XAT 2021 Question Paper

Let speed of deer = 5steps/second and speed of tiger = 6 steps/sec

Let deer cover 1 m in a step => tiger covers 2/3 m in a step

Hence speed of deer = 5m/s and spped of tiger = 6 x 2/3 m/s = 4m/s

Hence time taken by a deer to catch tiger = 40 seconds

Distance travelled by deer in 40 seconds = 5 x 40 =200 steps

Total percentage incentive when number of team members = 1 = 100%

Total percentage incentive when the number of team members =2 =160%

Total percentage incentive when the number of team members =3=180%

Total percentage incentive when the number of team members =4= 190%

Total percentage incentive when the number of team members >4 = 200%

From 1, Number of people in 8 different projects = 6, 3, 3,3,3, 2,2,2 respectively

From 2, Given, exactly three projects are rated C and 4.8 lakh is paid in total

A minimum of 3 lakhs has to be paid for rating C => 3 *1.6 = 4.8lakhs => All 2 member teams have been rated C

From 3, one project has been rated A*. Let that project be handled by the team of 3 members => Incentives = 180% of 6 = 10.8 lakh

Now remaining 6,3,3,3 should be either rated A or B and the total incentives should be equal to 45 - 10.8-4.8 = 29.4 lakhs

Let us assume 6 has been rated B => Incentives = 200% of 3 = 6 lakhs

The remaining 23.4 lakhs should come from 180%. $$\frac{23.4}{1.8}=13\ lakhs$$

Hence the remaining 3,3,3 can be rated as A, A, B

Hence final ratings are and total payouts are

6 - B - 6lakhs

3- A - 9 lakhs

3-A - 9 lakhs

3-B - 5.4 lakhs

3-A* - 10.8lakhs

2-C - 1.6 lakhs

2-C - 1.6 lakhs

2-C - 1.6 lakhs

Total percentage incentive when number of team members = 1 = 100%

Total percentage incentive when the number of team members =2 =160%

Total percentage incentive when the number of team members =3=180%

Total percentage incentive when the number of team members =4= 190%

Total percentage incentive when the number of team members >4 = 200%

From 1, Number of people in 8 different projects = 6, 3, 3,3,3, 2,2,2 respectively

From 2, Given, exactly three projects are rated C and 4.8 lakh is paid in total

A minimum of 3 lakhs has to be paid for rating C => 3 *1.6 = 4.8lakhs => All 2 member teams have been rated C

From 3, one project has been rated A*. Let that project be handled by the team of 3 members => Incentives = 180% of 6 = 10.8 lakh

Now remaining 6,3,3,3 should be either rated A or B and the total incentives should be equal to 45 - 10.8-4.8 = 29.4 lakhs

Let us assume 6 has been rated B => Incentives = 200% of 3 = 6 lakhs

The remaining 23.4 lakhs should come from 180%. $$\frac{23.4}{1.8}=13\ lakhs$$

Hence the remaining 3,3,3 can be rated as A, A, B

Hence final ratings are and total payouts are

6 - B - 6lakhs

3- A - 9 lakhs

3-A - 9 lakhs

3-B - 5.4 lakhs

3-A* - 10.8lakhs

2-C - 1.6 lakhs

2-C - 1.6 lakhs

2-C - 1.6 lakhs

Total percentage incentive when number of team members = 1 = 100% 

Total percentage incentive when the number of team members =2 =160%

Total percentage incentive when the number of team members =3=180%

Total percentage incentive when the number of team members =4= 190%

Total percentage incentive when the number of team members >4 = 200%

From 1, Number of people in  8 different projects = 6, 3, 3,3,3, 2,2,2 respectively

From 2, Given, exactly three projects are rated C and 4.8 lakh is paid in total

A minimum of 3 lakhs has to be paid for rating C => 3 *1.6 = 4.8lakhs => All 2 member teams have been rated C

From 3, one project has been rated A*. Let that project be handled by the team of 3 members => Incentives = 180% of 6 = 10.8 lakh

Now remaining 6,3,3,3 should be either rated A or B and the total incentives should be equal to 45 - 10.8-4.8 = 29.4 lakhs

Let us assume 6 has been rated B => Incentives = 200% of 3 = 6 lakhs

The remaining 23.4 lakhs should come from 180%. $$\frac{23.4}{1.8}=13\ lakhs$$

Hence the remaining 3,3,3 can be rated as A, A, B

Hence final ratings are and total payouts are 

6 - B - 6lakhs

3- A - 9 lakhs

3-A - 9 lakhs

3-B - 5.4 lakhs

3-A* - 10.8lakhs

2-C - 1.6 lakhs

2-C - 1.6 lakhs

2-C - 1.6 lakhs

From the given data the following table can be created:

Hence the value of x=10

From the given data the following table can be created:

Hence the value of x=10

From the given options, number of neutral first time female shoppers are the least

From the given data the following table can be created:

Hence the value of x=10

All the values can be uniquely determined

Since A, B and C are adjacent faces. If we remove them, the resultant solid will also be a cube with side 5.

Hence total number of cubes unpainted = $$5^3$$ = 125

We will try to maximize the value of the angle ACD:

For a fixed triangle ABC, the angle ACD can be maximized when we take the median CD to be perpendicular to AB and the value of AC is as small as possible, so that the sine of angle ACD, and hence, the angle ACD itself if maximized, as the value of AD is fixed at half of AB at 0.5.

Now, the least possible value of AC is 2. The triangle will be of sides (1,2,2).

Value of sin(ACD)=$$\frac{0.5}{2}=0.25$$

$$\angle\ ACD=\sin^{-1}\left(0,25\right)=14.78\approx\ 15.$$

Since $$x^2-y^2=20$$ and x,y,z are positive integers, 

(x+y)*(x-y) = 20, Hence x-y, x+y are factors of 20.

Since x, y are positive integers, x+y is always positive, and for the product of (x+y)*(x-y)  to be positive x-y must be positive.

x, y are positive integers and x-y is positive x must be greater than y.

The possible cases are : (x+y = 10, x-y = 2), (x+y = 5, x-y = 4).

The second case fails because we get x =9/2, y = 1/2 but x, y are integral values

For case one x = 6, y = 4.

$$y^3 - 2x^2 - 4z \geq -12$$

Substituting  the values of x and y, we have :

64 - 72 - 4*z $$\ge\ -12$$

 -8 - 4*z $$\ge\ -12$$

z$$\le\ 1$$

Since x, y, z are positive integers, the only possible value for z is 1.