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Darla decides to mix lemonade with limeade to make a new drink

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Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 17 Jan 2016, 12:39
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Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade?

(A) 3 : 1
(B) 7 : 3
(C) 3 : 2
(D) 4 : 5
(E) 3 : 4
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 17 Jan 2016, 12:55
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harish1986 wrote:
Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade?

(A) 3 : 1
(B) 7 : 3
(C) 3 : 2
(D) 4 : 5
(E) 3 : 4


The lemonade is 50% water and 20% sugar.
The limeade is 40% water and 32% sugar.
The citrusade is more than 45% water and more than 24% sugar.

For the citrusade to be 45% water, the ratio of lemonade to limeade must 1:1. Since the citrusade is more than 45% water (the average of 50 and 40), then the ratio of lemonade to limeade must be more than 1:1. Eliminate D and E.

For the citrusade to be 24% sugar, the ratio of lemonade to limeade must 2:1. Since the citrusade is more than 24% water, then the ratio of lemonade to limeade must be less than 2:1. Eliminate A and B.

Answer: C.
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 17 Jul 2016, 11:41
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let x=lemonade
y=limeade
water:
.5x+.4y>.45(x+y)
x>y
sugar:
.2x+.32y>.24(x+y)
x<2y
plugging in x>y and x<2y, only answer c fits
3:2
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 04 Apr 2016, 19:33
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harish1986 wrote:
Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade?

(A) 3 : 1
(B) 7 : 3
(C) 3 : 2
(D) 4 : 5
(E) 3 : 4


You can use allegation.

To use allegation you relate the weighted averages of percentages of the ingredients to the ratio of the parts of the mixture.

For example if you use a 1:1 ratio of the two parts of the mixture, then the weighted average of the percentages of the ingredients will be the mean of the percentages found in the two parts. in other words, in a 1:1 mixture the weighted average of the percentages will be exactly halfway between the percentages found in each of the ingredients.

The mixture is to contain more than 45% water.

45% is the mean of the percentages of water found in the two parts, lemonade, which contains 50% water, and limeade, which contains 40% water. So a mixture containing a 1:1 ratio of lemonade to limeade would contain 45% water.

Since the mixture is to contain more than 45% water, it must contain more lemonade than limeade.

Eliminate answer choices D and E.

The mixture is also to contain more than 24% sugar. 24% is 1/3 of the way from 20%, the proportion of sugar in lemonade, to 32%, the proportion of sugar in limeade. So to get a sugar percentage greater than 24%, we need the mixture to be more than 1/3 limeade.

A indicates that limeade is 1/4 of the mixture. 1/4 < 1/3. Eliminate A.

B indicates that limeade is 3/10 of the mixture. 3/10 < 1/3. Eliminate B.

C indicates that limeade is 2/5 of the mixture. 2/5 > 1/3.

The correct answer is .
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 22 Aug 2016, 01:54
Bunuel wrote:
harish1986 wrote:
Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade?

(A) 3 : 1
(B) 7 : 3
(C) 3 : 2
(D) 4 : 5
(E) 3 : 4


The lemonade is 50% water and 20% sugar.
The limeade is 40% water and 32% sugar.
The citrusade is more than 45% water and more than 24% sugar.

For the citrusade to be 45% water, the ratio of lemonade to limeade must 1:1. Since the citrusade is more than 45% water (the average of 50 and 40), then the ratio of lemonade to limeade must be more than 1:1. Eliminate D and E.

For the citrusade to be 24% sugar, the ratio of lemonade to limeade must 2:1. Since the citrusade is more than 24% water, then the ratio of lemonade to limeade must be less than 2:1. Eliminate A and B.

Answer: C.


Bunuel can you please explain this further
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 22 Aug 2016, 02:19
deeksha6 wrote:
Bunuel wrote:
harish1986 wrote:
Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade?

(A) 3 : 1
(B) 7 : 3
(C) 3 : 2
(D) 4 : 5
(E) 3 : 4


The lemonade is 50% water and 20% sugar.
The limeade is 40% water and 32% sugar.
The citrusade is more than 45% water and more than 24% sugar.

For the citrusade to be 45% water, the ratio of lemonade to limeade must 1:1. Since the citrusade is more than 45% water (the average of 50 and 40), then the ratio of lemonade to limeade must be more than 1:1. Eliminate D and E.

For the citrusade to be 24% sugar, the ratio of lemonade to limeade must 2:1. Since the citrusade is more than 24% water, then the ratio of lemonade to limeade must be less than 2:1. Eliminate A and B.

Answer: C.


Bunuel can you please explain this further


Can you please be a little bit more specific? Thank you.
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 23 Aug 2016, 01:57
Apologies! I figured out where I was going wrong
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 09 Aug 2017, 07:43
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harish1986 wrote:
Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade?

(A) 3 : 1
(B) 7 : 3
(C) 3 : 2
(D) 4 : 5
(E) 3 : 4


Let Lemonade be LE, Limeade be LI and Citrusade be CI.
So, it can be represented as below.

Water Juice Sugar
LE 50% 30% 20%
LI 40% 28% 32%
CI >45% .... >24%

Now we will use mixture formula.

Let LE/LI be x/y in the mixture CI.
x/y > (45-40)/(50-45). since >45 means skewed towards 50% i.e. LE
x/y >1

Similarly,

x/y <(32-24)/(24-20). Since >24 is skewed towards 32% i.e. LI
x/y <2

So, 1<x/y<2

Only C option satisfies this condition.
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 20 Aug 2017, 03:41
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I used method of elimination and weighted averages (sort of):
Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade?

(A) 3 : 1
(B) 7 : 3
(C) 3 : 2
(D) 4 : 5
(E) 3 : 4

I took a case : 46% water and 25% sugar (as per condition above) --> this would mean more water is overall contributed by lemonade and sugar would be more contributed by limeade. (more than 25% sugar) --> but the water content isn't overwhelmingly high (almost like 46% water, 25% sugar and rest juice = 1/2 water, 1/4th sugar rest juice) --> eliminate A and B
D and E state the opposite --> meaning water content would lower (in comparison to sugar -- sugar content at an average would increase)
This leaves us C which can result in 46% water and 25% sugar
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 20 Aug 2017, 07:41
Using allegation :

Let conc. of water in citrusade be 46%
40.........46.........50
W(lemonade)/W(limeade) = 4/6 = 2/3

Ans. : c
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 11 Oct 2018, 22:52
Let, L for lemonade, l for limeade, C for citrusade
Given ratios for water, lemon juice, and sugar
L = 50 30 20
l = 40 28 32
C = >45 __ >24

Weighted Average formulae = W1/W2 = (A2 - Aavg) / (Aavg - A1)

Since water in Citrusade is >45, let us consider 46

Hence, L/l = (50 - 46) / (46 - 40)
L/l = 4 / 6 = 2 / 3

Option C
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Re: Darla decides to mix lemonade with limeade to make a new drink  [#permalink]

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New post 12 Oct 2018, 00:08
harish1986 wrote:
Darla decides to mix lemonade with limeade to make a new drink called citrusade. The lemonade is 50% water, 30% lemon juice, and 20% sugar. The limeade is 40% water, 28% lime juice, and 32% sugar. If the citrusade is more than 45% water and more than 24% sugar, which of the following could be the ratio of lemonade to limeade?

(A) 3 : 1
(B) 7 : 3
(C) 3 : 2
(D) 4 : 5
(E) 3 : 4


Lemonade: 50% water, 20% sugar, 30% lemon juice
Limeade: 40% water, 32% sugar, 28% lime juice

Citrusade:
>45% water (implies lemonade is more than 1/2. Options (D) and (E) are out)
> 24% sugar
If sugar were exactly 24%, ratio of lemonade/limeade = (32 - 24)/(24 - 20) = 8:4 = 2:1 i.e. lemonade would be 2/3rd of total. But since sugar is more than 24%, lemonade is less than 2/3.

Check for option (C) which has more than 50% lemonade but the least of the leftover 3 options. Option (C) has 3/5 = 9/15 lemonade. This is less than 2/3 i.e. 10/15.
Answer (C)
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Re: Darla decides to mix lemonade with limeade to make a new drink   [#permalink] 12 Oct 2018, 00:08
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