Last year Department Store X had a sales total for December that was

Question

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

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

Bunuel · Accepted Answer

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

(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.

PareshGmat · Answer

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

m3equals333 · Answer

Jan-Nov Avg Monthly Sales:Dec Sales
1:4

Dec Sales/(Jan-Nov Sales Total+Dec Sales)
4/ 
4/15

B

nutshell · Answer

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)

WoundedTiger · Answer

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

(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

CCMBA · Answer

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.

AKG1593 · Answer

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.

Posted from my mobile device

ScottTargetTestPrep · Answer

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

Abhishek009 · Answer

Total sales from January to November is  11x  (say)

Sales for December is  4x

Total sales of the year is  15x 
  
So, the sales total for December was  \frac{4}{15}  part of the sales total for the year, answer will be (E)

CyberStein · Answer

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)

MathRevolution · Answer

Conventional Approach:

December Sales = 4  \frac{(J + F + M + A + M + J + J + A + S + O + N) }{ 11}

=> Total December Sales = x * Total Sales for year

=>   4  \frac{(J + F + M + A + M + J + J + A + S + O + N) }{ 11}    = x *

=>   4  \frac{(J + F + M + A + M + J + J + A + S + O + N) }{ 11}    = x *    4  \frac{(J + F + M + A + M + J + J + A + S + O + N) }{ 11}   }]

=> 4 (J + F + M + A + M + J + J + A + S + O + N) = x * 15 * (J + F + M + A + M + J + J + A + S + O + N)

=> x =  \frac{4 }{ 15 }

Answer B

Quick Approach:

Let the average be x.

For 11 months if the average was 'x' then sum: 11x

December: 4x

Total: 11x + 4x = 15x

Decemeber = p * Total

=> 4x = p * 15x

=> p =  \frac{4}{15}

Answer B

BrentGMATPrepNow · Answer

An easy approach is to  assign values  that satisfy the given information.

So, it could be the case that, for each month from January to November, the store made  $1  in sales.
This means the average monthly sale was  $1 
This means the sales total for December = (4)( $1 ) =   $4

So the total sales for the entire year = (11)( $1 ) +   $4   =   $15  
  $4   of the total sales of   $15   were from December.

So, the sales total for December was   4  /  15   of the sales total for the year.

Answer: B

MasteringGMAT · Answer

Flagging this for expert review  GMATNinja   ScottTargetTestPrep   Bunuel

I am not able to understand why everyone is taking x to be the average monthly sales for the period Jan to Nov. by doing so, isn't one assuming that the average sales for each month from Jan to Nov was same? Can we make such assumptions in these types of GMAT Quant questions?

All we are given is => Dec sales = 4*

if we take Dec sales to be x, then the following equation can be formed.

x=4*

=> jan to nov sales = 11x/4

=> Total sales = 11x/4+x, => 15x/4

naveeng15 · Answer

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.

BLTN · Answer

Dear  Traj201090 
 
That is the definition of arithmetic average. (A+B+C)/3 = x then sum of A+B+C = 3x

Your approach is valid, yet you have to make the last step:

ArnauG · Answer

Let's assume the sales total for December is represented by "D" and the average of the monthly sales totals for January through November is represented by "M."

According to the given information, the sales total for December was 4 times the average of the monthly sales totals for January through November:

D = 4M

Now, let's consider the sales total for the year, which includes the sales for all 12 months. We can represent the sales total for the year as "Y."

Sales total for the year = D + M + M + M + M + M + M + M + M + M + M + M
Sales total for the year = D + 11M

To find the fraction of the sales total for the year that represents the sales total for December, we need to determine D/Y.

D/Y = D / (D + 11M)

Substituting D = 4M:

D/Y = 4M / (4M + 11M)

Simplifying the expression:

D/Y = 4M / 15M

D/Y = 4/15

Therefore, the sales total for December was 4/15 of the sales total for the year.

The correct answer is (B) 4/15.

GMATCoachBen · Answer

Short video solution here (1:11):

https://www.youtube.com/watch?v=7r6Hm9YchEI

ManishaPrepMinds · Answer

Solution:
Let the total sales from January to November be S.
1. Step 1:
The average sales from January to November = S/11.
2. Step 2:
The sales total for December is 4 times the average from January to November, so: December sales = 4 * (S/11) = 4S/11.
3. Step 3:
The total sales for the year = S + 4S/11 = (11S + 4S)/11 = 15S/11.
4. Step 4:
The fraction of the total sales for December out of the total for the year is: December sales / Total sales for the year = (4S/11) / (15S/11) = 4/15.
Answer:
(B) 4/15

hemanthPA · Answer

avg sales from Jan to Nov * 4 = total sales in dec

take avg sales from jan to Nov as x
so total sales in dec would be 4x

they are asking, whats dec/total sales = 4x/(11 months)*x + 4x = 4x/11x + 4x = 4/15

(dont miss the part of multiplying 11 in the total as x is avg for each month, so from jan to nov the total would be 11*x )

Last year Department Store X had a sales total for December that was

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions

Last year Department Store X had a sales total for December that was

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia