How many 12 ounces cans of Orange juice is required?

[shrads.jp]

Yet another pick from GMAT Prep...

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?
1) 25
2) 34
3) 50
4) 67
5) 100

OA - 25

My approach -->
Since the ratio of concentrate to water is 1:3 so in a can of 12 ounce concentrate the water required will be 12 * 3= 36 ounce
So therefore if there are "˜X’ cans of 12- ounces then the juice will be
(12+36) * X which is the required quantity.
i.e
48 * x = 200 * 6
So X= 25

Pls correct if the approach is wrong
Thanks

[RonPurewal]

Yet another pick from GMAT Prep...

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?
1) 25
2) 34
3) 50
4) 67
5) 100

OA - 25

My approach -->
Since the ratio of concentrate to water is 1:3 so in a can of 12 ounce concentrate the water required will be 12 * 3= 36 ounce
So therefore if there are "˜X’ cans of 12- ounces then the juice will be
(12+36) * X which is the required quantity.
i.e
48 * x = 200 * 6
So X= 25

Pls correct if the approach is wrong
Thanks

looks good.

[Gerald.M.Williams]

Or:

1: 3 ratio Concentrate: Water
200 * 6 Oz = 1200 total ounce of Juice containing proportionate 300 ounce concentrate

Therefore 300/12 = 25 cans of concentrate required

[mschwrtz]

Fine, but you're doing a bit in your head that OP spelled out. Concentrate:water:juice=1:3:4=300:900:1200

[dianapaolasanchez]

1 : 3 : 4; orange juice concentrate : water : orange juice

and, 200 6-ounce = 100 12-ounce

4/100=1/x
x=100/4
x=25

[RonPurewal]

1 : 3 : 4; orange juice concentrate : water : orange juice

and, 200 6-ounce = 100 12-ounce

4/100=1/x
x=100/4
x=25

that works, too.

[I_need_a_700plus]

Any chance someone can explain this a different way? I'm having a hard time following the explanations.

Thanks!

[RonPurewal]

Any chance someone can explain this a different way? I'm having a hard time following the explanations.

Thanks!

Just do this problem the way you'd do it in your kitchen at home.

If you were actually going to make orange juice, there's no way you would have any difficulty with this problem at all -- it's thinking of it as "academic" that causes all the trouble.

1 can of concentrate is to be mixed with 3 cans of water to make orange juice.

This means that every 1 can of concentrate + 3 cans of water makes 4 cans of orange juice. So, whatever amount of concentrate you started with, you'll have 4 times that much juice. (Just think about ilterally pouring two liquids together.)

You want 1200 ounces of orange juice.
So, that's 1200/4 = 300 ounces of concentrate.
There are 12 ounces of concentrate in a can, so that's 300/12 = 25 cans.

[GauravB257]

The "imagining the scenario in the kitchen" works perfectly! Thanks!!

[tim]

Good advice in general for math problems - and critical reasoning as well!

[RonPurewal]

The "imagining the scenario in the kitchen" works perfectly! Thanks!!

there are many many things on this exam whose real-world equivalents are shockingly easy. (this is an even more apt observation on critical reasoning, where almost every problem becomes perfectly clear if translated into appropriate real-world terms.)

the problem, of course, lies in breaking down that giant Berlin Wall that has been erected between 'real world' and 'academic stuff' inside your brain.

[sahilk47]

Hi Ron

The question says: 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.

I am not able to understand why is the ratio Concentrate: Water: Juice = 1: 3: 4

Why don't we have 1 in place of the ratio component of Juice 4 there ? We are not told that we are making 4 cans of Juice.

Please guide.

Thank you.

[tim]

We are very clearly told that we are making 4 cans of juice. If you mix 1 can of concentrate with 3 cans of water, how much juice does that make?

[numberonelabouchefan]

Aren't all these explanations assuming that each can of water is the same volume as each can of concentrate(12 oz). This is never explicitly stated in the question and therefore isn't it possible that we would get a different answer for different volumes per can of water???

[Sage Pearce-Higgins]

Yes, the problem is assuming that. Part of dealing with these word problems is the challenge of interpreting the phrasing to make sense of the situation. Actually, your comment opens the way to a very useful approach: reductio ad absurdum. If we followed your suggestion that the cans of water could have different volumes, then we would have no way of answering the problem. Any of the answers could be correct and the problem would make no sense at all. Since this is an absurd result, that suggestion (that the cans could have different volumes) is wrong. On reflection, if someone says: "mix one can of X with 3 cans of Y", they mean "mix X and Y in the ration 1:3"; that's just how we use language.