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Party Cranberry is 3 parts cranberry juice and 1 part seltze
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19 Aug 2018, 03:00
19 Aug 2018, 03:00
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Question Stats:
39% (01:25) correct
60% (01:17) wrong based on 142 sessions
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Party Cranberry is 3 parts cranberry juice and 1 part seltzer. Fancy Lemonade is 1 part lemon juice and 2 parts seltzer. An amount of Party Cranberry is mixed with an equal amount of Fancy Lemonade.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The fraction of the resulting mix that is cranberry juice |
The fraction of the resulting mix that is seltzer |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: Party Cranberry is 3 parts cranberry juice and 1 part seltze
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19 Jun 2019, 13:13
19 Jun 2019, 13:13
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sandy wrote:
Party Cranberry is 3 parts cranberry juice and 1 part seltzer. Fancy Lemonade is 1 part lemon juice and 2 parts seltzer. An amount of Party Cranberry is mixed with an equal amount of Fancy Lemonade.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The fraction of the resulting mix that is cranberry juice |
The fraction of the resulting mix that is seltzer |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
GIVEN:
Party Cranberry is 3 parts cranberry juice and 1 part seltzer
So, for every 4 parts of Party Cranberry, there are 3 parts cranberry juice and 1 part seltzer
In other words, Party Cranberry is 3/4 cranberry juice and 1/4 seltzer
Fancy Lemonade is 1 part lemon juice and 2 parts seltzer.
So, for every 3 parts of Fancy Lemonade, there are 1 part lemon juice and 2 parts seltzer
In other words, Fancy Lemonade is 1/3 lemon juice and 2/3 seltzer
IMPORTANT CONCEPT: If EQUAL VOLUMES of 2 solutions are combined, the concentration of the resulting mixture will be the AVERAGE of the 2 solutions.
Example: If 3 liters of a 10% alcohol solution are combined with 3 liters of a 30% alcohol solution, the resulting solution will be 20% alcohol.
Likewise, if 11 liters of 6% alcohol solution are combined with 11 liters of a 7% alcohol solution, the resulting solution will be 6.5% alcohol.
QUANTITY A: The fraction of the resulting mix that is cranberry juice
Party Cranberry is 3/4 cranberry juice, and Fancy Lemonade is 0/4 cranberry juice
So, the fraction of cranberry juice in the resulting mix = (3/4 + 0/4)/2 = 3/8
QUANTITY B: The fraction of the resulting mix that is seltzer
Party Cranberry is 1/4 seltzer, and Fancy Lemonade is 2/3 seltzer
So, the fraction of seltzer in the resulting mix = (1/4 + 2/3)/2 = (3/12 + 8/12)/2 = (11/12)/2 = 11/24
Since 3/8 < 11/24, the answer is B
Cheers,
Brent
General Discussion
Re: Party Cranberry is 3 parts cranberry juice and 1 part seltze
[#permalink]
11 Oct 2019, 01:02
11 Oct 2019, 01:02
4
You can also do this in whole relationship :
Party Cranebery ----> 3:1 -----Sum the parts which will be equal to (3+1) ---- 4
Fancy Lemonade -----> 1:2 ------------------------------------------(1+2) ---- 3
common multiple of both = 12.
party craneberry *3 and fancy * 4
party --> 9 : 3
fancy --> 4 : 8
quantity B is bigger cause seltzer is 11 parts greater than craneberry which 9 parts.
Party Cranebery ----> 3:1 -----Sum the parts which will be equal to (3+1) ---- 4
Fancy Lemonade -----> 1:2 ------------------------------------------(1+2) ---- 3
common multiple of both = 12.
party craneberry *3 and fancy * 4
party --> 9 : 3
fancy --> 4 : 8
quantity B is bigger cause seltzer is 11 parts greater than craneberry which 9 parts.
