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

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

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)

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

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.

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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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

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)

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)

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 [J + F + M + A + M + J + J + A + S + O + N + D]

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

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

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

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* [(jan to nov sales)/11]

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

x=4* [(jan to nov sales)/11]

=> jan to nov sales = 11x/4

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

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.

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:

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.

Short video solution here (1:11):