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How many cans of orange concentrate???

This topic has 3 expert replies and 3 member replies

How many cans of orange concentrate???

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I came across this problem while solving the GMAT Prep

Question: If 1 can of orange concentrate requires 3 can of water to make orange juice. How many 12 ounce cans of orange concentrate are required to prepare 200 6 ounce serving of orange juice?
A. 25
B. 34
C. 50
D. 67
E. 100

Answer: A

Pls help me with this question!

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sbhawal wrote:
I came across this problem while solving the GMAT Prep

Question: If 1 can of orange concentrate requires 3 can of water to make orange juice. How many 12 ounce cans of orange concentrate are required to prepare 200 6 ounce serving of orange juice?
A. 25
B. 34
C. 50
D. 67
E. 100

Answer: A

Pls help me with this question!
Concentrate (C) Water (W)

The ratio C to W is 1 to 3 in the prepared orange juice. Hence, if x number of 12-ounce cans of C are required to prepare 200 6 ounce serving of orange juice, then the total orange juice made will be 200 times 6 or 1200 ounce. In those 1200 ounces, 1part is C, and 3 parts W. Means 300 ounces of C and 900 ounces of W.

Now ask over how many 12 ounce cans of orange concentrate are required. Just divide 300 by 12 to answer 25.


Take A

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Hi Sbhawal,

What given in the question is,

1 can of Orange Concentrate + 3 can of water = 4 can of orange Juice

What we asked to find is,
for 1200 ounce of orange juice how many 12 ounce of orange concentrate are required.

Multiply first equation by 300

300 can of orange concentrate + 900 can of water = 1200 can of orange juice

300/12 = 25

Hence answer is A

Regards,
Uva.

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Quote:
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 prepate 200 6-ounce servings of orange juice?

A) 25
B) 34
C) 50
D) 67
E) 100
Total = 200 6-ounce servings = 200*6 = 1200 ounces.
Since each can = 12 ounces, the total = 1200/12 = 100 cans.
In these 100 cans of mixture, since concentrate:water = 1:3 and 1+3=4, concentrate/total = 1/4.
Thus, in the 100 cans of mixture, the number of cans of concentrate = (1/4)100 = 25.

The correct answer is A.

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sbhawal wrote:
If 1 can of orange concentrate requires 3 can of water to make orange juice. How many 12 ounce cans of orange concentrate are required to prepare 200 6 ounce serving of orange juice?
A. 25
B. 34
C. 50
D. 67
E. 100

Here's a slightly different approach that uses equivalent ratios.

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. This is acceptable since 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 x = 25
So, the answer is A

Cheers,
Brent

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Using ratios:

Orange:Water:Total
1:3:4
x 50 becomes
50:150:200 (6 oz servings)
25:75:60 (12oz servings)

So answer = 25

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Junior | Next Rank: 30 Posts Default Avatar
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Thanks Brent!!
Your explanation worked the best for me.



Brent@GMATPrepNow wrote:
sbhawal wrote:
If 1 can of orange concentrate requires 3 can of water to make orange juice. How many 12 ounce cans of orange concentrate are required to prepare 200 6 ounce serving of orange juice?
A. 25
B. 34
C. 50
D. 67
E. 100

Here's a slightly different approach that uses equivalent ratios.

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. This is acceptable since 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 x = 25
So, the answer is A

Cheers,
Brent

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