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A bakery sold an average (arithmetic mean) of 820...

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A bakery sold an average (arithmetic mean) of 820...

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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

The OA is E.

I'm really confused with this PS question. Experts, any suggestion about the solution? Thanks in advance.

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Quote:
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

The OA is E.

I'm really confused with this PS question. Experts, any suggestion about the solution? Thanks in advance.
Hi LUANDATO,
Let's take a look at your question.

Let G be the number of good days and F be the number of fair days during the operating period, then
Sum of Cookies during Good days + Sum of Cookies during Fair days = Sum of Cookies during the operating period ... (i)

We know that,
$$\text{Sum of quantities}=\left(Average\right)\left(\text{Number of Quantities}\right)$$

Therefore, we can write Eq(i) as:
(Average cookies during good days)(Number of Good days) + (Average cookies during Fair days)(Number of fair days) = (Average Cookies during operating period)(Number of days in operating period)
$$980G+640F=820\left(G+F\right)$$
$$980G+640F=820G+820F$$
$$980G-820G=820F-640F$$
$$160G=180F$$
$$\frac{G}{F}=\frac{180}{160}$$
$$\frac{G}{F}=\frac{9}{8}$$

Hence, the ratio of the number of "good" days to the number of "fair" days for the bakery's operating period is 9 : 8.

Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
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Hi LUANDATO,

We're told that 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. We're asked for the ratio of the number of "good" days to the number of "fair" days for the bakery's operating period. This question is essentially a 'Weighted Average', so here's how you can use that formula to answer the question:

X = number of 'good' days
Y = number of 'fair days

(980X + 640Y)/(X+Y) = 820

980X + 640Y = 820X + 820Y
160X = 180Y
16X = 18Y
8X = 9Y
X/Y = 9/8

Final Answer: E

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

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Contact Rich at Rich.C@empowergmat.com

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