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SVP  V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1702
Location: India
GPA: 3.01
WE: Engineering (Real Estate)
A juice company is creating a new fruit punch that is 60% orange juice  [#permalink]

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18 00:00

Difficulty:   95% (hard)

Question Stats: 46% (02:56) correct 54% (03:09) wrong based on 158 sessions

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A juice company is creating a new fruit punch that is 60% orange juice, 25% grape juice, and 15% apple juice by weight. If the cost for the company is x cents per kg for orange juice, y cents per kg for grape juice, and z cents per kg for apple juice, is the cost of k kg of the fruit punch more than d dollars?

1. $$12x+5y+3z >$$ $$\frac{2000d}{k}$$

2. $$10d$$ $$=$$$$2^$$$$\sqrt{3x}$$ $$=$$ $$\sqrt{5y}$$$$=$$$$\sqrt{3z}$$$$=$$ $$\frac{100}{k}$$

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Math Expert V
Joined: 02 Aug 2009
Posts: 8305
Re: A juice company is creating a new fruit punch that is 60% orange juice  [#permalink]

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QZ wrote:
A juice company is creating a new fruit punch that is 60% orange juice, 25% grape juice, and 15% apple juice by weight. If the cost for the company is x cents per kg for orange juice, y cents per kg for grape juice, and z cents per kg for apple juice, is the cost of k kg of the fruit punch more than d dollars?

1. $$12x+5y+3z >$$ $$\frac{2000d}{k}$$

2. $$10d$$ $$=$$$$2^$$$$\sqrt{3x}$$ $$=$$ $$\sqrt{5y}$$$$=$$$$\sqrt{3z}$$$$=$$ $$\frac{100}{k}$$

60% orange juice, 25% grape juice, and 15% apple juice by weight.
Means per kg cost = 0.6x+0.25y+0.15z.... is it >100d/k..
So 0.6x+0.25y+0.15z>100d/k.....
$$12x+5y+3z>\frac{20*100d}{k}$$

Let's see what each statement tells us..

Statement I tells us exactly that..
Sufficient

Second statement tells us 12x=5y=3z=10d*10d..
Therefore 12x+5y+3z=3*10d*10d=3*10d*100/k=3000d/k which is >2000d/k
Ans YES
Sufficient

D
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Joined: 15 Jan 2017
Posts: 332
Re: A juice company is creating a new fruit punch that is 60% orange juice  [#permalink]

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I thought of a slightly different approach. Please give me kudos if it you felt this method was useful.
Basically the stem asks if K > D? (kg or dollar)

1) 12x + 5y + 3z > 2000D/ k
subsituting values from above --> 12[0.6] + 5[0.25] + 3[0.15]> 2000D/K

[8.9] > 2000DK

so K [8.9]> 2000K --> if ~9 of k> 2000 * D --> of course K>D . suff

2) we can directly ignore the variables in the middle and see 100 d^2 = 100^2/ K --> d = 10/ K. D = K = 1 cannot happen but DK = 10 can. In each case [1,10,5,2..fitting back into D = 10/ K] D < K.

Manager  B
Joined: 07 May 2018
Posts: 61
Re: A juice company is creating a new fruit punch that is 60% orange juice  [#permalink]

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chetan2u wrote:
QZ wrote:
A juice company is creating a new fruit punch that is 60% orange juice, 25% grape juice, and 15% apple juice by weight. If the cost for the company is x cents per kg for orange juice, y cents per kg for grape juice, and z cents per kg for apple juice, is the cost of k kg of the fruit punch more than d dollars?

1. $$12x+5y+3z >$$ $$\frac{2000d}{k}$$

2. $$10d$$ $$=$$$$2^$$$$\sqrt{3x}$$ $$=$$ $$\sqrt{5y}$$$$=$$$$\sqrt{3z}$$$$=$$ $$\frac{100}{k}$$

60% orange juice, 25% grape juice, and 15% apple juice by weight.
Means per kg cost = 0.6x+0.25y+0.15z.... is it >100d/k..
So 0.6x+0.25y+0.15z>100d/k.....
$$12x+5y+3z>\frac{20*100d}{k}$$

Let's see what each statement tells us..

Statement I tells us exactly that..
Sufficient

Second statement tells us 12x=5y=3z=10d*10d..
Therefore 12x+5y+3z=3*10d*10d=3*10d*100/k=3000d/k which is >2000d/k
Ans YES
Sufficient

D

Hi,

Could you explain the detailed working out of the below:

"Second statement tells us 12x=5y=3z=10d*10d..
Therefore 12x+5y+3z=3*10d*10d=3*10d*100/k=3000d/k which is >2000d/k"
Manager  B
Status: As cheeks from my insta feed say: soon...
Joined: 17 Jan 2016
Posts: 56
Re: A juice company is creating a new fruit punch that is 60% orange juice  [#permalink]

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menonrit wrote:
chetan2u wrote:
QZ wrote:
A juice company is creating a new fruit punch that is 60% orange juice, 25% grape juice, and 15% apple juice by weight. If the cost for the company is x cents per kg for orange juice, y cents per kg for grape juice, and z cents per kg for apple juice, is the cost of k kg of the fruit punch more than d dollars?

1. $$12x+5y+3z >$$ $$\frac{2000d}{k}$$

2. $$10d$$ $$=$$$$2^$$$$\sqrt{3x}$$ $$=$$ $$\sqrt{5y}$$$$=$$$$\sqrt{3z}$$$$=$$ $$\frac{100}{k}$$

60% orange juice, 25% grape juice, and 15% apple juice by weight.
Means per kg cost = 0.6x+0.25y+0.15z.... is it >100d/k..
So 0.6x+0.25y+0.15z>100d/k.....
$$12x+5y+3z>\frac{20*100d}{k}$$

Let's see what each statement tells us..

Statement I tells us exactly that..
Sufficient

Second statement tells us 12x=5y=3z=10d*10d..
Therefore 12x+5y+3z=3*10d*10d=3*10d*100/k=3000d/k which is >2000d/k
Ans YES
Sufficient

D

Hi,

Could you explain the detailed working out of the below:

"Second statement tells us 12x=5y=3z=10d*10d..
Therefore 12x+5y+3z=3*10d*10d=3*10d*100/k=3000d/k which is >2000d/k"

menonrit

Square the entire line and substitute (10d)^2 with 10d*100/K
Intern  B
Joined: 07 Sep 2019
Posts: 5
Re: A juice company is creating a new fruit punch that is 60% orange juice  [#permalink]

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Means per kg cost = 0.6x+0.25y+0.15z.... is it >100d/k.. -- how did we get this statement. Can you please explain Re: A juice company is creating a new fruit punch that is 60% orange juice   [#permalink] 02 Dec 2019, 00:54
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