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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 38% (02:14) correct 62% (02:09) wrong based on 309 sessions

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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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Current Student P
Joined: 18 Aug 2016
Posts: 603
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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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

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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Luckisnoexcuse
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Joined: 18 Aug 2015
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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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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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Manager  P
Joined: 14 Oct 2015
Posts: 244
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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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3
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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Intern  B
Joined: 25 Mar 2016
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Concentration: Finance, General Management
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Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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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 ?
Manager  P
Joined: 14 Oct 2015
Posts: 244
GPA: 3.57
Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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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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Manager  B
Joined: 09 Oct 2015
Posts: 225
Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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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

Posted from my mobile device
Intern  B
Joined: 12 Aug 2018
Posts: 8
GMAT 1: 630 Q48 V28 Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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Bunuel , can you please help with the solution for this?
Intern  B
Joined: 29 Apr 2017
Posts: 28
Location: India
Concentration: Finance, Accounting
Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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Hey guys...Please do explain the answer elaborately
Manager  B
Joined: 01 May 2018
Posts: 64
Re: Three containers A, B and C have wine concentrations a, b and c, respe  [#permalink]

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1
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 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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