CAT 2018 LRDI Questions

The multi-layered pie-chart below shows the sales of LED television sets for a big retail electronics outlet during 2016 and 2017. The outer layer shows the monthly sales during this period, with each label showing the month followed by sales figure of that month. For some months, the sales figures are not given in the chart. The middle-layer shows quarter-wise aggregate sales figures (in some cases, aggregate quarter-wise sales numbers are not given next to the quarter). The innermost layer shows annual sales. It is known 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.


Question No. 1:
What is the percentage increase in sales in December 2017 as compared to the sales in December 2016?
Options:
  1. 28.57
  2. 22.22
  3. 50.00
  4. 38.46

Question No. 2:
In which quarter of 2017 was the percentage increase in sales from the same quarter of 2016 the highest?
Options:
  1. Q1
  2. Q3
  3. Q4
  4. Q2

Question No. 3:
During which quarter was the percentage decrease in sales from the previous quarter’s sales the highest?
Options:
  1. Q2 of 2017
  2. Q1 of 2017
  3. Q4 of 2017
  4. Q2 of 2016

Question No. 4:
During which month was the percentage increase in sales from the previous month’s sales the highest?
Options:
  1. March of 2017
  2. October of 2017
  3. October of 2016
  4. March of 2016

Explanation:

It is given that the sales figures during the three months of the second quarter (April, May, June) of 2016 form an arithmetic progression.

So 40 + (40 + x) + (40 + 2x) = 150

Or x = 10

April 2016 = 40

May 2016 = 50

June 2016 = 60

Also, the same case holds for October, November, December of 2016.

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

Or x = 20

October 2016 = 100

November 2016 = 120

December 2016 = 140

Sales in December 2017 = 180

Sales in December 2016 = 140

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

So the percentage increase in the sales is highest for Q1

$\rightarrow \mathrm { Q } _ { 1 }$ of 2017$\mathrm { compared }$ with $\mathrm { Q } _ { 4 }$ of 2016

$= \frac { 380 - 360 } { 360 } \times 100 = 5.55 \%$ increase.

$\rightarrow \mathrm { Q } _ { 2 }$ of 2016$\mathrm { compared }$ with $\mathrm { Q } _ { 1 }$ of 2016

$= \frac { 150 - 240 } { 240 } \times 100 = - 37.5 \%$ increase or 37.5$\%$ decrease

$\rightarrow \mathrm { Q } _ { 4 }$ of 2017 with compared with $\mathrm { Q } _ { 3 }$ of 2017

There is an increase from 220 to 500 .

$\rightarrow \mathrm { Q } _ { 2 }$ of 2017 with compared with $\mathrm { Q } _ { 1 }$ of 2017

$= \frac { 200 - 380 } { 380 } \times 100 = - 47.36$ or 47.36$\%$ decrease

So, sales of $\mathrm { Q } _ { 2 }$ of $2017 ,$ had the highest percentage decrease compared with $\mathrm { Q } _ { 1 }$ of $2017 .$


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