CAT 2021 Question Paper Slot 1

The total sales from products in the office supply category in 2019 is :

Sum of sales of :

Binders: 3.6 million

Art : 0.4 million.

Appliances:  1.9 million

Envelops: 0.3 million

Fasteners: 0.1 million

Labels: 0.2 million

Paper = 1.5 million.

Storage: 4.3 million.

Supplies: 1.1 million.

The sum of sales of these products = 3.6+0.4+1.9+0.3+0.1+0.2+1.5+4.3+1.1 = 13.4 million.

The closest among the option is 13.5 million.

The percentage increase in sales in the furniture category from 2019 to 2020 are :

Bookcases: 1.9 million in 2019 and 2.2 million in 2020.

Chairs: 6.2 million in 2019 and 7 million in 2020.

Furnishings: 2.05 million in 2019 and 2.1 million in 2020.

Tables: 4.4 million in 2019 and 4.5 million in 2020.

Hence the percentage increase is given by :

$$\frac{\left(\left(2.2+7+2.1+4.5\right)-\left(1.9+6.2+2.05+4.4\right)\right)}{1.9+6.2+2.05+4.4}$$

$$\frac{\left(15.8-14.55\right)}{14.55}\cdot100\ =\ \frac{125}{14.55}=\ 8.53\%$$

The number of subcategories had sales of ₹ 4 million or more in 2019 and registered an increase in sales in excess of 25% in 2020 :

The subcategories with more than 4 million in sales in 2019 are :

Chairs: 6.2 million in 2019 and 7 million in 2020. ( For a 25 percent increase the sales must be at least 7.8 million and hence fails)

Tables: 4.4 million in 2019 and 4.5 million in 2020. ( For a 25 percent increase the sales must be at least 5.5 million and hence fails)

Storage: 4.3 million sales in 2019 and 5.1 million in 2020. ( For a 25 percent increase the sales must be at least 5.4 and hence fails)

Phones: 5.75 million in 2019 and 7.5 million in 2020. ( An increase of 30.5 percent)

Hence only one subcategory satisfies the condition.

The improvement index for a category is the maximum percentage increase in sales from 2019 to 2020 among any of its subcategories.

Hence based on the information provided in the tabular data we need to look for the different subcategories where the rise in sales from 2019 to 2020 is higher.

Based on the visual data :

In the furniture category :

Bookcases and Chairs have a relatively high percentage increase :

Books cases: 1.9 million to 2.2 million ( 15.7 percent increase )

Chairs: 6.2 million to 7 million ( 12.9 percent increase)

In the office supply category :

Binders and Appliances have a relatively high percentage increase :

Binders: 3.6 million to 5.3 million (47 percent increase )

Appliances: 1.9 million to 3.15 million ( 65.7 percent increase)

In technology product category :

Accessories: 3.1 to 4.4 million. (41.9 percent increase)

Phones: 5.8 million to 7.7 million ( 32.7 percent increase)

Hence among the categories :

The highest increase among them is in the order :

Furniture < Technology product < office supply.

Speed of the faster train = $$\frac{160}{12}=\frac{40}{3}\ $$ m/s

Speed of the slower train = $$\frac{40}{3}-\left(6\times\ \frac{5}{18}\right)=\frac{35}{3}$$ m/s

Sum of speeds (when the trains travel towards each other) = $$\frac{40}{3}+\frac{35}{3}=25$$ m/s

Let the slower train be $$x$$ metres long; then: $$\frac{160+x}{25}=14$$

On solving, $$x=190\ m$$

Area of a regular hexagon = $$\frac{3\sqrt{3}}{2}x^2$$

Area of an equilateral triangle = $$\frac{\sqrt{3}}{4}\left(a\right)^2$$ ; where a = side of the triangle

Since the area of the two figures are equal, we can equate them as folllows: $$\frac{3\sqrt{3}}{2}x^2=\frac{\sqrt{3}}{4}\left(12\right)^2$$

On simplifying: $$x^2=24\ $$

$$\therefore\ x=2\sqrt{6}$$

Since a regular hexagon can be considered to be made up of 6 equilateral triangles, a line joining the farthest vertices of a hexagon can be considered to be made up using the sides of two opposite equilateral triangle forming the hexagon. Hence, its length should be twice the side of the hexagon, in this case, 4 cm.

Now, AD divided the hexagon into two symmetrical halves. Hence, AD bisects angle D, and hence, angle ADC is $$60^{\circ\ }$$.

We can find out the value of AT using cosine formula:

$$AT^2=\ 4^2+1^2-2\times\ 1\times\ 4\cos60$$

$$AT^2=\ 17-4=13$$

$$AT=\sqrt{\ 13}$$

Let the total amount of work be 60 units.

Then Anu, Vinu, and Manu do 4, 5, and 3 units of work per day respectively.

On the 1st day, Anu and Vinu work. Work done on the 1st day = 9 units

On the 2nd day, Manu and Vinu work. Work done on the 2nd day = 8 units

This cycle goes on. And in 6 days, the work completed is 9+8+9+8+9+8 = 51 units.

On the 7th day, again Anu and Vinu work and complete the remaining 9 units of work. Thus, the number of days taken is 7 days.

Let the amounts Neeta, Geeta, and Sita earn in a day be n, g, and s respectively. 

Then, it has been given that:

n+g=6s -i

s+n=2g -ii

ii-i, we get: s-g = 2g-6s

7s = 3g.

Let g be 7a. Then s earns 3a.

Then n earns 6s-g = 18a-7a = 11a.

Thus, the ratio is 11a:3a = 11:3

Let us assume the family spends Rs. 100 each month for the first 3 months and then spends Rs. 50 in each of the next two months.

Then amount of onions bought = 10, 5, 4, 2, 1, for months 1-5 respectively.

Total amount bought = 22kg.

Total amount spent = 100+100+100+50+50 = 400.

Average expense = $$\frac{400}{22}=Rs.18.18\approx\ 18$$