Confusing Word Problem
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Here's one approach: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
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
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Brent
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HI,Emeka N. wrote:Is there some rubric or step process that will work for these types of problems?
the most important thing is to get both the cans in SAME ounces- concentrate is in 12-ounces can and juice or final product is in 6-ounces..
1 ounce concentrate mixes with 3-ounces of water to give us (1+3) ounces of juice..
so 4 ounces of juice requires 1 ounce of concentrate..( that is the ratio of conc/juice = 1/4)
-- 1 ounce will require 1/4 ounce of concentrate..
-- 200 *6 ounce will require 1/4 * 200*6 = 300 ounces..
But we are looking at number of 12 ounces can s of conc = 300/12 = 25
A
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Hi Emeka N.,
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.
GMAT assassins aren't born, they're made,
Rich
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.
GMAT assassins aren't born, they're made,
Rich
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Since our ratio of concentrate to water is 1 : 3, we'll have three times as much water as concentrate.
We've got 200*6 = 1200 ounces total. 1 part of that is concentrate, 3 parts are juice, so concentrate = 1/(1+3) = 1/4 of the total.
That gives us 300 ounces. We've working with 12 ounce cans, so 300 / 12 = 25 cans, and we're set.
We've got 200*6 = 1200 ounces total. 1 part of that is concentrate, 3 parts are juice, so concentrate = 1/(1+3) = 1/4 of the total.
That gives us 300 ounces. We've working with 12 ounce cans, so 300 / 12 = 25 cans, and we're set.