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Cans of OJ concentrate

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by Rastis » Mon Dec 08, 2014 12:49 pm
According to the directions of a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How man 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

a) 25

b) 34

c) 50

d) 67

e) 100
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by [email protected] » Mon Dec 08, 2014 2:27 pm
Hi Rastis,

This question comes down to how you choose to organize your work and do the math. The individual "steps" involved aren't that tough, but you really have to stay organized to work through this question efficiently.

To start, we're given a "recipe" for making orange juice: 1 can of concentrate + 3 cans of water = 4 CANS of juice

Next, we're told that each "can" = 12 ounces. Combined with the prior info (above)....

1 can of concentrate + 3 cans of water = 4 cans of juice = 48 OUNCES of juice

We're told to make 200 6-ounce servings of juice, which is 200(6) = 1,200 ounces of juice. The question asks how many cans of CONCENTRATE are needed to get us 1,200 ounces (according to the recipe).

Since 1 can of concentrate --> 48 ounces of juice, we can do division to figure out the number of cans needed:

1200/48 = 25 cans of concentrate

Final Answer: A

As I mentioned earlier, there are a number of different ways to "do the math" on this question (and you can even TEST THE ANSWERS), so I'm sure that there will be other approaches mentioned by other posters.

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by Brent@GMATPrepNow » Mon Dec 08, 2014 4:45 pm
According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce can of the concentrate are required to prepare 200 6-ounces serving of orange juice?
a)25
b)34
c)50
d)67
e)100
Here's another approach:

The first part tells that, for every 1 can of concentrate, we can make 4 cans of juice.
Let's be even more generic, for 1 volume of concentrate, we can make 4 volumes of juice.

Okay, now notice that we have a problem with the volume mismatch in the question. It involves 12-ounce cans of concentrate and 6-ounce servings.
So, let's reword the question. Instead of making 200 6-ounce servings of juice, let's make 100 12-ounce servings of juice. We're still making the SAME AMOUNT OF JUICE.

We're now asking, "How many 12-ounce cans of the concentrate are required to prepare 100 12-ounce serving of orange juice?

We can solve this question using equivalent ratios.

(volume of concentrate)/(volume of juice): 1/4 = x/100

Solve for x to get [spoiler]x=25[/spoiler]
So, the answer is A

Cheers,
Brent
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by Rastis » Tue Dec 09, 2014 6:19 am
Rich,

Can you show how you would Test the Answers?
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by ceilidh.erickson » Tue Dec 09, 2014 7:59 am
You could easily Test Answers on this question by plugging the answer choices into the given information. When working backwards from the answer, I recommend a) starting with the easiest number, or b) if they all seem easy to work with, start in the middle with answer choice C. That way, you can easily decide whether to go up or down from there.

C) 50
50 cans concentrate means (50)(12) = 600 ounces concentrate
150 cans of water means (150)(12) = 1800 ounces of water
600 + 1800 = 2400 ounces total

We need 200 6-oz servings, in other words 1200 ounces total. 2400 is twice the amount that we need, so we need to go lower. But since it's exactly twice the amount we need, let's try half that amount of concentrate...

A) 25
25 cans concentrate means (25)(12) = 300 ounces concentrate
75 cans of water means (75)(12) = 900 ounces of water
300 + 900 = 1200 ounces total

This is the amount we need, so A is the correct answer.
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by Rastis » Tue Dec 09, 2014 8:29 am
Ceilidh,

Where are you getting 150 cans of water in C) and 75 cans of water in A)?


Jesse
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by ceilidh.erickson » Tue Dec 09, 2014 8:37 am
Apologies: I skipped writing out that step in my explanation. We're told:
1 can of concentrate is to be mixed with 3 cans of water to make orange juice.
So, I simply multiplied the ounces of concentrate by 3 to get the ounces of water in each case.
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by wings.ap » Sat Aug 29, 2015 2:29 am
Here's another way.

Forget all the info given except the ratio and the absolute value.

so ratio is 1 Concentrate : 3 Water
Absolute value is = 200 * 6 = 1200 ounces are needed.
1 can = 12 ounce.
Now 1200/(1 part + 3 part)*12 = 1200/48 = 25

Now once you get thorough with parts in ratio this problem will take you no more than 20 seconds to solve.

Answer is A
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by Max@Math Revolution » Sat Aug 29, 2015 8:40 pm
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.



According to the directions of a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How man 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

a) 25

b) 34

c) 50

d) 67

e) 100
==> As we mix water and orange concentrate to make juice, we need to mix it with ratio 3:1. In other words, water = 3k, concentrate = k and the juice = 3k+1k = 4k. The question asks for how many 12 ounce orange concentrate we need. Since 200 6 ounce concentrate is the same as 100 ounce concentrate, having 100 = 4k, k = 25. Therefore water is 3k = 75, and concentrate is k = 25 Therefore we need 25 cans. Therefore the answer is A.


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by sushantsahaji » Wed Dec 23, 2015 10:05 am
A very easy method is to first simplify the concentrate hitch.

1 can juice con + 3 can water = 48 ounce juice
Total juice req= 1200ounce

if 48ounce - 1 can concentrate
then for 1200 ounce -1200/48= 25
thus ans 25 cans of concentrate
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by Vipul1991 » Sat Aug 12, 2017 10:46 am
Concentrate\Water are in ratio 1:3

12 ounces of orange cans for 200 6 ounce orange juice
Hence 2 - 6 ounces concentrate from 1 - 12 ounce can of concentrate, we need to worry about 100 cans now.

1*x + 3*x=100
4*x=100
x=25
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by Brent@GMATPrepNow » Sat Jan 13, 2018 9:55 am
Rastis wrote:According to the directions of a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How man 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?

a) 25

b) 34

c) 50

d) 67

e) 100
Here's another approach:

The first part tells that, for every 1 can of concentrate, we can make 4 cans of juice.
Let's be even more generic, for 1 volume of concentrate, we can make 4 volumes of juice.

Okay, now notice that we have a problem with the volume mismatch in the question. It involves 12-ounce cans of concentrate and 6-ounce servings.
So, let's reword the question. Instead of making 200 6-ounce servings of juice, let's make 100 12-ounce servings of juice. We're still making the SAME AMOUNT OF JUICE.

We're now asking, "How many 12-ounce cans of the concentrate are required to prepare 100 12-ounce serving of orange juice?

We can solve this question using equivalent ratios.

We're comparing (volume of concentrate)/(volume of juice)

We get: 1/4 = x/100

Solve for x to get x=25

So, the answer is A

Cheers,
Brent
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