difficult problem solving question...

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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 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
[spoiler]
The OA given is A[/spoiler]. I did not get it.. please help....[/img]

[sam2304]

orange juice = 1:3 => 1 can of juice concentrate to 3 cans of water

200 6 ounce servings = 100 12 ounce servings of orange juice.

So we need 25 cans of concentrate + 75 cans of water to make 100 12 ounce servings of orange juice or 200 6 ounce servings of juice.

IMO A.

[mdavidm_531]

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 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
[spoiler]
The OA given is A[/spoiler]. I did not get it.. please help....[/img]

I think this question requires a firm grasp of ratios.

I also had a hard time answering this question but after a while you'll get the entire logic behind it. Here's my though process.

The first idea that helped me solve this is to drill in my head that ratios should be of the same units. For example, 1:3 should be 1 can:3 cans or 2:4 should be 2 phones:4 phones

As such, if we present the ratios in this question it should be cans:cans or ounces:ounces

The second idea that helped me solve this is to think logically that if you add one can and three cans then you have four cans (this should be intuitive). Know this by heart because you will use this in other problems (e.g. mixture, etc.)

Third, I always remind myself that the GMAT is just trying to confuse me. The problem is simple in itself, it just becomes hard because the GMAT is twisting it a little bit.

Now let's go to the problem.

The problem gives us the ratio:

1 can of concentrate : 3 cans of water : 4 cans of orange juice (see how I arrived at 4?)

Now how would you interpret the second part of the statement?

200 6-ounce servings would be equal to 1,200 ounces, right?

as such we have the ratio:

ounces of concentrate : ounces of water : ounces of orange juice

we fill up the "ounces of orange juice"

ounces of concentrate : ounces of water : 1,200 ounces of orange juice

So how do we go ahead from here? Remember that we have the ratio 1:3:4

As such we could use unknown multiplier 4x = 1,200 x = 300

As such we have 1(300):3(300):4(300)
multiplying we have 300 ounces of concentrate : 900 ounces of water : 1200 ounces of orange juice

Now, what is the question asking for? How many 12-ounce cans of concentrate

Now that we have the total ounces of concentrate, we just divide it by 12.
300 ounces of concentrate/12 ounces/can = 25 cans

Answer A

[aneesh.kg]

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 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
[spoiler]
The OA given is A[/spoiler]. I did not get it.. please help....[/img]

How much Orange Juice is required to be prepared?
200*6 ounces = 1200 ounces

In Orange Juice,
(Concentrate/Water) = 1/3
or
(Concentrate/Juice) = 1/4

In 1200 ounces, Amount of concentrate = (1/4)*(1200) = 300 ounces

How many cans of concentrate do we require?
Since each can has 12 ounces of concentrate,
Number of cans of concentrate = (300/12) = 25

[spoiler](A)[/spoiler] is correct.