The following table shows the sale of different brands of watches by a shop during 2014 — 2018.

Year	Brand		(in thousands)
	Titan	Fastrack	Timex	Fossil
2014	366	205	247	96
2015	398	188	285	108
2016	312	175	388	112
2017	412	312	401	146
2018	288	202	255	126

Based on the data given in the table above which of the following statements is TRUE? ​

Correct option is B

Solution:

Statement 1:The total sales of Fossil brand of watches for the given period is less than 50% of the sales of every other brand for the given period.

​To check this, we calculate the total sales for each brand over the 5 years:

​Titan's Total Sales = 366 + 398 + 312 + 412 + 288 = 1776 

​Fastrack's Total Sales = 205 + 188 + 175 + 312 + 202 = 1082 

​Timex's Total Sales = 247 + 285 + 388 + 401 + 255 = 1576 

Fossil's Total Sales = 96 + 108 + 112 + 146 + 126 = 588 

Now, compare Fossil's total sales with 50% of the sales of other brands:

50% of Titan's Sales = $$\frac{1776} 2$$​ = 888

50% of Fastrack's Sales = $$\frac{1082} 2$$​ = 541

50% of Timex's Sales = $$\frac{ 1576 } 2$$​ = 788 

Fossil's total sales (588) are less than 50% of Titan's and Timex's sales, but greater than 50% of Fastrack's sales. Therefore, Statement 1 is false.

Statement 2:Only two brands showed year-on-year increase in sales during the period 2014-2017. 

​Titan:

2014 → 2015: $398-366=+32$ (increase)

2015 → 2016: $312-398=-86$ (decrease)

​2016 → 2017: $412-312=+100$ (increase)

​Titan has 2 increases: 2014-2015 and 2016-2017.

​Fastrack:

2014 → 2015: $188-205=-17$ (decrease)

​2015 → 2016: $175-188=-13$ (decrease)

​2016 → 2017: $312-175=+137$ (increase)

​Fastrack has 1 increase: 2016-2017.

​Timex:

2014 → 2015: $285-247=+38$ (increase)

​2015 → 2016: $388-285=+103$ (increase)

​2016 → 2017: $401-388=+13$ (increase)

Timex has 3 increases: 2014-2015, 2015-2016, and 2016-2017.

​Fossil:

2014 → 2015: $108-96=+12$ (increase)

​2015 → 2016: $112-108=+4$ (increase)

​2016 → 2017: $146-112=+34$ (increase)

​Fossil has 3 increases: 2014-2015, 2015-2016, and 2016-2017.

Therefore, only Titan and Fastrack had exactly year-on-year increases in sales during 2014-2017.

Thus, Statement 2 is indeed TRUE

Statement 3: The total sales of all brands of watches was highest in 2016.

​To verify this, we calculate the total sales for all brands for each year:

​2014: 366 + 205 + 247 + 96 = 914 

​2015: 398 + 188 + 285 + 108 = 979 

​2016: 312 + 175 + 388 + 112 = 987 

​2017: 412 + 312 + 401 + 146 = 1271 

​2018: 288 + 202 + 255 + 126 = 871 

​The highest total sales occurred in 2017, not 2016. Therefore, Statement 3 is false 

Statement 4: The brand with the highest sales for the given period is Timex. 

​As we calculated earlier, the total sales for each brand over the 5 years:

​Titan: 1776

​Fastrack: 1082

​Timex: 1576

​Fossil: 588

The brand with the highest sales is Titan (1776), not Timex. Therefore, Statement 4 is false. 

Thus, option(b) is correct.