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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?

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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

Let x be the average sales per month for the first 11 months, then the total sales for the whole year would be (11 months) + (December) = 11x + 4x = 15x.

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

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05 Mar 2014, 15:57

Lets consider each month sales as X, the december sales is 4 times the average of the other months, so december is 4X, to define what fraction of the total year sales must be fraction / total so will be 4x / 11x + 4x, 4x / 16x, and will be

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

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06 Mar 2014, 04:02

1

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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

Sol: Let the average sale for Jan to Nov period is X then total sales in this period is 11X Now sale in Dec 4X. Total sale for Jan-Dec: 15X Dec sale as fraction of Total sales 4X/15X or 4/15 Ans is B
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Re: Last year Department Store X had a sales total for December [#permalink]

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08 Mar 2014, 06:51

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Let sum of sales from Jan to Nov=x Sales in dec=y To calculate:y/x+y We're given 4x/11=y x/y=11/4 Add 1 to both sides and reciprocate. We get 4/15 Option B.

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 be the average sales per month for the first 11 months, then the total sales for the whole year would be (11 months) + (December) = 11x + 4x = 15x.

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

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01 Dec 2014, 21:25

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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

We can use just some smart numbers here December = 8; means that the average for each month Jan-Nov = 2 --> \(\frac{8}{8+11*2}=\frac{4}{15}\)Answer B
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