficient

On combining we will be able to answer the question C

I think something might be flawed in my approach and hence will wait for Bunuel to answer
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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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New post 05 Jul 2017, 11:44
I came to the conclusion of E.

Neither statement compares A,B,C to P,Q,R. P,Q,R could be greater or less.

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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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New post 18 Jul 2017, 05:02
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Bunuel wrote:
Three containers A, B and C have wine concentrations a, b and c, respectively, such that a > b > c. If quantities p, q and r , of wine are taken from the three containers A, B and
C, respectively, and mixed, is the concentration of the resulting mixture greater than b?

(1) a − b = b − c
(2) p > q > r


It is C.

Statement 1: Insufficient

a - b = b -c tells us the difference in concentrations is same but we do not know the ratio in which these are mixed and hence cannot tell if resulting concentration is greater than b.

Statement 2: Insufficient

p > q > r tells us solution with concentration a has the highest proportion in the resulting solution but without knowing the concentrations of each, we do not know whether the eventual concentration is greater than b or not.

Combining 1 and 2, we know concentrations are equidistant and b lies exactly in the middle. Now resulting solution will depend on the proportion that is mixed and if p is greatest, we know the resulting concentration is tilted towards a and not towards c. Hence, resulting concentration is less than b.
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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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New post 19 Jul 2017, 07:25
jedit wrote:
Bunuel wrote:
Three containers A, B and C have wine concentrations a, b and c, respectively, such that a > b > c. If quantities p, q and r , of wine are taken from the three containers A, B and
C, respectively, and mixed, is the concentration of the resulting mixture greater than b?

(1) a − b = b − c
(2) p > q > r


It is C.

Statement 1: Insufficient

a - b = b -c tells us the difference in concentrations is same but we do not know the ratio in which these are mixed and hence cannot tell if resulting concentration is greater than b.

Statement 2: Insufficient



p > q > r tells us solution with concentration a has the highest proportion in the resulting solution but without knowing the concentrations of each, we do not know whether the eventual concentration is greater than b or not.

Combining 1 and 2, we know concentrations are equidistant and b lies exactly in the middle. Now resulting solution will depend on the proportion that is mixed and if p is greatest, we know the resulting concentration is tilted towards a and not towards c. Hence, resulting concentration is less than b.



Shouldn't the answer depend on values of a,b,c & p,q,r ?
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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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New post 19 Jul 2017, 07:38
PK32 wrote:
jedit wrote:
Bunuel wrote:
Three containers A, B and C have wine concentrations a, b and c, respectively, such that a > b > c. If quantities p, q and r , of wine are taken from the three containers A, B and
C, respectively, and mixed, is the concentration of the resulting mixture greater than b?

(1) a − b = b − c
(2) p > q > r


It is C.

Statement 1: Insufficient

a - b = b -c tells us the difference in concentrations is same but we do not know the ratio in which these are mixed and hence cannot tell if resulting concentration is greater than b.

Statement 2: Insufficient



p > q > r tells us solution with concentration a has the highest proportion in the resulting solution but without knowing the concentrations of each, we do not know whether the eventual concentration is greater than b or not.

Combining 1 and 2, we know concentrations are equidistant and b lies exactly in the middle. Now resulting solution will depend on the proportion that is mixed and if p is greatest, we know the resulting concentration is tilted towards a and not towards c. Hence, resulting concentration is less than b.



Shouldn't the answer depend on values of a,b,c & p,q,r ?



It does. Say we have concentrations 60%, 40% and 20% and we mix them in equal quantity, resulting concentration would be 40%.
But if we have these concentrations where we add more of 60% solution (statement 2), concentration would sway from the mean towards the 60% concentration.
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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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New post 15 Aug 2018, 23:20
Luckisnoexcuse wrote:
Bunuel wrote:
Three containers A, B and C have wine concentrations a, b and c, respectively, such that a > b > c. If quantities p, q and r , of wine are taken from the three containers A, B and
C, respectively, and mixed, is the concentration of the resulting mixture greater than b?

(1) a − b = b − c
(2) p > q > r


In question we are asked if (pa+qb+rc)/3 > b
Please note that all p,q,r,a,b,c are positive

(1) says b is (a+c)/2 but we do not know about p,q,r hence not sufficient

(2) says p>q>r

but we do not know about distance between a & b & c (What if a-b is far less than b-c) hence not sufficient

On combining we will be able to answer the question C

I think something might be flawed in my approach and hence will wait for Bunuel to answer


Actually the divisor is not 3 but is (p+q+r)

so the question is :

(pa+qb+rc)/(p+q+r) > b?

on simplification, we get :
is p> r(b-c)/(a-b) ?

we need 1 and 2 to answer this

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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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New post 29 Aug 2018, 22:50
Bunuel , can you please help with the solution for this?
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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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New post 11 Nov 2018, 09:55
Hey guys...Please do explain the answer elaborately
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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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New post 17 Dec 2018, 10:03
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The solution is:
Amt of wine after taking p,q,r of each wine is ap+bq+cr. Let this be A
A=Concentration(C)*Volume(V)
C=A/V= (ap+bq+cr)/p+q+r
Question is C>b --> is (ap+bq+cr)/p+q+r>b --> ap+bq+cr>bp+bq+br -->ap+cr>b(p+r) .....(1)

Stmt 1 a-b=b-c..no info on p,r so NOT suff
Stmt 2 p>q>r, no info on a,b,c...NOT suff
Using both
from eqn 1
IS ap-bp>br-cr
IS p(a-b)>r(b-c)
using both stmt a-b=b-c, and p>r, STMT is true. so BOTH are sufficient. Answer is C
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Re: Three containers A, B and C have wine concentrations a, b and c, respe   [#permalink] 17 Dec 2018, 10:03
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