One morning each member of Angela's family drank a Bounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?
A. 3
B. 4
C. 5
D. 6
E. 7
[spoiler]https://www.gmatmaths.com[/spoiler]
Angela's family drank
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 sanju09
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Can you please check that again, is it Bounce mixture of coffee with milk? That should be a number instead.sanju09 wrote:One morning each member of Angela's family drank a Bounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?
A. 3
B. 4
C. 5
D. 6
E. 7
[spoiler]https://www.gmatmaths.com[/spoiler]
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 sanju09
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If each member of Angela's family drank a Bounce mixture of coffee with milk, then it means that each of them have drunk an equal amount of mixture.[email protected] wrote:Can you please check that again, is it Bounce mixture of coffee with milk? That should be a number instead.sanju09 wrote:One morning each member of Angela's family drank a Bounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?
A. 3
B. 4
C. 5
D. 6
E. 7
[spoiler]https://www.gmatmaths.com[/spoiler]
The mind is everything. What you think you become. Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review  Manya Abroad
Lucknow226001
www.manyagroup.com
Sanjeev K Saxena
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The Princeton Review  Manya Abroad
Lucknow226001
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I'm coming up with [spoiler]5 (inluding Angela)[/spoiler]
I solved it by selecting/plugging in values for the coffee and milk:
6 ounces coffee
4 ounces milk
(10 ounces of milk+coffee total)
Using the above selected values:
1/6 coffee + 1/4 milk = Bounces
1 ounce coffee + 1 ounce milk = 2 ounce mixture
Therefore you can make FIVE 2 ounce mixtures of coffee+milk
Curious to see if my above logic is correct, also, I would like to see an algebraic solution to this.
I wasn't able to solve using variables fast enough...
[/spoiler]
I solved it by selecting/plugging in values for the coffee and milk:
6 ounces coffee
4 ounces milk
(10 ounces of milk+coffee total)
Using the above selected values:
1/6 coffee + 1/4 milk = Bounces
1 ounce coffee + 1 ounce milk = 2 ounce mixture
Therefore you can make FIVE 2 ounce mixtures of coffee+milk
Curious to see if my above logic is correct, also, I would like to see an algebraic solution to this.
I wasn't able to solve using variables fast enough...
[/spoiler]
 anshumishra
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Algebraically :sanju09 wrote:One morning each member of Angela's family drank a Bounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?
A. 3
B. 4
C. 5
D. 6
E. 7
[spoiler]https://www.gmatmaths.com[/spoiler]
n> people in the family
c > no. of cups of coffee
m > no. of cups of milk
As, everybody consumes equal (Bounce) of the mixture (milk/coffee)
=> c/6+m/4 = (c+m)/n
=> 4cn + 6 mn = 24c + 24m
=> 2cn + 3mn = 12c + 12m
=> 3m(n4) = 2c(6n)
Since, m > 0, c> 0, the only integral value of "n" for which both sides have same sign is 5.
Therefore, the answer is 5. C
Thanks
Anshu
(Every mistake is a lesson learned )
Anshu
(Every mistake is a lesson learned )
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@sanju, this is very tricky problem. I first deducted the amounts Angela drank of milk and coffee, and I got 3/4 of milk and 5/6 of coffee left with her family. So the remaining family members' number should be derived from (3M/4 + 5C/6)/(M/4 + C/6) where M is milk and C is coffee. The resulting number should be an integer!
(3M/4 + 5C/6)/(M/4 + C/6) = i {i is integer}
(9M+10C)/(3M+2C) = i OR (9M+10C)=i*(3M+2C).
Now let's try the answer choices. Start with A) (9M+10C)=(31)(3M+2C), we plug in (31) because our ratio does not include Angela. So 9M+10C=6M+4C, and 3M=6C this cannot be correct;
B) (9M+10C)=(41)(3M+2C), 9M+10C=9M+6C, AND 4C=0 this cannot be correct;
C) (9M+10C)=(51)(3M+2C), 9M+10C=12M+8C, AND 3M=2C this is correct;
D) (9M+10C)=(61)(3M+2C), 9M+10C=15M+10C, AND 6M=0 this cannot be correct;
E) (9M+10C)=(71)(3M+2C), 9M+10C=18M+12C, AND 9M=2C this cannot be correct;
answer is C
(3M/4 + 5C/6)/(M/4 + C/6) = i {i is integer}
(9M+10C)/(3M+2C) = i OR (9M+10C)=i*(3M+2C).
Now let's try the answer choices. Start with A) (9M+10C)=(31)(3M+2C), we plug in (31) because our ratio does not include Angela. So 9M+10C=6M+4C, and 3M=6C this cannot be correct;
B) (9M+10C)=(41)(3M+2C), 9M+10C=9M+6C, AND 4C=0 this cannot be correct;
C) (9M+10C)=(51)(3M+2C), 9M+10C=12M+8C, AND 3M=2C this is correct;
D) (9M+10C)=(61)(3M+2C), 9M+10C=15M+10C, AND 6M=0 this cannot be correct;
E) (9M+10C)=(71)(3M+2C), 9M+10C=18M+12C, AND 9M=2C this cannot be correct;
answer is C
sanju09 wrote:One morning each member of Angela's family drank a Bounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?
A. 3
B. 4
C. 5
D. 6
E. 7
[spoiler]https://www.gmatmaths.com[/spoiler]
My knowledge frontiers came to evolve the GMATPill's methods  the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com

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congrats Anshu, nice work done!
anshumishra wrote:Algebraically :sanju09 wrote:One morning each member of Angela's family drank a Bounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?
A. 3
B. 4
C. 5
D. 6
E. 7
[spoiler]https://www.gmatmaths.com[/spoiler]
n> people in the family
c > no. of cups of coffee
m > no. of cups of milk
As, everybody consumes equal (Bounce) of the mixture (milk/coffee)
=> c/6+m/4 = (c+m)/n
=> 4cn + 6 mn = 24c + 24m
=> 2cn + 3mn = 12c + 12m
=> 3m(n4) = 2c(6n)
Since, m > 0, c> 0, the only integral value of "n" for which both sides have same sign is 5.
Therefore, the answer is 5. C
My knowledge frontiers came to evolve the GMATPill's methods  the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com