According to the directions on a can of frozen orange juice concentrat

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 an orange juice. How many 12 ounce cans of concentrate are required to prepare 200 6-ounce servings of orange juice?

A. 25
B. 34
C. 50
D. 67
E. 100

\(\frac{concentrate}{juice}=\frac{1}{4}\), as 1 part of concentrate is to be mixed with 3 parts of water to get 4 parts of juice;

200 6-ounce of orange juice = 100 12-ounce of orange juice;

As 1/4 th 100 12-ounce of orange juice must be concentrate --> 100*1/4=25 12-ounce of cans of concentrate are required.

Answer: A.
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We need concentrate:water in 1:3 ratio.

We need to prepare 200 x 6-ounce servings or 1200 ounces
Let there be x ounces of concentrate and hence 3x ounces of water

x+3x=1200 , so x=300 ounces

How many cans ? 300/12 = 25

Answer is (A)
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1 can --->12 ounce (Orange Concentrate)
3(water Can)+1(Orange Concentrate) =12*4=48 ounce
total cans of concentrate needed=200*6/48=25

I'm surprised I got this right...here's how I approached this.
X can concentrate : 3X can water is given as the ratio
200 cans of 6 oz each = 1200 oz total fluid.

x+3x = 1200
Therefore x=300 oz of orange juice concentrate
Now we are asked how many 12 oz cans of concentrate are required. From 300, 12 goes 25 times so the answer is A

Hi Bunuel,

How do we know that the can is of 12-ounce? Because its given in the last sentence that how many 12-ounce cans are required. But its not given that the can of concentrate in the mixture: (1 can of concentrate + 3cans of water) is of 12-ounce.

Please clarify.

That's true. But what the first sentence is saying is that 1 part of concentrate is to be mixed with 3 parts (thrice of that of concentrate) of water to make an orange juice. So, whatever amount of concentrate you take, you'll have to mix it with 3 times as much water.

Does this make sense?
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Total juice prepared = 200*6 = 1200

Orange juice concentrate required\(= \frac{25}{100} * 1200 = 300\)

12 ounce jars required\(= \frac{300}{12} = 25\)

Answer = A

Hi,

I know this might be a really simple problem for most, but I am somehow not able to understand this one. Could you someone please explain this step by step at the earliest as I taking the GMAT in a week and don't wanna commit a mistake on a simple ratio problem.

Thanks

Hi aj0809,

This question comes down to how you choose to organize your work and do the math (and there are several ways to approach the math, including TESTing THE ANSWERS). 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:

GMAT assassins aren't born, they're made,
Rich
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How much counts for the GMAT score mixture problems?
I have some difficulties to solve them, for this reason I am used to take an educated guess always.
Can you recommend some sources where I can learn and make some practice?

Here is how I have solved the question. Please give me some feedback about it.

we have the ration of 1 Can of juice oncentrate, to 3 can of water; 1:3.
The question asks how many 12 ounces of juice we need to 200 6 ounce servings (total of 1200);
So I set the following proportion: 1:3=12:x, which gives me x=36;
So I know that for every 12 ounce of concentrate, there are 26 ounces of water that make a total of 48 ounces (water + juice);
Dividing 1200 by 48 I get the desired result --> 25 :D

hi
you are correct in your approach..

An easier and less time consuming method would be..
we have to prepare 200 6-ounces of juice..
200 6-ounces is same as 100 12-ounces, since rae concentrate is in 12 ounces can..
we also know from 1:3 ratio that the concentrate forms 1/4 of this total..
1/4 of 100 = 25, this is the answer we are looking for..
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Try to bring everything in one unit of measurement.
4 cans of orange juice = 1 can of concentrate + 3 cans of water.
Hence 1 can of juice contains 1 part concentrate and 3 parts water.

Required: How many 12 ounce cans of the concentrate are required to prepare 200 6 ounce servings of orange juice?

We would calculate everything in the form of 12 ounce cans.
200 6 ounce juice = 100 12 ounce juice.

For 100 12 ounce juice, 23 need (1/4)*100 cans of concentrate and (3/4)*100 cans of water. Each measuring 12 ounce

Hence 12 ounce cans of concentrate needed = (1/4)*100 = 25 cans

Correct Option: A

don't you need to know how many oz are in the one can of concentrate that is mixed with the 3 cans of water? Why doesn't that matter?

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Hi Nawz,

You bring up a fair point. However, the prompt does define "12-ounce can" as the 'unit of measurement' - so we're meant to infer that we're dealing with 12-ounce cans of everything. If you don't make that inference, then the question cannot be answered.

GMAT assassins aren't born, they're made,
Rich
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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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We are given that in order to make orange juice, 1 can of concentrate is used and 3 cans of water. Thus, we can set up the following ratio:

Concentrate: water = x : 3x

We need to determine how many cans of concentrate are needed to prepare 200 6-ounce servings of orange juice, or 200 x 6 = 1,200 ounces.

We can create the following equation to determine the number of ounces of concentrate needed:

x + 3x = 1,200

4x = 1,200

x = 300 ounces of concentrate is needed

Since there are 12 ounces per can, 300/12 = 25 cans are needed to make 1,200 ounces of orange juice.

Answer: A
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Hi EMPOWERgmatRichC, Could you help me with a small query?
I know I might sound silly asking this but I got this question on my Practice test and I thought this question was easy until I came across this wording, .
Why should we multiply 200*6-ounce servings?
Isn't it 6-ounce per servings and 200 is the total? (That's what I thought at first. Anyways I am still not clear... )

Thank You,
Dablu

Hi Dablu,

You might find it useful to think in terms of what the individual 'pieces' of the wording actually mean. For example, if the prompt stated... "200 servings of juice"... then we would know the number of servings (but we would NOT not how big a 'serving' was).

If the prompt stated... "one 6-ounce serving"... then we would know exactly how much juice is required (re: one 6-ounce serving would be 6 total ounces).

The prompt refers to "200 6-ounce servings", so each serving is 6-ounces and there are 200 servings... so (6)(200) = 1200 total ounces.

GMAT assassins aren't born, they're made,
Rich
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Given: 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 an orange juice.

Asked: How many 12 ounce cans of concentrate are required to prepare 200 6-ounce servings of orange juice.

1 can of concentrate & 3 cans of water makes = 4 cans of orange juice
1 can of orange juice = 1/4 cans of concentrate
200 6-ounce serving of orange juice = 100 12-ounce serving of orange juice = (100*1/4 = 25 12 ounce cans of concentrate

IMO A
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