A bakery sold an average(arithmetic mean) of 820 cookies per

[alanforde800Maximus]

A bakery sold an average(arithmetic mean) of 820 cookies per day in an operating period. On "good" days, the bakery sold an average of 980 cookies per day, and on "fair" days, the bakery sold an average of 640 cookies per day. If every day in the operating period was either "good" or "fair", what was the ratio of the number of "good" days to the number of "fair" days for the bakery's operating period?


a) 2:1
b) 3:2
c) 5:4
d) 7:6
e) 9:8

Please assist with above problem.

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Hi alanforde800Maximus,

This question can be solved in a couple of different ways. Since it's essentially just a Weighted Average question, here's how you can solve it Algebraically:

G = number of "good" days
F = number of "fair" days

Total Days = G + F

Average of all days = (980G + 640F)/(G + F) = 820

980G + 640F = 820G + 820F
160G = 180F
16G = 18F
8G = 9F

The ratio of the number of 'good' days to the number of "fair" days = G/F

8G = 9F
8G/F = 9
G/F = 9/8

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[crackverbal]

Hi alanforde800Maximus,

Questions of this kind can be easily solved by making use of the mixture diagram given below.



The mixture diagram always gives you a ratio in which two quantities are mixed. The only thing that you need to keep in mind is that the values you need to use as the higher value, lower value and mean value have to be associated with the word 'per' (percents, average, per km, per kg etc.). The mixture diagram can also be used to explain the weighted average concept which is what this question tests you on.

Please find below the mixture diagram approach for the given question.



CrackVerbal Academics Team

[Scott@TargetTestPrep]

A bakery sold an average(arithmetic mean) of 820 cookies per day in an operating period. On "good" days, the bakery sold an average of 980 cookies per day, and on "fair" days, the bakery sold an average of 640 cookies per day. If every day in the operating period was either "good" or "fair", what was the ratio of the number of "good" days to the number of "fair" days for the bakery's operating period?


a) 2:1
b) 3:2
c) 5:4
d) 7:6
e) 9:8

We are given that a bakery sold an average (arithmetic mean) of 820 cookies per day in an operating period, and that on good days the bakery sold an average of 980 cookies per day, and on fair days the bakery sold an average of 640 cookies per day.

If we let G = the number of good days, and F = the number of fair days, we can create the following equation:

820 = (980G + 640F)/(G + F)

820G + 820F = 980G + 640F

180F = 160G

9F = 8G

G/F = 9/8

Answer: E