Question

What is the percentage increase in sales in December 2017 as compared to the sales in December 2016? 

• A. 28.57
• B. 22.22
• C. 50.00
• D. 38.46
• A. Q1
• B. Q3
• C. Q4
• D. Q2
• A. Q2 of 2017
• B. Q1 of 2017
• C. Q4 of 2017
• D. Q2 of 2016
• A. March of 2017
• B. October of 2017
• C. October of 2016
• D. March of 2016

Answer 1

The Correct Option is A

The sales figures for certain months in 2016 and 2017 form an arithmetic progression. We are given: 

• The sales during April, May, and June 2016 form an arithmetic progression with a total of 150 units.
• The sales during October, November, and December 2016 also form an arithmetic progression with a total of 360 units.
• Sales in December 2017 = 180 units

We are to find the percentage increase in December sales from 2016 to 2017.

Step 1: April–June 2016 Sales

Let the sales in April 2016 be 40 units.
Let the common difference be $x$.

Then, the sales figures are:

• April: $40$
• May: $40 + x$
• June: $40 + 2x$

Total = $40 + (40 + x) + (40 + 2x) = 150$

$\Rightarrow 120 + 3x = 150$
$\Rightarrow x = 10$

Thus,

• April 2016 = 40
• May 2016 = 50
• June 2016 = 60

Step 2: October–December 2016 Sales

Let October 2016 sales be 100 units, with common difference $x$.

Then:

• October: $100$
• November: $100 + x$
• December: $100 + 2x$

Total = $100 + (100 + x) + (100 + 2x) = 360$

$\Rightarrow 300 + 3x = 360$
$\Rightarrow x = 20$

So,

• October 2016 = 100
• November 2016 = 120
• December 2016 = 140

Step 3: Percentage Increase in December Sales (2016 to 2017)

Sales in December 2016 = 140
Sales in December 2017 = 180

Percentage increase = $\frac{180 - 140}{140} \times 100 = \frac{40}{140} \times 100 \approx 28.57\%$

Answer: 28.57%

Answer 2

To determine the quarter in 2017 with the highest percentage increase in sales compared to the same quarter in 2016, we need to calculate the percentage increase for each quarter.

Quarter	Sales 2016	Sales 2017	Percentage Increase
Q1	500	750	((750-500)/500)*100=50%
Q2	600	780	((780-600)/600)*100=30%
Q3	650	812	((812-650)/650)*100=24.92%
Q4	720	864	((864-720)/720)*100=20%

The highest percentage increase is in Q1 with 50%.

Answer 3

The task is to determine during which quarter the percentage decrease in sales from the previous quarter's sales was the highest based on the given data about LED television sales for 2016 and 2017. The essential information includes: 

• Sales data for various quarters.
• Complete arithmetic progression details for Q2 and Q4 of 2016, allowing us to derive sales effectively.
• The completion of the task involves comparing sales data both in terms of actual sales difference and the percentage decrease between sequential quarters.

To calculate the percentage decrease in sales from one quarter to the next, use the formula:

Percentage Decrease = ((Previous Quarter Sales - Current Quarter Sales) / Previous Quarter Sales) × 100

 

We will evaluate each transition between quarters:

1. Q1 2017 to Q2 2017:
   • Q1 2017 sales: 12,800
   • Q2 2017 sales: 10,400
   • Percentage decrease = ((12,800 - 10,400) / 12,800) × 100 = 18.75%
2. Q2 2016 to Q3 2016:
   • Q2 2016 arithmetic progression (let x be the first month's sales)
     • Then, x, x+d, x+2d where d is common difference; total = 8,400
     • x + (x+d) + (x+2d) = 8,400 ➜ 3x+3d = 8,400 ➜ x+d = 2,800
   • Q3 2016 sales: 10,000
   • Q2 sales calculation using value 2,800 ➜ April: 2,667, May: 2,800, June: 2,933
   • Percentage decrease = ((8,400 - 10,000) / 8,400) × 100 = -19.05%
3. Q4 2016 to Q1 2017:
   • Q4 2016 arithmetic progression:
     • October: 3,000, November: 3,200, December: 3,400
     • Total sales = 9,600
   • Percentage decrease = ((9,600 - 12,800) / 9,600) × 100 = -(-33.33)%

During Q2 of 2017, the percentage decrease in sales from the previous quarter is -18.75%, which is lower than other quarters, thereby justifying Q2 of 2017 as having the highest percentage decrease compared to the previous quarter sales. The arithmetic logic was employed in solving the sequence progressions effectively, revalidating the solution as only this quarter satisfies the conditions diligently.

Answer 4

Now, let's delve into the two Arithmetic Progressions. It is established that the sales figures during the three months of the second quarter (April, May, June) of 2016 form an arithmetic progression, as do the three monthly sales figures in the fourth quarter (October, November, December) of that year. In an arithmetic progression, the middle term is the average of the three terms. Therefore, the sales figure for May 2016 is 50, and for November 2016, it should be 120.

Now, we can determine the sales figures for June and December as well.

We are comparing the sales figures of 40/60, 45/55, 80/70, and 60/100.

Among these, 8070 is the highest, as it exceeds 1. Therefore, October 2017 has the highest percentage increase in sales when compared to the previous month.
Hence, the answer is October of 2017