Problem Solving

Last year Bakery A had total sales of cookies in December that was 4 times the average (arithmetic mean) of the monthly cookie sales totals for January through June and 3 times the average total cookie sales for July through November. The cookie sales total for December was what fraction of the total cookie sales for the year?


(A) 3/14
(B) 6/25
(C) 1/4
(D) 2/3
(E) 12/19

mmmm not sure, B??

Agree with, Cris! It should be - 6/25 i.e. B.
Dec : Cookies sold = 12x (Say)
Jan - Jun: Cookies sold = avg cookies sold * no of months = 3x * 6 = 18x
Jul-Nov: Cookies sold = avg cookies sold * no of months = 4x * 5 = 20x
So fraction = 12x/(12x + 18x + 20x) = 6/25
Magical Cook, what's the OA?

camitava wrote:Agree with, Cris! It should be - 6/25 i.e. B.
Dec : Cookies sold = 12x (Say)
Jan - Jun: Cookies sold = avg cookies sold * no of months = 3x * 6 = 18x
Jul-Nov: Cookies sold = avg cookies sold * no of months = 4x * 5 = 20x
So fraction = 12x/(12x + 18x + 20x) = 6/25
Magical Cook, what's the OA?

Correct!

We can make life even a bit easier by forgetting about the "x".

Let's pick 12 for December cookie sales (since that's the lowest common multiple of 3 and 4, the other numbers involved).

In that case, each of Jan-June will average 3 cookies and each of July-Nov will average 4 cookies.

So, we have 6*3 + 5*4 + 12 = 18+20+12 = 50 total cookies

December is 12/50 or 6/25 of the whole year.

Hi stuart,

Jan - Jun: Cookies sold = avg cookies sold * no of months = 3 * 6 = 18 i was thinking 4*6 as mentioned in the question

Jul-Nov: Cookies sold = avg cookies sold * no of months = 4* 5 = 20 i was thinking 5*3 as mentioned in the question

can you please explain the answer.

Thanks,
Sibbineni

sibbineni wrote:Hi stuart,

Jan - Jun: Cookies sold = avg cookies sold * no of months = 3 * 6 = 18 i was thinking 4*6 as mentioned in the question

Jul-Nov: Cookies sold = avg cookies sold * no of months = 4* 5 = 20 i was thinking 5*3 as mentioned in the question

can you please explain the answer.

Thanks,
Sibbineni

sibbineni, why it will be 4 * 6 and 3 * 5 for Jan - Jun & Jul-Nov respectively? The Qs is saying -

total sales of cookies in December that was 4 times the average (arithmetic mean) of the monthly cookie sales totals for January through June and 3 times the average total cookie sales for July through November

So if in december, no of cookies = 12x
so jan-Jun: 4k = 12x -> k = 3x -> so avg is 3x or 3 (according to Stuart!)

Got me?

thanks - answer is b.

sibbineni wrote:Hi stuart,

Jan - Jun: Cookies sold = avg cookies sold * no of months = 3 * 6 = 18 i was thinking 4*6 as mentioned in the question

Jul-Nov: Cookies sold = avg cookies sold * no of months = 4* 5 = 20 i was thinking 5*3 as mentioned in the question

can you please explain the answer.

Thanks,
Sibbineni

According to the question stem, December was 4 times the average for Jan-June. So, if we let December = 12, we get:

12 = 4 * Jan-June
Jan-June = 12/4 = 3

Similarly, for July-Nov, if December is 3 times the average for July-Nov, we get:

12 = 3 * July-Nov
July-Nov = 12/3 = 4

Thanks Stuart

Thanks Stuart