For the life of me I can't seem to wrap my head around this question, any short cuts for this one? I've tried putting this into a linear equation but to no avail.
Help me solve this GMAT Quant Question (GMATPrep) #5
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- EricImasogie
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This can be solved using equivalent ratios.According to the direction 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 of the concentrate are required to prepare 2006-ounce serving of orange juice.
A)25
B)34
C)50
D)67
E)100
OAA
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'll 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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Hi EricImasogie,
One of the great aspects about most GMAT questions is that they can be approached in a variety of ways. Here, even the "math approach" can be done in a number of different ways. Here's another:
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
GMAT assassins aren't born, they're made,
Rich
One of the great aspects about most GMAT questions is that they can be approached in a variety of ways. Here, even the "math approach" can be done in a number of different ways. Here's another:
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
GMAT assassins aren't born, they're made,
Rich
- EricImasogie
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Thanks guys. I guess the real confusion for me was believing or assuming that the 1 can of concentrate + 3 cans of water was used to actually make 4 cans of orange juice. The problem didn't state this explicitly but i guess you could assume that 4 cans of orange juice is being made.
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I'd do this this way.
Our ratio of concentrate to water = 1 : 3. This means that we have FOUR total parts, ONE of which is concentrate. So the concentrate is 1/4 of the total.
If we're making 200*6, or 1200 ounces, we know that 1/4 of that, or 300 ounces, must be concentrate.
If we're using 12 ounce cans, we must use 300/12, or 25 such cans, so A.
Lots of deductions here - not as easy as it looks!
Our ratio of concentrate to water = 1 : 3. This means that we have FOUR total parts, ONE of which is concentrate. So the concentrate is 1/4 of the total.
If we're making 200*6, or 1200 ounces, we know that 1/4 of that, or 300 ounces, must be concentrate.
If we're using 12 ounce cans, we must use 300/12, or 25 such cans, so A.
Lots of deductions here - not as easy as it looks!