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Last year Department Store X had a sales total for December

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Last year Department Store X had a sales total for December [#permalink]

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New post 03 Dec 2007, 18:11
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Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C. 1/3
D. 4/11
E. 4/5
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Jan 2014, 06:58, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.

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Re: Need help solving [#permalink]

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New post 03 Dec 2007, 18:28
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kamal101 wrote:
Last year Deparment Store x had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C. 1/3
D. 4/11
E. 4/5


December Sales = D

Arithmetic mean for Jan thourgh Nov=X,
sales total for Jan-Nov = 11X
Sales total for the year =11X+D
December sales total =4X
D/(11X+D)?

=4x/(11x+4x)=4x/15x=4/15
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Re: Need help solving [#permalink]

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New post 03 Dec 2007, 22:54
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kamal101 wrote:
Last year Deparment Store x had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C. 1/3
D. 4/11
E. 4/5


Let avg for 11 mos. = 10
Therefore, Dec = 40
Year total = 11*10 + 40 = 150

Answer = 40/150 = 4/15 = B

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Re: Need help solving [#permalink]

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New post 03 Dec 2007, 22:59
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kamal101 wrote:
Last year Deparment Store x had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C. 1/3
D. 4/11
E. 4/5


JtoN/11=x D/1=4x D=4x JtoN=11x

total sales: 4x+11x = 15x

so we want D/total sales ---> 4x/15x = 4/15

B

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Re: PS Department Sto' [#permalink]

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New post 30 Jan 2008, 15:54
sales for 11 months = 11*x/4, where x - sales for december.
total sales = x + 11*x/4 = 15x/4 -> x/total sales = 4/15 -> B

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Re: PS Department Sto' [#permalink]

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New post 30 Jan 2008, 18:43
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Perfect # pickin problem. Just pick a number. $100 a month for Jan--> Nov and $400 for Dec. 400/1500 = 4/15 B.

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Re: PS Department Sto' [#permalink]

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New post 30 Jan 2008, 19:53
4/15, but i for some reason took a long time to get this. i realized i didnt read the question properly the first time around. anyways:

d = 4*(x/11) where d=december sales and x=sales total for jan-nov

we are ultimately after d/x+d

so, rearranging the first eqn, we get x=11d/4. substitute this into number two:

d/(11d/4 + d) = d/((11d+4d)/4) = d/(15d/4) = 4d/15d = 4/15

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Re: PS Department Sto' [#permalink]

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New post 30 Jan 2008, 20:15
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young_gun wrote:
here's easy pickin's:

Last year Department store X had a sales total for December that was 4 times the aver of the monthly sales totals for january through november. The sales total for decemeber was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C. 1/3
D. 4/11
E. 4/5


x is the average monthy sales. So Dec=4x and the other 11 months are 11x

So 4x+11x = total. 4x/15x --> 4/15

B

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Re: Last year Department Store X had a sales total for December [#permalink]

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New post 11 Jul 2017, 06:05
Sale total of Decemeber = 4 * A.M of Sales from Jan to Nov.
= 4 * Total sales from Jan to Nov/11
11/4* Sales total of December = Total sales from Jan to Nov.

Adding sale total of Dec. both sides,

15/4* Sale total of Dec. = Total sales of the year
So, Sale total of Dec = 4/15

B should be correct.

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Kshitij

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Re: Last year Department Store X had a sales total for December [#permalink]

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New post 12 Jul 2017, 05:58
I tried to solve this question using variable approach but ended up with so many variables to solve.

So I took December sales as 20 (a multiple of 4)

20= 4*(x/11)

x= Sum of January to November sales

x= 55


So 20/75= 4/15


I also rechecked the answer using another value for December sales i.e.28 (again a multiple of 4).

Same answer.
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Re: Last year Department Store X had a sales total for December [#permalink]

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New post 12 Jul 2017, 06:27
plug in is the best method. 11 months total =11. Avg is 1 and for Dec 4xthe avg=4. Total sales for the year 4+11=15. Fraction =Dec/Total =4/15

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Re: Last year Department Store X had a sales total for December [#permalink]

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New post 12 Jul 2017, 17:14
kamal101 wrote:
Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C. 1/3
D. 4/11
E. 4/5


We can let n = the average sales for months January through November, inclusive, and thus December = 4n.

Thus, the sum of sales for the year is 11n + 4n = 15n, so December was 4n/15n = 4/15 of the sales for the year.

Answer: B
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Re: Last year Department Store X had a sales total for December [#permalink]

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New post 07 Oct 2017, 06:50
kamal101 wrote:
Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C. 1/3
D. 4/11
E. 4/5



let x = average sales from jan-nov(11 months)
11x = total sales from jan-nov
4x = sales on december
11x + 4x = 15x = total sales of the year
since total sales consists of two fractions (i.e. 11 and 4) and since the stem asks specifically for December's fraction of the total sales of the year
Thus, 4/15 is the answer (B)

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Re: Last year Department Store X had a sales total for December   [#permalink] 07 Oct 2017, 06:50
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