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# 24 oz of juice P and 25 oz of juice V are mixed to make smot

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Manager
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24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink]

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26 Apr 2011, 07:17
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24 oz of juice P and 25 oz of juice V are mixed to make smothies X and Y . The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?

A. 5
B. 10
C. 15
D. 20
E. 25
Manager
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26 Apr 2011, 07:58
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shalu wrote:
24 oz of juice P and 25 oz of juice V are mixed to make smothies X and Y . The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?

5
10
15
20
25

Equation 1: Xsmoothie + Ysmoothie = 24 + 25 = 49 oz
Using the ratio of 4 is to 1 for Xsmoothie then, we know 4/(1+4) is P juice in Xsmoothie
Using the ratio of 1 is to 5 for Ysmoothie, we know 1/(1+5) is P jiuce in Ysmoothie

Equation 2: (4/5)X + (1/6)Y = 24

Let us now solve for x:
(4/5)X + (1/6)(49-X) = 24
24x + 5(49-x) = (24)(30)
24x + 245-5x = (24)(30)
19x = 720 -245
19x = 475
x=25

There is (4/5)(25) in Xsmoothie.
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26 Apr 2011, 07:58
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shalu wrote:
24 oz of juice P and 25 oz of juice V are mixed to make smothies X and Y . The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?

Let there be x units of smothies X and y units of smothies Y.
For X:
P = 4x/5
V= x/5

For Y
P= y/6
V= 5y/6

Also, 4x/5 + y/6 = 24 ( 24 oz of P )--------(1)
x/5 + 5y/6 = 25 ( 25 oz of V)--------(2)
Solving above two equations: x= 25, y= 24

Hence, ounces of juice P contained in smothie X = 4x/5 => 4*25/5 = 20.

OA. 20.
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Manager
Joined: 07 Oct 2010
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26 Apr 2011, 08:04
Easy way to solve this question is start from the answer and then conform the information provided in the question.

we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to V ratio is 4:1

this gives us that quantity of juice P in X = 20 therefore quantity of Juice V will be 5 ... hence ratio = 4:1

This will lead to quantity of juice P in X = 4 and quantity of Juice V = 20 ... hence ratio 1:5

if we calculate total Juice P = 24 and total of juice V = 25
it fits because totals are same as what mentioned in the question ...

thus ans is D
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26 Apr 2011, 09:03
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p1 + p2 = 24

v1 + v2 = 25

p1 = 4v1

p2 = v2/5

4v1 + v2/5 = 24

v1 + v2 = 25

4v2 - v2/5 = 76

19v2/5 = 76 => v2 = 20

=> v1 = 5

=> p1 = 20

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26 Apr 2011, 18:52
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shalu wrote:
24 oz of juice P and 25 oz of juice V are mixed to make smothies X and Y . The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?

5
10
15
20
25

There isn't much of mixture concept you need here. It is actually based on ratios.
Smoothie X -> Juice P: 4n oz, Juice V: n oz
Juice P left for Smoothie Y: 24 - 4n
Juice V left for Smoothie Y: 25 - n
Smoothie Y ratio of P/V = $$\frac{1}{5} = \frac{(24-4n)}{(25-n)}$$
n = 5
Juice P in smoothie X = 4*5 = 20 oz
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing. Affiliations: University of Chicago Booth School of Business Joined: 03 Feb 2011 Posts: 807 Re: mixture problem [#permalink] ### Show Tags 26 Apr 2011, 20:54 Karishma Pls see this. Lets evaluate the ratio of X : Y. If I mix X and Y smoothie then they should yield the ratio of p:q = 24:25. The net ratio is 24:25 or 0.96 (mean) The ratio of X is 4:1 or 4.0 The ratio of Y is 1:5 or 0.2 Since the ratio of Y is near the weighted mean, when I combine X and Y then Y > X i.e. the quantity of Y is more than that of X -----(1) However, I am getting X = 25 oz and Y = 24 oz by using algebra - exactly opposite of inference (1). I thought that quantity that is closer to mean will pull the mean - the quantity of Y should be more. Did I miss something? On the other hand equations yield- In X : p and q are in ratio 4a:a In Y : p and q are in ratio b:5b Now, 4a + b = 24 (total quantity of juice P) a + 5b = 25 (total quantity of juice Q) Solving we get a = 5, b = 4 Hence X = 5a = 5 * 5 = 25 oz Y = 6b = 6*4 = 24 oz or X : Y = 25 : 24 VeritasPrepKarishma wrote: There isn't much of mixture concept you need here. It is actually based on ratios. Smoothie X -> Juice P: 4n oz, Juice V: n oz Juice P left for Smoothie Y: 24 - 4n Juice V left for Smoothie Y: 25 - n Smoothie Y ratio of P/V = $$\frac{1}{5} = \frac{(24-4n)}{(25-n)}$$ n = 5 Juice P in smoothie X = 4*5 = 20 oz Director Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing. Affiliations: University of Chicago Booth School of Business Joined: 03 Feb 2011 Posts: 807 Re: mixture problem [#permalink] ### Show Tags 27 Apr 2011, 19:42 VeritasPrepKarishma wrote: 24/25 doesn't have any physical meaning. Thanks ! So for using the "balance" I can use any one of the ingredients in the mix. Current Student Joined: 06 Sep 2013 Posts: 1901 Concentration: Finance Re: 24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink] ### Show Tags 22 Nov 2013, 08:45 5 This post received KUDOS 2 This post was BOOKMARKED shalu wrote: 24 oz of juice P and 25 oz of juice V are mixed to make smothies X and Y . The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X? A. 5 B. 10 C. 15 D. 20 E. 25 Pretty straightforward. For X: P/V = 4X/X For Y: P/V = Y/5Y Then 4x + y = 24 Also x+5y=25 So x=5 4x = 20 Answer is D Hope it helps Cheers! J Director Joined: 03 Aug 2012 Posts: 830 Concentration: General Management, General Management GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32 GPA: 3.7 WE: Information Technology (Investment Banking) Re: 24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink] ### Show Tags 18 Apr 2014, 21:43 24-P 25-V Solutions X and Y X - P:V = 4:1 Y - P:V = 1:5 Now since total P and V are consumed to make X and Y, so 4X + Y = 24 X + 5Y = 25 X=5 We need to know what is 4X Hence 20 _________________ Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________ Current Student Joined: 06 Sep 2013 Posts: 1901 Concentration: Finance Re: 24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink] ### Show Tags 23 Apr 2014, 13:31 TGC wrote: 24-P 25-V Solutions X and Y X - P:V = 4:1 Y - P:V = 1:5 Now since total P and V are consumed to make X and Y, so 4X + Y = 24 X + 5Y = 25 X=5 We need to know what is 4X Hence 20 Same way I did it. Bunuel could you please validate? Thanks Cheers! J SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1837 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: 24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink] ### Show Tags 23 Apr 2014, 22:47 1 This post received KUDOS 1 This post was BOOKMARKED Mixture I P solution = p V solution = v Mixture II P solution = 24-p V solution = 25-v Total = 49 ounces Ratio in Mixture I $$\frac{p}{v} = \frac{4}{1}$$ Ratio in Mixture II $$\frac{24-p}{25-v} = \frac{1}{5}$$ Solving both equations above, p = 20 Answer = D _________________ Kindly press "+1 Kudos" to appreciate Manager Joined: 07 May 2015 Posts: 93 Re: 24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink] ### Show Tags 02 Aug 2015, 18:19 shalu wrote: 24 oz of juice P and 25 oz of juice V are mixed to make smothies X and Y . The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X? A. 5 B. 10 C. 15 D. 20 E. 25 This is how I did it and just want to make sure that this is a correct approach and not just a co-incidence. x = p/v = 4/1 y = p/v = 1/5 so asusming that total solution is a multiple of = 5 ( taking 1 from first fractions denominator and 5 from second denominator so 5x1 = 5) So x = 4x5/1x4 = 20/4 y = 1x5/5x5 = 5/25 Hence P in X = 20 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8064 Location: Pune, India Re: 24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink] ### Show Tags 02 Aug 2015, 23:34 1 This post received KUDOS Expert's post neeraj609 wrote: shalu wrote: 24 oz of juice P and 25 oz of juice V are mixed to make smothies X and Y . The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X? A. 5 B. 10 C. 15 D. 20 E. 25 This is how I did it and just want to make sure that this is a correct approach and not just a co-incidence. x = p/v = 4/1 y = p/v = 1/5 so asusming that total solution is a multiple of = 5 ( taking 1 from first fractions denominator and 5 from second denominator so 5x1 = 5) So x = 4x5/1x4 = 20/4 y = 1x5/5x5 = 5/25 Hence P in X = 20 Not sure what you did here. Cannot say if it is correct. "total solution is a multiple of = 5 ( taking 1 from first fractions denominator and 5 from second denominator so 5x1 = 5)" doesn't sound correct. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: 24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink]

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12 Nov 2016, 21:52
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24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink]

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12 Nov 2016, 23:38
shalu wrote:
24 oz of juice P and 25 oz of juice V are mixed to make smothies X and Y . The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?

A. 5
B. 10
C. 15
D. 20
E. 25

total ounces in X are divisible by 5
total ounces in Y are divisible by 6
if X+Y=49, then
X must have a ones digit of 5
Y must have a ones digit of 4
only possible option for X=25 ounces
25*4/5=20 ounces of P in X
D
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Re: 24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink]

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04 Sep 2017, 07:49
I somehow did (4/5)*24=19.2 and since it was close to 20, assumed it to be the answer. Was my approach on the right track?
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24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink]

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Updated on: 08 Sep 2017, 07:13
I understand the answer is D.

My approach was to create as many equations as possible:
X+Y=49 (Eq 1)
Px+Py=24 (Eq 2)
Vx+Vy=25 (Eq 3)
X=Px/Vy=4/1=Px=4Vy (Eq 4)
Y=Px/Vy=1/5=Px=Vy/5 (Eq 5)

Then I saw, I can substitute Px=4Py in Eq 2.
I did that to get the following:
4Py+Py=24
5Py=24
Py=4.8
Px+4.8=24
Px=24-4.8=19.2.

Please help me understand where is my understanding wrong/what is the concept here/where am I going wrong?

Originally posted by aashishagarwal2 on 08 Sep 2017, 03:23.
Last edited by aashishagarwal2 on 08 Sep 2017, 07:13, edited 1 time in total.
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Re: 24 oz of juice P and 25 oz of juice V are mixed to make smot [#permalink]

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08 Sep 2017, 05:22
Total juice = 24+25=49 (X+Y=49)
P juice in X is 4/5X.
V juice in Y is 1/6Y
Then
4/5X+1/6Y=24
CALCULATE X=25.
IN X, JUICE P equals to 4/5*25=20.

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Re: 24 oz of juice P and 25 oz of juice V are mixed to make smot   [#permalink] 08 Sep 2017, 05:22
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