XAT 2020 QADI questions and solutions

Previous year paper questions for XAT 2020 QA

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1. XAT 2020 QADI | Geometry - Triangles

Two lighthouses, located at points A and B on the earth, are 60 feet and 40 feet tall respectively. Each lighthouse is perfectly vertical and the land connecting A and B is perfectly flat. The topmost point of the lighthouse at A is A’ and of the lighthouse at B is B’. Draw line segments A’B and B’A, and let them intersect at point C’. Drop a perpendicular from C’ to touch the earth at point C. What is the length of CC’ in feet?

A.
20
B.
30
C.
24
D.
The distance between A and B is also needed to solve this
E.
25

Answer: Option C

Video Explanation

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Explanation :

∆BAA’ ~ ∆BCC’
∴ $\frac{B C}{B A} = \frac{C C'}{A A'}$ …(1)

Also, ∆ABB’ ~ ∆ACC’
∴ $\frac{A C}{A B} = \frac{C C'}{B B'}$ …(2)

Adding (1) and (2) we get

$\frac{A C + B C}{A B} = \frac{C C'}{A A'} + \frac{C C'}{B B'}$

⇒ 1 = $\frac{C C'}{A A'} + \frac{C C'}{B B'}$

⇒ $\frac{1}{C C'} = \frac{1}{A A'} + \frac{1}{B B'}$

⇒ $\frac{1}{C C'} = \frac{1}{60'} + \frac{1}{40}$ = $\frac{1}{24}$

∴ CC’ = 24.

Hence, option (c).

2. XAT 2020 QADI | Miscellaneous

If A ʘ B = (A + B) × B, then what is (5 ʘ 2) ʘ 5 ?

A.
95
B.
275
C.
125
D.
74
E.
200

3. XAT 2020 QADI | Arithmetic - Percentage

Nalini has received a total of 600 WhatsApp messages from four friends Anita, Bina, Chaitra and Divya. Bina and Divya have respectively sent 30% and 20% of these messages, while Anita has sent an equal number of messages as Chaitra. Moreover, Nalini finds that of Anita’s, Bina’s, Chaitra’s and Divya’s messages, 60%, 40%, 80% and 50% respectively are jokes. What percentage of the jokes, received by Nalini, have been sent neither by Divya nor by Bina?

A.
65.12
B.
61.4
C.
57
D.
38.6
E.
34.88

4. XAT 2020 QADI | Algebra - Progressions

A man is laying stones, from start to end, along the two sides of a 200-meter-walkway. The stones are to be laid 5 meters apart from each other. When he begins, all the stones are present at the start of the walkway. He places the first stone on each side at the walkway’s start. For all the other stones, the man lays the stones first along one of the walkway’s sides, then along the other side in an exactly similar fashion. However, he can carry only one stone at a time. To lay each stone, the man walks to the spot, lays the stone, and then walks back to pick another. After laying all the stones, the man walks back to the start, which marks the end of his work. What is the total distance that the man walks in executing this work? Assume that the width of the walkway is negligible.

A.
16,200 meters
B.
8,200 meters
C.
8,050 meters
D.
16,400 meters
E.
4,100 meters

5. XAT 2020 QADI | Arithmetic - Time, Speed & Distance

Two friends, Ram and Shyam, start at the same point, at the same time. Ram travels straight north at a speed of 10km/hr, while Shyam travels straight east at twice the speed of Ram. After 15 minutes, Shyam messages Ram that he is just passing by a large telephone tower and after another 15 minutes Ram messages Shyam that he is just passing by an old banyan tree. After some more time has elapsed, Ram and Shyam stop. They stop at the same point of time. If the straight-line distance between Ram and Shyam now is 50 km, how far is Shyam from the banyan tree (in km)? (Assume that Ram and Shyam travel on a flat surface.)

A.
20√5 + 5
B.
20√5 - 5
C.
5√21
D.
45
E.
115/3

6. XAT 2020 QADI | Geometry - Mensuration

A rectangular swimming pool is 50 meters long and 25 meters wide. Its depth is always the same along its width but linearly increases along its length from 1 meter at one end to 4 meters at the other end. How much water (in cubic meters) is needed to completely fill the pool?

A.
3750
B.
2500
C.
1250
D.
1874
E.
3125

7. XAT 2020 QADI | Geometry - Circles | Geometry - Quadrilaterals & Polygons

A rectangular field is 40 meters long and 30 meters wide. Draw diagonals on this field and then draw circles of radius 1.25 meters, with centers only on the diagonals. Each circle must fall completely within the field. Any two circles can touch each other but should not overlap.

What is the maximum number of such circles that can be drawn in the field?

A.
39
B.
40
C.
37
D.
36
E.
38

8. XAT 2020 QADI | Algebra - Number Theory

What is the remainder if 19²⁰ – 20¹⁹ is divided by 7?

A.
5
B.
1
C.
6
D.
0
E.
3

Answer: Option A

Video Explanation

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Explanation :

$R [\frac{19^{20}}{7}]$ = $R [\frac{5^{20}}{7}]$ = $R [\frac{25^{10}}{7}]$ = $R [\frac{4^{10}}{7}]$ = $R [\frac{16^{5}}{7}]$ = $R [\frac{2^{5}}{7}]$ = $R [\frac{32}{7}]$ = 4

$R [\frac{20^{19}}{7}]$ = $R [\frac{{(- 1)}^{19}}{7}]$ = -1

$R [\frac{19^{20} - 20^{19}}{7}]$ = 4 - (-1) = 5

Hence, option (a).

9. XAT 2020 QADI | Geometry - Mensuration

Six drums are used to store water. Five drums are of equal capacity, while the sixth drum has double the capacity of each of these five drums. On one morning, three drums are found half full, two are found two-thirds full and one is found completely full. It is attempted to transfer all the water to the smaller drums. How many smaller drums are adequate to store the water?

A.
Four but not three
B.
Three or four, depending on which drum had how much water initially
C.
Five but not four
D.
Five may be inadequate, depending on which drum had how much water initially
E.
Three but not two

10. XAT 2020 QADI | Algebra - Number Theory

When expressed in a decimal form, which of the following numbers will be nonterminating as well as non-repeating?

A.
$(\frac{π}{2}) [\frac{1}{π} + 1] - \frac{π}{2}$
B.
sin²1° + sin²2° + … + sin²89°
C.
$\frac{\sqrt[3]{729}}{3} + \frac{22}{7}$
D.
$(4 - π) [1 + \frac{π}{4} + {(\frac{π}{4})}^{2} + {(\frac{π}{4})}^{3} + . . . i n f i n i t e t e r m s]$
E.
$\sqrt{2} (3 \sqrt{2} - \frac{4}{\sqrt{2}}) + \sqrt{3}$

Answer: Option E

Video Explanation

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Explanation :

We need to check options.

Option (a): $\frac{π}{2} [\frac{1}{π} + 1] - \frac{π}{2}$
= $\frac{1}{2} + \frac{π}{2} - \frac{π}{2}$ = $\frac{1}{2}$ = 0.5 (terminating)

Option (b): sin21° + sin22° + … + sin288° + sin289°
= sin21° + sin22° + … + sin245° + … + cos22° + cos21°
= 44 + ½ = 44.5 (terminating)

Option (c): $\frac{\sqrt[3]{729}}{3} + \frac{22}{7}$
= $\frac{9}{3} + \frac{22}{7}$ = 3 + 22/7 (terminating)

Option (d): $(4 - π) [1 + \frac{π}{4} + {(\frac{π}{4})}^{2} + {(\frac{π}{4})}^{3} + . . . i n i f i n i t e t e r m s]$
= $(4 - π) [\frac{1}{1 - \frac{π}{4}}]$ = 4 (non-terminating)

Option (e): $\sqrt{2} (3 \sqrt{2} - \frac{4}{\sqrt{2}}) + \sqrt{3}$
= 6 - 4 + √3 = 2 + √3 (non-terminating and non-repeating)

Hence, option (e).

11. XAT 2020 QADI | Arithmetic - Time & Work

X, Y, and Z are three software experts, who work on upgrading the software in a number of identical systems. X takes a day off after every 3 days of work, Y takes a day off after every 4 days of work and Z takes a day off after every 5 days of work.

Starting afresh after a common day off,
i) X and Y working together can complete one new upgrade job in 6 days
ii) Z and X working together can complete two new upgrade jobs in 8 days
iii) Y and Z working together can complete three new upgrade jobs in 12 days

If X, Y and Z together start afresh on a new upgrade job (after a common day off), exactly how many days will be required to complete this job?

A.
2 days
B.
3.5 days
C.
2.5 days
D.
4 days
E.
5 days

12. XAT 2020 QADI | Modern Math - Probability

Ashok has a bag containing 40 cards, numbered with the integers from 1 to 40. No two cards are numbered with the same integer. Likewise, his sister Shilpa has another bag containing only five cards that are numbered with the integers from 1 to 5, with no integer repeating. Their mother, Latha, randomly draws one card each from Ashok’s and Shilpa’s bags and notes down their respective numbers. If Latha divides the number obtained from Ashok’s bag by the number obtained from Shilpa’s, what is the probability that the remainder will not be greater than 2?

A.
0.91
B.
0.87
C.
0.94
D.
0.73
E.
0.8

13. XAT 2020 QADI | Geometry - Circles

In the figure given below, the circle has a chord AB of length 12 cm, which makes an angle of 60° at the center of the circle, O. ABCD, as shown in the diagram, is a rectangle. OQ is the perpendicular bisector of AB, intersecting the chord AB at P, the arc AB at M and CD at Q. OM = MQ. The area of the region enclosed by the line segments AQ and QB, and the arc BMA, is closest to (in cm²):

A.
137
B.
63
C.
35
D.
69
E.
215

14. XAT 2020 QADI | Arithmetic - Ratio, Proportion & Variation

A box contains 6 cricket balls, 5 tennis balls and 4 rubber balls. Of these, some balls are defective. The proportion of defective cricket balls is more than the proportion of defective tennis balls but less than the proportion of defective rubber balls. Moreover, the overall proportion of defective balls is twice the proportion of defective tennis balls. What BEST can be said about the number of defective rubber balls in the box?

A.
It is exactly 3
B.
It is either 3 or 4
C.
It is exactly 2
D.
It is either 2 or 3
E.
It is either 0 or 1

15. XAT 2020 QADI | Geometry - Circles | Geometry - Quadrilaterals & Polygons

Mohanlal, a prosperous farmer, has a square land of side 2 km. For the current season, he decides to have some fun. He marks two distinct points on one of the diagonals of the land. Using these points as centers, he constructs two circles. Each of these circles falls completely within the land, and touches at least two sides of the land. To his surprise, the radii of both the circles are exactly equal to 2/3 km. Mohanlal plants potatoes on the overlapping portion of these circles.

A.
5( 𝜋 + 4)/27
B.
2(2 𝜋 − 3 √3 )/27
C.
4(𝜋 − 3 √3 )/27
D.
𝟐(𝝅 − 2)/9
E.
(𝝅 − 2)/9

Answer: Option D

Video Explanation

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Explanation :

Length of the diagonal AC = 2√2
⇒ AX = ½ of diagonal = √2

Length of AC₁ = 2/3 × √2 = 2√2/3

⇒ C₁X = AX – AC₁ = √2 - 2√2/3 = √2/3

Using Pythagoras theorem:
XM = $\sqrt{{(\frac{2}{3})}^{2} - {(\frac{\sqrt{2}}{3})}^{2}}$ = $\frac{\sqrt{2}}{3}$

In ∆C₁XM,
C₁X = XM = √2/3 and ∠C₁XM = 90°
⇒ ∠XC₁M = 45°

And ∠LC₁M = 90°

∴ Area of ∆LC₁M = ½ × 2/3 × 2/3 = 2/9

Area of minor arc LM = Area of sector LC₁M - Area of ∆LC₁M

= $\frac{90}{360} \times π \times {(\frac{2}{3})}^{2} - \frac{2}{9}$ = $\frac{π - 2}{9}$

∴ Area of overlapping region = $2 (\frac{π - 2}{9})$

Hence, option (d).

16. XAT 2020 QADI | Arithmetic - Time, Speed & Distance

A hare and a tortoise run between points O and P located exactly 6 km from each other on a straight line. They start together at O, go straight to P and then return to O along the same line. They run at constant speeds of 12 km/hr and 1 km/hr respectively. Since the tortoise is slower than the hare, the hare shuttles between O and P until the tortoise goes once to P and returns to O. During the run, how many times are the hare and the tortoise separated by an exact distance of 1 km from each other?

A.
40
B.
24
C.
48
D.
42
E.
22

17. XAT 2020 QADI | Arithmetic - Ratio, Proportion & Variation

X, Y and Z start a web-based venture together. X invests Rs. 2.5 lakhs, Y invests Rs. 3.5 lakhs, and Z invests Rs. 4 lakhs. In the first year, the venture makes a profit of Rs. 2 lakhs. A part of the profit is shared between Y and Z in the ratio of 2 : 3, and the remaining profit is divided among X, Y and Z in the ratio of their initial investments.

The amount that Z receives is four times the amount that X receives. How much amount does Y receive?

A.
Rs. 80,200
B.
Rs. 75,000
C.
Rs. 93,750
D.
Rs. 74,250
E.
Rs. 1,02,500

18. XAT 2020 QADI | Algebra - Simple Equations

A shop sells bags in three sizes: small, medium and large. A large bag costs Rs.1000, a medium bag costs Rs.200, and a small bag costs Rs.50. Three buyers, Ashish, Banti and Chintu, independently buy some numbers of these types of bags. The respective amounts spent by Ashish, Banti and Chintu are equal. Put together, the shop sells 1 large bag, 15 small bags and some medium bags to these three buyers. What is the minimum number of medium bags that the shop sells to them?

A.
7
B.
5
C.
9
D.
4
E.
10

19. XAT 2020 QADI | Algebra - Number Theory

Consider the four variables A, B, C and D and a function Z of these variables, Z = 15A² − 3B⁴ + C + 0.5D. It is given that A, B, C and D must be non-negative integers and that all of the following relationships must hold:
i) 2A + B ≤ 2
ii) 4A + 2B + C ≤ 12
iii) 3A + 4B + D ≤ 15

If Z needs to be maximised, then what value must D take?

A.
15
B.
12
C.
0
D.
10
E.
5

20. XAT 2020 QADI | Geometry - Circles

XYZ is an equilateral triangle, inscribed in a circle. P is a point on the arc YZ such that X and P are on opposite sides of the chord YZ. Which of the following MUST always be true?

A.
XZ + YP = XY + PZ
B.
XP = YP + PZ
C.
XP + PZ = XY + YP
D.
XP = XY
E.
XP = XY + YZ

21. XAT 2020 QADI | DI - Tables & Graphs

Which of the given companies has seen the highest year-on-year growth (in percentage) in any single year during this five-year period?

A.
R
B.
Q
C.
S
D.
P
E.
There was a tie among multiple companies

22. XAT 2020 QADI | DI - Tables & Graphs

It was discovered later that one of the companies misreported its revenue of one of the years. If the misreported revenue is replaced by the correct revenue, the revenues of that company over the five-year period will be in an arithmetic progression. The company that misreported its revenue was

A.
S only
B.
P or S
C.
P only
D.
R or S
E.
P or R

23. XAT 2020 QADI | DI - Tables & Graphs

During the period from 2014 to 2015, the revenue increased by 25% for three of the companies and by 50% for the remaining company. The total increase in revenue, for all four companies put together, was Rs. 125 lakhs.

Which of the following CANNOT be true?

A.
The 2014 revenues of P and R cannot be determined uniquely
B.
From 2014 to 2015, the increases in revenues of at least two companies were the same
C.
From 2014 to 2015, the revenues of P and R increased by different amounts
D.
The company that experienced the 50% increase in revenue also experienced the maximum increase in revenue in absolute terms
E.
The revenue of Q in 2014 was the same as the revenue of R in 2014

24. XAT 2020 QADI | LR - Venn Diagram

Which of the following CANNOT be obtained from the given information?

A.
Number of students choosing exactly one elective
B.
Number of students choosing E1
C.
Number of students choosing E3
D.
Number of students choosing both E1 and E2
E.
Number of students choosing either E1 or E2 or both, but not E3

25. XAT 2020 QADI | LR - Venn Diagram

In addition to the given information, which of the following information is NECESSARY and SUFFICIENT to compute the number of students choosing only E1, only E2 and only E3?

A.
Number of students choosing both E1 and E2
B.
Number of students choosing only E1, and number of students choosing both E2 and E3
C.
Number of students choosing only E2, and number of students choosing both E2 and E3
D.
No extra information is necessary
E.
Number of students choosing both E1 and E2, number of students choosing both E2 and E3, and number of students choosing both E3 and E1

XAT 2020 QADI | Previous Year XAT Paper

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