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

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

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05 Mar 2014, 02:12
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 129
Category: Algebra; Arithmetic Applied problems; Statistics
Page: 78
Difficulty: 600

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

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05 Mar 2014, 02:12
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SOLUTION

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.

(December)/(Whole year) = 4x/(15x) = 4/15.

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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
[Reveal] Spoiler:
1/4
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Re: Last year Department Store X had a sales total for December [#permalink]

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05 Mar 2014, 17:20
1
KUDOS
Jan-Nov Avg Monthly Sales:Dec Sales
1:4

Dec Sales/(Jan-Nov Sales Total+Dec Sales)
4/[(11*1)+(1*4)]
4/15

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

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05 Mar 2014, 21:28
1
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Let the monthy sales, on average, be x.
Monthly sales totals for January through November = 11x;
Sales Total for December = 4x;

We can write the equation: 4x/(11x + 4x) = 4x/15x = 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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06 Mar 2014, 03:08
1
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Let sales from Jan to Nov = J + F +....... +N
Let sales in December = d

$$Avg = \frac{(J + F +....... +N)}{11}$$

$$d = 4 * \frac{(J + F +....... +N)}{11}$$

$$(J + F +....... +N) = \frac{11d}{4}$$ ...... Sales from Jan through Nov

Total sales Jan to Dec $$= \frac{11d}{4} + d = \frac{15d}{4}$$

The sales total for December is $$\frac{4}{15}$$ fraction of the sales total for the year

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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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06 Mar 2014, 15:34
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Plugged in numbers. Set average to 1. Total for Jan-Nov is 11. Sales for Dec = 4. Yearly total 15. Dec = 4/15 of total.
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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
1
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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.

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

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08 Mar 2014, 12:29
SOLUTION

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.

(December)/(Whole year) = 4x/(15x) = 4/15.

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

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01 Dec 2014, 21:19
By picking:

x/11=2, 22 in eleven months

2*4=8 in December, so

8/22+8=8/30=4/15

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

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16 Nov 2015, 13:23
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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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Re: Last year Department Store X had a sales total for December   [#permalink] 16 Nov 2015, 13:23
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