XAT 2023 QADI questions and solutions

XAT 2023 QADI

Join our Telegram Channel for CAT/MBA Preparation.

1. XAT 2023 QADI | Algebra - Simple Equations

Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?

A.
67
B.
58
C.
49
D.
40
E.
None of the above

2. XAT 2023 QADI | Geometry - Coordinate Geometry

ABC is a triangle and the coordinates of A, B and C are (a, b - 2c), (a, b + 4c) and (-2a, 3c) respectively where a, b and c are positive numbers. The area of the triangle ABC is:

A.
6abc
B.
9abc
C.
6bc
D.
9ac
E.
None of the above

3. XAT 2023 QADI | Arithmetic - Simple & Compound Interest

Jose borrowed some money from his friend at simple interest rate of 10% and invested the entire amount in stocks. At the end of the first year, he repaid 1/5th of the principal amount. At the end of the second year, he repaid half of the remaining principal amount. At the end of third year, he repaid the entire remaining principal amount. At the end of the fourth year, he paid the last three years’ interest amount. As there was no principal amount left, his friend did not charge any interest in the fourth year. At the end of fourth year, he sold out all his stocks. Later, he calculated that he gained Rs. 97500 after paying principal and interest amounts to his friend. If his invested amount in the stocks became double at the end of the fourth year, how much money did he borrow from his friend?

A.
250000
B.
200000
C.
150000
D.
125000
E.
None of the above

4. XAT 2023 QADI | Geometry - Coordinate Geometry

ABC is a triangle with BC = 5. D is thefoot of the perpendicular from A on BC. E is a point on CD such that BE = 3.

The value of AB² - AE² + 6CD is:

A.
5
B.
10
C.
14
D.
18
E.
21

5. XAT 2023 QADI | Arithmetic - Average

Amit has forgotten his 4-digit locker key. He remembers that all the digits are positive integers and are different from each other. Moreover, the fourth digit is the smallest and the maximum value of the first digit is 3. Also, he recalls that if he divides the second digit by the third digit, he gets the first digit. How many different combinations does Amit have to try for unlocking the locker?

A.
2
B.
1
C.
4
D.
5
E.
3

6. XAT 2023 QADI | Algebra - Progressions

Suppose Haruka has a special key ∆ in her calculator called delta key:

Rule 1: If the display shows a one-digit number, pressing delta key ∆ replaces the displayed number with twice its value.

Rule 2: If the display shows a two-digit number, pressing delta key ∆ replaces the displayed number with the sum of the two digits.

Suppose Haruka enters the value 1 and then presses delta key ∆ repeatedly.

After pressing the ∆ key for 68 times, what will be the displayed number?

A.
7
B.
4
C.
10
D.
2
E.
8

7. XAT 2023 QADI | Algebra - Simple Equations

There are three sections in a question paper and each section has 10 questions. First section only has multiple-choice questions, and 2 marks will be awarded for each correct answer. For each wrong answer, 0.5 marks will be deducted. Any unattempted question in this section will be treated as a wrong answer. Each question in the second section carries 3 marks, whereas each question in the third section carries 5 marks. For any wrong answer or un-attempted question in the second and third sections, no marks will be deducted. A student’s score is the addition of marks obtained in all the three sections. What is the sixth highest possible score?

A.
92.5
B.
94
C.
95.5
D.
95
E.
None of the above

8. XAT 2023 QADI | Geometry - Quadrilaterals & Polygons

ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB. Kindly note that BC < AD. P is a point on AD such that CPD is an equilateral triangle. Q is a point on BC such that AQ is parallel to PC. If the area of the triangle CPD is 4√3, find the area of the triangle ABQ.

A.
2√3
B.
4√3
C.
4
D.
4√3
E.
None of the above

9. XAT 2023 QADI | Arithmetic - Profit & Loss

Rajnish bought an item at 25% discount on the printed price. He sold it at 10% discount on the printed price. What is his profit in percentage?

A.
10
B.
15
C.
17.5
D.
20
E.
None of the above

Answer: Option D

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Let the printed price be Rs. 100.

Cost price for Rajnish after 25% discount = Rs. 75

Rajnish sold it at 10% discount in printed price i.e., at Rs. 90

∴ Required profit % = $\frac{90 - 75}{75} \times 100$ = $\frac{15}{75} \times 100$ = 20%

Hence, option (d).

10. XAT 2023 QADI | Geometry - Trigonometry

Find the value of:

$\frac{\sin^{6} 15 ° + \sin^{6} 75 ° + 6 \sin^{2} 15 ° \sin^{2} 75 °}{\sin^{4} 15 ° + \sin^{4} 75 ° + 5 \sin^{2} 15 ° \sin^{2} 75 °}$

A.
sin 15° + sin 75°
B.
6/5
C.
1
D.
sin 15° cos 15°
E.
None of the above

Answer: Option C

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

$\frac{\sin^{6} 15 ° + \sin^{6} 75 ° + 6 \sin^{2} 15 ° \sin^{2} 75 °}{\sin^{4} 15 ° + \sin^{4} 75 ° + 5 \sin^{2} 15 ° \sin^{2} 75 °}$

Let sin²15° = a and sin²75° = b

∴ $\frac{\sin^{6} 15 ° + \sin^{6} 75 ° + 6 \sin^{2} 15 ° \sin^{2} 75 °}{\sin^{4} 15 ° + \sin^{4} 75 ° + 5 \sin^{2} 15 ° \sin^{2} 75 °}$ = $\frac{a^{3} + b^{3} + 6 ab}{a^{2} + b^{2} + 5 ab}$

Now, a³ + b³ = (a + b)³ - 3ab(a + b), and
a² + b² = (a + b)² - 2ab

∴ $\frac{\sin^{6} 15 ° + \sin^{6} 75 ° + 6 \sin^{2} 15 ° \sin^{2} 75 °}{\sin^{4} 15 ° + \sin^{4} 75 ° + 5 \sin^{2} 15 ° \sin^{2} 75 °}$ = $\frac{{(a + b)}^{3} - 3 ab (a + b) + 6 ab}{{(a + b)}^{2} - 2 ab + 5 ab}$

Now, a + b = sin²15° + sin²75° = sin²15° + cos²15° = 1 [∵ Sin𝜃 = Cos(90 - 𝜃)]

∴ $\frac{\sin^{6} 15 ° + \sin^{6} 75 ° + 6 \sin^{2} 15 ° \sin^{2} 75 °}{\sin^{4} 15 ° + \sin^{4} 75 ° + 5 \sin^{2} 15 ° \sin^{2} 75 °}$ = $\frac{1 - 3 ab + 6 ab}{1 - 2 ab + 5 ab}$ = $\frac{1 + 3 ab}{1 + 3 ab}$ = 1

Hence, option (c).

11. XAT 2023 QADI | Modern Math - Probability

A painter draws 64 equal squares of 1 square inch on a square canvas measuring 64 square inches. She chooses two squares (1 square inch each) randomly and then paints them. What is the probability that two painted squares have a common side?

A.
$\frac{112}{2016}$
B.
$\frac{1}{3}$
C.
$\frac{512}{100034}$
D.
$\frac{3}{97}$
E.
$\frac{7}{108}$

Answer: Option A

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Required probability = $\frac{No . of ways of selecting 2 smaller squares with having common side}{No . of ways of selecting 2 smaller squares}$

No. of ways of selecting 2 smaller squares = ⁶⁴C₂ = 32 × 63

Now, to select 2 squares with common side, there are two cases possible.

Case 1: Horizontal pair is selected.
In the first row 2 squares can be selected in 7 ways i.e., (R₁C₁, R₂C₂), (R₁C₂, R₂C₃), ..., (R₁C₇, R₂C₈)
Similarly 2 squares can be selected from each row in 7 ways.
∴ No. of ways of selecting 2 smaller horizontal pair of squares = 7 × 8 = 56.

Case 2: Vertical pair is selected.
In the first column 2 squares can be selected in 7 ways i.e., (C₁R₁, C₁R₂), (C₁R₂, C₁R₃), ..., (C₁R₇, C₁R₈)
Similarly 2 squares can be selected from each column in 7 ways.
∴ No. of ways of selecting 2 smaller vertical pair of squares = 7 × 8 = 56.

⇒ Total no. of ways of selecting 2 smaller squares with common side = 56 + 56 = 112

∴ Required probability = $\frac{112}{32 \times 63}$ = $\frac{112}{2016}$

Hence, option (a).

12. XAT 2023 QADI | Algebra - Number Theory

Let x and y be two positive integers and p be a prime number. If x(x – p) – y(y + p) = 7p, what will be the minimum value of x – y?

A.
1
B.
3
C.
5
D.
7
E.
None of the above

13. XAT 2023 QADI | Arithmetic - Average

Five students appeared for an examination. The average mark obtained by these five students is 40. The maximum mark of the examination is 100, and each of the five students scored more than 10 marks. However, none of them scored exactly 40 marks. Based on the information given, which of the following MUST BE true?

A.
At least, three of them scored a maximum of 40 marks
B.
At least, three of them scored more than 40 marks
C.
At least, one of them scored exactly 41 marks
D.
At most, two of them scored more than 40 marks
E.
At least, one of them scored less than 40 marks

14. XAT 2023 QADI | Algebra - Progressions

Consider a_{n + 1} = $\frac{1}{1 + \frac{1}{a_{n}}}$ for n = 1, 2, ...., 2008, 2009 where a₁ = 1. Find the value of a₁ a₂+ a₂ a₃+ a₃ a₄+ ... + a₂₀₀₈ a₂₀₀₉

A.
_{$\frac{2009}{1000}$}
B.
_{$\frac{2009}{2008}$}
C.
_{$\frac{2008}{2009}$}
D.
_{$\frac{6000}{2009}$}
E.
_{$\frac{2008}{6000}$}

Answer: Option C

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Given, a_{n + 1} = $\frac{1}{1 + \frac{1}{a_{n}}}$

⇒ a₁ = 1

⇒ a₂ = $\frac{1}{1 + \frac{1}{a_{1}}}$ = $\frac{1}{2}$

⇒ a₃ = $\frac{1}{1 + \frac{1}{a_{2}}}$ = $\frac{1}{3}$
...
⇒ a_n = $\frac{1}{n}$

Now: a₁ a₂+ a₂ a₃+ a₃ a₄+ ... + a₂₀₀₈ a₂₀₀₉ = $\frac{1}{1 \times 2}$ + $\frac{1}{2 \times 3}$ + $\frac{1}{3 \times 4}$ + ... + $\frac{1}{2008 \times 2009}$

= $(\frac{1}{1} - \frac{1}{2})$ + $(\frac{1}{2} - \frac{1}{3})$ + $(\frac{1}{3} - \frac{1}{4})$ + ... + $(\frac{1}{2008} - \frac{1}{2009})$

= $\frac{1}{1} - \frac{1}{2009}$ = $\frac{2008}{2009}$

Hence, option (c).

15. XAT 2023 QADI | Arithmetic - Percentage

The Guava club has won 40% of their football matches in the Apple Cup that they have played so far. If they play another n matches and win all of them, their winning percentage will improve to 50. Further, if they play 15 more matches and win all of them, their winning percentage will improve from 50 to 60. How many matches has the Guava club played in the Apple Cup so far? In the Apple Cup matches, there are only two possible outcomes, win or loss; draw is not possible.

A.
50
B.
40
C.
30
D.
Cannot be determined, as the value of n is not given
E.
60

16. XAT 2023 QADI | Arithmetic - Simple & Compound Interest

Separately, Jack and Sristi invested the same amount of money in a stock market. Jack’s invested amount kept getting reduced by 50% every month. Sristi’s investment also reduced every month, but in an arithmetic progression with a common difference of Rs. 15000. They both withdrew their respective amounts at the end of the sixth month. They observed that if they had withdrawn their respective amounts at the end of the fourth month, the ratio of their amounts would have been the same as the ratio after the sixth month. What amount of money was invested by Jack in the stock market?

A.
Rs. 100000
B.
Rs. 120000
C.
Rs. 150000
D.
Rs. 180000
E.
None of the above

Answer: Option A

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Let their initial amounts be Rs. x

After 4 months:
Jack's investment after 4 months = x × ${(\frac{1}{2})}^{4}$ = $\frac{x}{16}$
Sristi's investment after 4 months = x - 15000 × 4 = x - 60000

After 6 months:
Jack's investment after 6 months = x × ${(\frac{1}{2})}^{6}$ = $\frac{x}{64}$
Sristi's investment after 6 months = x - 15000 × 6 = x - 90000

Ratio of their investments after 4 months = Ratio of their investments after 6 months.

⇒ $\frac{x / 16}{x - 60000}$ = $\frac{x / 64}{x - 90000}$

⇒ 4(x - 90,000) = x - 60,000
⇒ 3x = 3,00,000
⇒ x = 1,00,000

Hence, option (a).

17. XAT 2023 QADI | Arithmetic - Time, Speed & Distance

The problem below consists of a question and two statements numbered 1 & 2. You have to decide whether the data provided in the statements are sufficient to answer the question.

Rahim is riding upstream on a boat, from point A to B, at a constant speed. The distance from A to B is 30 km. One minute after Rahim leaves from point A, a speedboat starts from point A to go to point B. It crosses Rahim’s boat after 4 minutes. If the speed of the speedboat is constant from A to B, what is Rahim’s speed in still water?

1. The speed of the speedboat in still water is 30 km/hour.

2. Rahim takes three hours to reach point B from point A.

A.
Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient
B.
Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient
C.
Each statement alone is sufficient
D.
Both statements together are sufficient, but neither of them alone is sufficient
E.
Statements 1 & 2 together are not sufficient

Answer: Option D

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Let the speed of river be 'r' kmph.

Rahim and Speedboat start from A and meet at a point M (say).

Going upstream, Rahim takes 5 minutes to cover this distance while Speedboat takes 4 minutes to cover the same distance.
∴ $\frac{S_{Rahim} - r}{S_{Speedboat} - r}$ = $\frac{4}{5}$ ...(1)

We need to find S_Rahim

Statement (1): S_Speedboat = 30
If we put S_Speedboat = 30 in (1), this alone would not be sufficient to calculate S_Rahim.
∴ Statement (1) alone is not sufficient to answer the question.

Statement (2): Rahim takes 3 hours to reach B.
⇒ S_Rahim - r = 30/3 = 10 kmph.
Since we don't know the value of r, we cannot determine the S_Rahim.
∴ Statement (2) alone is not sufficient to answer the question.

Using both statements together we have, S_Speedboat = 30 kmph and S_Rahim - r = 10 kmph.

Putting these values in (1), we get
$\frac{10}{30 - r}$ = $\frac{4}{5}$
⇒ r = 17.5 kmph.

⇒ S_Rahim - 17.5 = 10
⇒ S_Rahim - 17.5 = 27.5 kmph

∴ Using both statements we can get the answer.

Hence, option (d).

18. XAT 2023 QADI | Geometry - Mensuration

A non-flying ant wants to travel from the bottom corner to the diagonally opposite top corner of a cubical room. The side of the room is 2 meters. What will be the minimum distance that the ant needs to travel?

A.
6 meters
B.
(2√2 + 2) meters
C.
2√3 meters
D.
2√6 meters
E.
2√5 meters

Answer: Option E

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

In a 2D plane, minimum distance between 2 points is the straight line joining these points.

We can convert the cubical room in a 2D plane as shown in the figure.

∴ Shortest route from A to F = $\sqrt{4^{2} + 2^{2}}$ = 2√5.

Hence, option (e).

19. XAT 2023 QADI | Algebra - Inequalities & Modulus

Given A = |x + 3| + |x - 2| - |2x - 8|. The maximum value of |A| is:

A.
111
B.
9
C.
6
D.
3
E.
∞

20. XAT 2023 QADI | Arithmetic - Mixture, Alligation, Removal & Replacement

A small jar contained water, lime and sugar in the ratio of 90 : 7 : 3. A glass contained only water and sugar in it. Contents of both (small jar and glass) were mixed in a bigger jar and the ratio of contents in the bigger jar was 85 : 5 : 10 (water, lime and sugar respectively). Find the percentage of water in the bigger jar?

A.
70
B.
75
C.
80
D.
72.5
E.
85

Answer: Option E

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Let the quantity of water, line and sugar in the bigger jar be 85x, 5x and 10x respectively.

Now, percentage of water in bigger jar = $\frac{85 x}{85 x + 5 x + 10 x} \times 100 %$ = 85%

Hence, option (e).

21. XAT 2023 QADI | Arithmetic - Time, Speed & Distance | Data Sufficiency

The problem below consists of a question and two statements numbered 1 & 2. You have to decide whether the data provided in the statements are sufficient to answer the question.

In a cricket match, three slip fielders are positioned on a straight line. The distance between 1st slip and 2nd slip is the same as the distance between 2nd slip and the 3rd slip. The player X, who is not on the same line of slip fielders, throws a ball to the 3rd slip and the ball takes 5 seconds to reach the player at the 3rd slip. If he had thrown the ball at the same speed to the 1st slip or to the 2nd slip, it would have taken 3 seconds or 4 seconds, respectively. What is the distance between the 2nd slip and the player X?

1. The ball travels at a speed of 3.6 km/hour.

2. The distance between the 1st slip and the 3rd slip is 2 meters.

A.
Statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient
B.
Statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient
C.
Each statement alone is sufficient
D.
Both statements together are sufficient, but neither of them alone is sufficient
E.
Statements 1 & 2 together are not sufficient

22. XAT 2023 QADI | DI - Tables & Graphs

Which of the following will BEST capture the relationship between GDP (x-axis) and Life Satisfaction (y-axis) of countries?

A.
y = x
B.
y = x²
C.
y = log(x)
D.
y = $\frac{1}{x^{2}}$
E.
y = e^x

23. XAT 2023 QADI | DI - Tables & Graphs

Which of the following, about the four islands, can be BEST inferred from the graphs?

A.
Whenever affect balance increases, satisfaction with life decreases
B.
Whenever Pleasant activities increase, satisfaction with life decreases
C.
Whenever Religion increases, satisfaction with life decreases
D.
Whenever satisfaction with life increases, family also increases
E.
Index of monetization varies maximum in Niijhum Dwip

24. XAT 2023 QADI | DI - Tables & Graphs

Which of the following site has the highest fishing to economic ratio?

A.
Gizo
B.
Chittagong
C.
Roviana
D.
Niijhum Dwip
E.
All four islands have equal dependence

25. XAT 2023 QADI | DI - Tables & Graphs

In unknown age category, the ratio of males (unknown age category) and females (unknown age category) to total unknown cases (unknown age category) is same as the ratio of males (All) and females (All) to the total (total confirmed covid positive cases). How many females were in the unknown age category (rounded to nearest integer)?

A.
120
B.
140
C.
110
D.
125
E.
130

26. XAT 2023 QADI | DI - Tables & Graphs

In which age category, the percentage of female covid patients is the HIGHEST?

A.
61-70
B.
31-40
C.
41-50
D.
51-60
E.
81+

27. XAT 2023 QADI | DI - Tables & Graphs

Which of the following is true for “unknown gender Category”?

Unknown age group patients are less likely (percentage term) to provide information about gender than any other age category
Between 31 and 80, when age increases patients, in percentage terms, are less likely to provide information about gender
Elderly (81+) category patients are more likely to give information about gender than 0-18 age group

A.
3 only
B.
2 only
C.
1 and 2
D.
1 and 3
E.
2 and 3

28. XAT 2023 QADI | DI - Tables & Graphs

The addition of 7 distinct positive integers is 1740. What is the largest possible “greatest common
divisor” of these 7 distinct positive integers?

A.
42
B.
60
C.
74
D.
140
E.
None of these

XAT 2023 QADI | Previous Year XAT Paper

Feedback