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Last year Bakery A had total sales of cookies in December that was 4

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Last year Bakery A had total sales of cookies in December that was 4 [#permalink]

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New post 09 Jan 2018, 22:34
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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
[Reveal] Spoiler: OA

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Last year Bakery A had total sales of cookies in December that was 4 [#permalink]

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New post 10 Jan 2018, 02:45
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Bunuel wrote:
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


We'll first translate the question into expressions so we understand what we need to do.
This is a Precise approach.

If D cookies were sold in December then D/4 cookies were sold on average from January to June and D/3 between July to November.
Then a total of D +(D/4 * 6) + (D/3 *5) = 25D/6 cookies were sold.
So, the fraction sold in December is D/ (25D/6) = 6/25.
(B) is our answer.
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Last edited by DavidTutorexamPAL on 18 Jan 2018, 08:05, edited 1 time in total.
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Re: Last year Bakery A had total sales of cookies in December that was 4 [#permalink]

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New post 10 Jan 2018, 05:48
Use reverse number approach for this

Assume variable which is lcm of 4,3 to make easy substitution=12

For 1-6 month avg =3,total : 18
For 7-11 avg =4 total:20
For last month :12

Ratio is =12/ total, 12/50=6/25

6/25



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Re: Last year Bakery A had total sales of cookies in December that was 4 [#permalink]

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New post 16 Jan 2018, 16:37
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Bunuel wrote:
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


We can let the average monthly sales of cookies for January through June = n and the average monthly sales of cookies for July through November = m; thus:

Sales in December = 4n = 3m

Furthermore, the total sales of cookies for January through June is 6n and that for July through November = 5m.

Thus, the total sales of cookies for the year is 6n + 5m + 3m = 6n + 8m.

Since 4n = 3m, n = 3m/4.

Thus, in terms of m, the total sales for the year is:

6(3m/4) + 8m = 9m/2 + 16m/2 = 25m/2.

The sales of cookies for December is 3m/(25m/2) = 3m x 2/(25m) = 6m/(25m) = 6/25 of the total sales for the year.

Answer: B
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Re: Last year Bakery A had total sales of cookies in December that was 4 [#permalink]

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New post 25 Jan 2018, 11:10
Let, No. of cookies sold in Dec => 3*4 = 12
So, cookies sold Jan through Jun (in 6 months) => (12/4)*6 = 18
And, cookies sold Jul through Nov (in 5 months) => (12/3)*5 = 20
Then total cookies sold throughout the year 18+20+12 = 50
Therefore, Dec/Total = 12/50 = 6/25
Re: Last year Bakery A had total sales of cookies in December that was 4   [#permalink] 25 Jan 2018, 11:10
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