# XAT 2021 QADI | Previous Year XAT Paper

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**1. XAT 2021 QADI | Algebra - Logarithms**

If log_{4} m + log_{4} n = log_{2} (m + n) where m and n are positive real numbers, then which of the following must be true?

- A.
$\frac{1}{m}$ + $\frac{1}{n}$ = 1

- B.
m = n

- C.
m

^{2}+ n^{2}= 1 - D.
$\frac{1}{m}$ + $\frac{1}{n}$ = 2

- E.
No values of m and n can satisfy the given equation

Answer: Option E

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**Explanation** :

log_{4} mn = log_{2} (m + n)

$\sqrt{mn}$ = (m + n)

Squaring on both sides

m^{2} + n^{2} + mn = 0

Since m, n are positive real numbers, no value of m and n satisfy the above equations.

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**2. XAT 2021 QADI | Arithmetic - Ratio, Proportion & Variation**

Mr. Jose buys some eggs. After bringing the eggs home, he finds two to be rotten and throws them away. Of the remaining eggs, he puts five-ninth in his fridge, and brings the rest to his mother’s house. She cooks two eggs and puts the rest in her fridge. If her fridge cannot hold more than five eggs, what is the maximum possible number of eggs bought by Mr. Jose?

- A.
9

- B.
17

- C.
11

- D.
20

- E.
29

Answer: Option C

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**Explanation** :

Let the number of eggs bought = 9x + 2

number of eggs left after throwing away 2 = 9x

number of eggs kept in fridge = 5x

number of eggs brought to his mothers' house = 4x

number of eggs left after cooking 2 which are kept in fridge = 4x - 2

Given, 4x - 2 <= 5

⇒ x ≤ $\frac{7}{4}$

Hence the max value of x is 1

Max number of eggs bought = 11

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**3. XAT 2021 QADI | Arithmetic - Simple & Compound Interest**

Mohan has some money (₹M) that he divides in the ratio of 1:2. He then deposits the smaller amount in a savings scheme that offers a certain rate of interest, and the larger amount in another savings scheme that offers half of that rate of interest. Both interests compound yearly. At the end of two years, the total interest earned from the two savings schemes is ₹830. It is known that one of the interest rates is 10% and that Mohan deposited more than ₹1000 in each saving scheme at the start. What is the value of M?

- A.
7500

- B.
6000

- C.
To solve this, the other interest rate must also be given.

- D.
4500

- E.
12000

Answer: Option B

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**Explanation** :

Let the total amount be 3x

Case 1:

Smaller amount = x, rate of interest = 10

Larger amount = 2x, rate of interest = 5

Total amount received at the end of two years (smaller amount) = ($1+\frac{10}{100}$)^{2} = 1.21 x. CI = 0.21x

Total amount received at the end of two years (larger amount) = 2x ($1+\frac{5}{100}$)^{2} = 2.205x CI = 0.205x

Given, 0.21x + 0.205x = 830

⇒ x = 2000

2x = 4000

Case 2:

Smaller amount = x, rate of interest = 20

Larger amount = 2x, rate of interest = 10

Total amount received at the end of two years (smaller amount) = x($1+\frac{20}{100}$)^{2} = 1.44x. CI = 0.44x

Total amount received at the end of two years (larger amount) = 2x ($1+\frac{10}{100}$)^{2} = 2.42x CI = 0.42x

Given, 0.44x+0.42x = 830

⇒ x = 965.11 which is not valid since it should be greater than 1000

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**4. XAT 2021 QADI | Modern Math - Probability**

A small store has five units of a new phone model in stock: two white, two black, and one red. Three customers arrive at the shop to buy a unit each. Each one has a pre- determined choice of the colour and will not buy a unit of any other colour. All the three customers are equally likely to have chosen any of the three colours. What is the probability that the store will be able to satisfy all the three customers?

- A.
$\frac{4}{5}$

- B.
$\frac{7}{9}$

- C.
$\frac{2}{3}$

- D.
$\frac{8}{9}$

- E.
$\frac{1}{3}$

Answer: Option C

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**Explanation** :

Number of white phones = 2

Number of black phones = 2

Number of red phones = 1

customer 1 will have 3 choices

customer 2 will have 3 choices

customer 3 will have 3 choices

Hence total choices = 3 x 3 x 3 = 27

The cases not possible = BBB, RRR,WWW, RRB,RBR,BRR, RRW,RWR, WRR

Possible cases = 18

Probability = 18/27 = 2/3

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**5. XAT 2021 QADI | Geometry - Basics**

At any point of time, let x be the smaller of the two angles made by the hour hand with the minute hand on an analogue clock (in degrees). During the time interval from 2:30 p.m. to 3:00 p.m., what is the minimum possible value of x?

- A.
45

- B.
105

- C.
90

- D.
0

- E.
75

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**6. XAT 2021 QADI | Arithmetic - Ratio, Proportion & Variation**

One third of the buses from City A to City B stop at City C, while the rest go non-stop to City B. One third of the passengers, in the buses stopping at City C, continue to City B, while the rest alight at City C. All the buses have equal capacity and always start full from City A. What proportion of the passengers going to City B from City A travel by a bus stopping at City C?

- A.
$\frac{1}{7}$

- B.
$\frac{1}{9}$

- C.
$\frac{1}{3}$

- D.
$\frac{7}{9}$

- E.
$\frac{4}{9}$

Answer: Option A

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**Explanation** :

Let us assume there are 9 buses.

3 of them stop at C and 6 go non-stop

Given, One-third of the passengers, in the buses stopping at City C, continue to City B, while the rest alight at City C

⇒ Since all buses have equal capacity. we can say 2 will elite at C and 1 will proceed to B.

Hence required proportion = 1/7

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**7. XAT 2021 QADI | Arithmetic - Time, Speed & Distance**

Rajesh, a courier delivery agent, starts at point A and makes a delivery each at points B, C and D, in that order. He travels in a straight line between any two consecutive points. The following are known:

(i) AB and CD intersect at a right angle at E, and

(ii) BC, CE and ED are respectively 1.3 km, 0.5 km and 2.5 km long.

If AD is parallel to BC, then what is the total distance (in km) that Rajesh covers in travelling from A to D?

- A.
10.2

- B.
12

- C.
11.5

- D.
5.5

- E.
18

Answer: Option C

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**Explanation** :

Given, CE = 0.5, BC = 1.3 and ED = 2.5

Triangle CEB is a right-angled triangle ⇒ EB = 1.2

Triangles ECB is similar to triangle EDA

EB/EC = AE/ED ⇒ AE = 6

Hence total distance travelled = AB + BC + CD = 7.2 + 1.3 + 3.5 = 11.5km

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**8. XAT 2021 QADI | Algebra - Functions & Graphs**

Let f(x) = $\frac{{x}^{2}+1}{{x}^{2}-1}$ if x ≠ 1, -1, and 1 if x = 1, -1. Let g(x) = $\frac{x+1}{x-1}$ if x ≠ 1, and 3 if x = 1. What is the minimum possible values of $\frac{f\left(x\right)}{g\left(x\right)}$?

- A.
$\frac{1}{2}$

- B.
-1

- C.
$\frac{1}{4}$

- D.
$\frac{1}{3}$

- E.
1

Answer: Option D

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**Explanation** :

$\frac{f\left(x\right)}{g\left(x\right)}$ = $\frac{({x}^{2}+1)}{{x}^{2}-1}$ . $\frac{(x-1)}{x+1}$ = $\frac{({x}^{2}+1)}{{(x+1)}^{2}}$

This function is definitely greater than 0

let y = $\frac{({x}^{2}+1)}{{(x+1)}^{2}}$

⇒ x^{2} (y − 1) + 2yx + (y − 1) = 0 which is quadratic in x

Disctiminant should be greater than 0

4y^{2} - 4(y - 1)^{2} ≥ 0

⇒ y >= 1/2

When x =1, f(x)/g(x) = 1/3

Hence either the value should be greater than 1/2 or should be equal to 1/3

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**9. XAT 2021 QADI | Arithmetic - Time, Speed & Distance**

Swati can row a boat on still water at a speed of 5 km/hr. However, on a given river, it takes her 1 hour more to row the boat 12 km upstream than downstream. One day, Swati rows the boat on this river from X to Y, which is N km upstream from X. Then she rows back to X immediately. If she takes at least 2 hours to complete this round trip, what is the minimum possible value of N?

- A.
3

- B.
4.8

- C.
2

- D.
3.6

- E.
2.1

Answer: Option B

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**Explanation** :

Let the speed of the stream be x

Let the speed of the stream be

$\frac{12}{5-X}$ = $\frac{12}{5+X}$ + 1

The value of x satisfying the above equation is 1

Now,

$\frac{N}{5+1}$ + $\frac{N}{5-1}$ ≥ 2

$\frac{2N+3N}{12}$ ≥ 2

⇒ N ≥ 4.8

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**10. XAT 2021 QADI | Modern Math - Probability**

Rahul has just made a 3 × 3 magic square, in which, the sum of the cells along any row, column or diagonal, is the same number N. The enries in the cells are given as expressions in x, y and Z. Find N

- A.
12

- B.
36

- C.
21

- D.
40

- E.
24

Answer: Option B

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**Explanation** :

Sum of 3rd row = sum of 2nd column

⇒ 2x + 4y = y + 2z - 1

⇒ 2x + 3y - 2z = -1 ...(A)

Sum of diagonals are also equal

⇒ 3x + 4y + z - 1 = y + z + 2x + y + z

⇒ x + 2y - z = 1 ...(B)

Solving A and B we get y = 3

Putting it in A, we get x - z = -5 ...(C)

Sum of 1st row = sum of 2nd column

5x + 5y + z = 3x + 4y + 2z

⇒ 2x + y - z = 0

Since y = 3, 2x - z = -3 ...(D)

Solving C and D we get x = 2 and z = 7

Hence N = 36

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**11. XAT 2021 QADI | Arithmetic - Time, Speed & Distance**

On the bank of the pristine Tunga river, a deer and a tiger are joyfully playing with each other. The deer notices that it is 40 steps away from the tiger and starts running towards it. At the same time, the tiger starts running away from the deer. Both run on the same straight line. For every five steps the deer takes, the tiger takes six. However, the deer takes only two steps to cover the distance that the tiger covers in three. In how many steps can the deer catch the tiger?

- A.
200

- B.
To solve this, the length of a deer’s step must also be given

- C.
120

- D.
360

- E.
320

Answer: Option A

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**Explanation** :

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

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**Read the following scenario and answer the three questions that follow.**

A company awards incentives to its employees for successful project performances. It rates successful project performance in categories A*, A, B, and C. Employees, in solo projects rated A*, A, B, and C, are awarded incentives ₹6 lakh, ₹5 lakh, ₹3 lakh, and ₹1 lakh respectively. When a project has multiple team members, the following scheme is used to award the incentives:

For example, for a project rated A, with three members, the team lead gets ₹4 lakh, and the other team members get ₹2.5 lakh each. A project always has a single team lead. Six employees: Altaf, Bose, Chakrabarthi, Dipa, Ernie, and Fatima receive a total of ₹45 lakh in incentives by participating in a total of eight different projects that does not involve any other person. Not all six employees are involved in all eight projects.

The following are additionally known about these eight projects:

1. One project involves all six employees. Four projects involve three each, and the rest, two each.

2. Exactly three projects are rated C, for which a total of ₹4.8 lakh is paid.

3. Only one project is rated A*

**12. XAT 2021 QADI | DI - Tables & Graphs**

What BEST is known about the team compositions for the projects rated C?

- A.
The three teams have two, three and six members respectively.

- B.
All are either two-member or three-member teams.

- C.
All are three-member teams.

- D.
One is the six-member team, the rest are two-member teams.

- E.
All are two-member teams.

Answer: Option E

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**Explanation** :

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

Workspace:

**Read the following scenario and answer the three questions that follow.**

A company awards incentives to its employees for successful project performances. It rates successful project performance in categories A*, A, B, and C. Employees, in solo projects rated A*, A, B, and C, are awarded incentives ₹6 lakh, ₹5 lakh, ₹3 lakh, and ₹1 lakh respectively. When a project has multiple team members, the following scheme is used to award the incentives:

For example, for a project rated A, with three members, the team lead gets ₹4 lakh, and the other team members get ₹2.5 lakh each. A project always has a single team lead. Six employees: Altaf, Bose, Chakrabarthi, Dipa, Ernie, and Fatima receive a total of ₹45 lakh in incentives by participating in a total of eight different projects that does not involve any other person. Not all six employees are involved in all eight projects.

The following are additionally known about these eight projects:

1. One project involves all six employees. Four projects involve three each, and the rest, two each.

2. Exactly three projects are rated C, for which a total of ₹4.8 lakh is paid.

3. Only one project is rated A*

**13. XAT 2021 QADI | Arithmetic - Percentage**

What BEST is known about the team composition for the project rated A*?

- A.
A three-member team

- B.
Either a three-member team or the six-member team

- C.
A two-member team

- D.
Either a two-member team or a three-member team

- E.
The six-member team

Answer: Option A

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**Explanation** :

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

Workspace:

**Read the following scenario and answer the three questions that follow.**

A company awards incentives to its employees for successful project performances. It rates successful project performance in categories A*, A, B, and C. Employees, in solo projects rated A*, A, B, and C, are awarded incentives ₹6 lakh, ₹5 lakh, ₹3 lakh, and ₹1 lakh respectively. When a project has multiple team members, the following scheme is used to award the incentives:

For example, for a project rated A, with three members, the team lead gets ₹4 lakh, and the other team members get ₹2.5 lakh each. A project always has a single team lead. Six employees: Altaf, Bose, Chakrabarthi, Dipa, Ernie, and Fatima receive a total of ₹45 lakh in incentives by participating in a total of eight different projects that does not involve any other person. Not all six employees are involved in all eight projects.

The following are additionally known about these eight projects:

1. One project involves all six employees. Four projects involve three each, and the rest, two each.

2. Exactly three projects are rated C, for which a total of ₹4.8 lakh is paid.

3. Only one project is rated A*

**14. XAT 2021 QADI | Algebra - Simple Equations**

Total amount of money paid for projects rated A (in lakhs of Rupees) is:

- A.
19

- B.
15

- C.
16

- D.
17

- E.
18

Answer: Option E

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**Explanation** :

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

Workspace:

**Read the following scenario and answer the three questions that follow.**

A quick survey at the end of a purchase at buyagain.com asks the following three questions to each shopper:

1. Are you shopping at the website for the first time? (YES or NO)

2. Specify your gender: (MALE or FEMALE)

3. How satisfied are you? (HAPPY, NEUTRAL or UNHAPPY)

240 shoppers answer the survey, among whom 65 are first time shoppers. Furthermore:

i. The ratio of the numbers of male to female shoppers is 1 : 2 while the ratio of the numbers of unhappy, happy and neutral shoppers is 3 : 4 : 5

ii. The ratio of the numbers of happy first-time male shoppers, happy returning male shoppers, unhappy female shoppers, neutral male shoppers, neutral female shoppers and happy female shoppers is 1 : 1 : 4 : 4 : 6 : 6

iii. Among the first-time shoppers, the ratio of the numbers of happy male, neutral male, unhappy female and the remaining female shoppers is 1 : 1 : 1 : 2, while the number of happy first-time female shoppers is equal to the number of unhappy first-time male shoppers

**15. XAT 2021 QADI | Algebra - Simple Equations**

What is the number of happy male shoppers?

- A.
10

- B.
15

- C.
5

- D.
20

- E.
40

Answer: Option D

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**Explanation** :

From the given data the following table can be created:

Hence the value of x=10

Workspace:

**Read the following scenario and answer the three questions that follow.**

A quick survey at the end of a purchase at buyagain.com asks the following three questions to each shopper:

1. Are you shopping at the website for the first time? (YES or NO)

2. Specify your gender: (MALE or FEMALE)

3. How satisfied are you? (HAPPY, NEUTRAL or UNHAPPY)

240 shoppers answer the survey, among whom 65 are first time shoppers. Furthermore:

i. The ratio of the numbers of male to female shoppers is 1 : 2 while the ratio of the numbers of unhappy, happy and neutral shoppers is 3 : 4 : 5

ii. The ratio of the numbers of happy first-time male shoppers, happy returning male shoppers, unhappy female shoppers, neutral male shoppers, neutral female shoppers and happy female shoppers is 1 : 1 : 4 : 4 : 6 : 6

iii. Among the first-time shoppers, the ratio of the numbers of happy male, neutral male, unhappy female and the remaining female shoppers is 1 : 1 : 1 : 2, while the number of happy first-time female shoppers is equal to the number of unhappy first-time male shoppers

**16. XAT 2021 QADI | Algebra - Simple Equations**

Which among the following is the lowest?

- A.
Number of neutral first-time female shoppers

- B.
Number of unhappy first-time female shoppers

- C.
Number of unhappy first-time male shoppers

- D.
Number of neutral first-time male shoppers

- E.
Number of happy returning male shoppers

Answer: Option A

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**Explanation** :

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

Workspace:

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