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Ratios, Cola, Root Beer and Ginger

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Ratios, Cola, Root Beer and Ginger

by anastasios1984 » Tue Feb 26, 2013 2:55 am
If Pei ordered a total of 63 bottles of Cola, Root Beer ang Ginger, How many of them are Cola bottles?

i) RB= 80/100 Ginger
ii)Cola= 75/100 (Root Beer + Ginger)

From the data given we have an equation with 3 unkown variables. We are looking for the number of Cola bottles. It seems that we are either looking for two equations with two known variables or one equation with the Cola variable included. Is this line of reasoning correct?

If yes, the answer B must also correct because alone is Sufficient.

Looking forward for an answer.
Thanks
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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Feb 26, 2013 3:39 am
anastasios1984 wrote:From the data given we have an equation with 3 unkown variables. We are looking for the number of Cola bottles. It seems that we are either looking for two equations with two known variables or one equation with the Cola variable included. Is this line of reasoning correct?
When there are n unknowns, you need n independent equations to uniquely solve any of them (provided there is no constraints). Hence, if you go by this logic you'll make a mistake to think that you need three equations to solve three unknowns because here we have a constraint, which is all the unknowns are integers and the all the three equations are not independent. If you look closely, you can see that you can replace (R + G) from statement 2 in the main equation.
anastasios1984 wrote:If Pei ordered a total of 63 bottles of Cola, Root Beer ang Ginger, How many of them are Cola bottles?

i) RB= 80/100 Ginger
ii)Cola= 75/100 (Root Beer + Ginger)
(C + R + G) = 63
C, R, and G must be integers only.

Statement 1: 5R = 4G
As R and G are integers, R must be multiple of 4 and G must be multiple of 5.
Consider the following two cases,
  • R = 4, G = 5 ---> C = 54
    R = 8, G = 10 ---> C = 45
Not sufficient

Statement 2: 4C = 3(R + G) ---> (R + G) = 4C/3
Hence, C + 4C/3 = 63 ---> (3C + 4C) = 3*63 ---> 7C = 3*63 ---> C = 3*9 = 21

Sufficient

The correct answer is B.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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