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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, 23:34
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69% (02:56) correct 31% (01:57) wrong based on 60 sessions

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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

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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 Updated on: 18 Jan 2018, 09:05
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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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Originally posted by DavidTutorexamPAL on 10 Jan 2018, 03:45.
Last edited by DavidTutorexamPAL on 18 Jan 2018, 09:05, 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, 06:48
1
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, 17:37
1
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, 12:10
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
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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 Apr 2018, 07:21
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





My approach is :

Sales in dec, D = 4(M/6) = 3(N/5) ..... Where M = sum of sales Jan to June & N = sum of sales July to Nov.

Now, writing M & N in terms of D, we get, M=6D/4 & N=5D/3

M + N + D = 6D/4 + 5D/3 + D

or, M + N + D = 6D/4 + 5D/3 + D .... (adding D to both sides)

we get Total Sales for the year, Y = (18D + 20D + 12D)/12 = 50D/12

Therefore, D/Y = 12/50 = 6/25

Answer is option B.


Kudos if it helped. :D
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Re: Last year Bakery A had total sales of cookies in December that was 4 &nbs [#permalink] 16 Apr 2018, 07:21
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Last year Bakery A had total sales of cookies in December that was 4

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