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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] New post 05 Mar 2014, 01:12
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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] New post 05 Mar 2014, 01:12
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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.

Answer: B.
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Re: Last year Department Store X had a sales total for December [#permalink] New post 05 Mar 2014, 14:57
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
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1/4
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Re: Last year Department Store X had a sales total for December [#permalink] New post 05 Mar 2014, 16:20
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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] New post 05 Mar 2014, 20:28
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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] New post 06 Mar 2014, 02:08
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

Answer = B
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Re: Last year Department Store X had a sales total for December [#permalink] New post 06 Mar 2014, 03:02
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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] New post 06 Mar 2014, 14:34
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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] New post 08 Mar 2014, 05:51
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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.

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Re: Last year Department Store X had a sales total for December [#permalink] New post 08 Mar 2014, 11:29
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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.

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: Last year Department Store X had a sales total for December   [#permalink] 08 Mar 2014, 11:29
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