XAT 2019 QADI questions and solutions

Previous year paper questions for XAT 2019 QA

Join our Telegram Channel for CAT/MBA Preparation.

1. XAT 2019 QADI | Arithmetic - Ratio, Proportion & Variation

Two numbers a and b are inversely proportional to each other. If a increases by 100%, then b decreases by

A.
200%
B.
50%
C.
100%
D.
80%
E.
150%

2. XAT 2019 QADI | Arithmetic - Percentage

A, B, C, D and E are five employees working in a company. In two successive years, each of them got hikes in his salary as follows:

A : p% and (p + 1)%,
B : (p + 2)% and (p - 1)%,
C : (p + 3)% and (p - 2)%,
D : (p + 4)% and (p - 3)%,
E : (p + 5)% and (p - 4)%.

If all of them have the same salary at the end of two years, who got the least hike in his salary?

A.
E
B.
B
C.
D
D.
A
E.
C

3. XAT 2019 QADI | Geometry - Mensuration

A gold ingot in the shape of a cylinder is melted and the resulting molten metal molded into a few identical conical ingots. If the height of each cone is half the height of the original cylinder and the area of the circular base of each cone is one ﬁfth that of the circular base of the cylinder, then how many conical ingots can be made?

A.
40
B.
30
C.
60
D.
20
E.
10

4. XAT 2019 QADI | Arithmetic - Average

A ﬁrm pays its ﬁve clerks Rs. 15,000 each, three assistants Rs. 40,000 each and its accountant Rs. 66,000. Then the mean salary in the ﬁrm comprising of these nine employees exceeds its median salary by rupees

A.
14600
B.
14000
C.
15480
D.
15200
E.
14720

5. XAT 2019 QADI | Algebra - Surds & Indices

If $\sqrt[3]{7^{a} \times (35)^{(b + 1)} \times (20)^{(c + 2)}}$ is a whole number then which one of the statements below is consistent with it?

A.
a = 3, b = 2, c = 1
B.
a = 3, b = 1, c = 1
C.
a = 2, b = 1, c = 2
D.
a = 2, b = 1, c = 1
E.
a = 1, b = 2, c = 2

6. XAT 2019 QADI | Geometry - Circles

Let C be a circle of radius √20 cm. Let l₁, l₂ be the lines given by 2x − y −1 = 0 and x + 2y −18 = 0, respectively. Suppose that l₁ passes through the center of C and that l₂ is tangent to C at the point of intersection of l₁ and l₂.

If (a, b) is the center of C, which of the following is a possible value of a + b?

A.
11
B.
14
C.
17
D.
8
E.
20

7. XAT 2019 QADI | Arithmetic - Profit & Loss

An article is marked x% above the cost price. A discount of 2/3x% if given on the marked price. If the profit is 4% of the cost price and the value of x lies between 25 and 50, then the value of 50% of x is:

A.
15
B.
13
C.
20
D.
16
E.
12

Answer: Option A

Video Explanation

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Let the CP of the article be Rs 100.

∴ M.P = 100 + x

As a discount of 2x/3 % is given on the Marked Price.

SP = (100 + x) $(1 - \frac{2 x / 3}{100})$ …(1)

Also, since profit is 4%, it means selling price = 100 + 4 = 104 …(2)

Equating (1) and (2)

⇒ (100 + x) $(1 - \frac{2 x / 3}{100})$ = 104

⇒ 100 + x – $\frac{2 x}{3}$ – $\frac{2 x^{2}}{300}$ = 104

⇒ $\frac{2 x^{2}}{300}$ - $\frac{x}{3}$ + 4 = 0

⇒ x² – 50x + 600 = 0

⇒ x = 20 or 30.

Since it is given that x is between 25 and 50 hence x = 30.

∴ 50% of 30 = 15.

Hence, option (a).

8. XAT 2019 QADI | Geometry - Coordinate Geometry

Let P be the point of intersection of the lines 3x + 4y = 2a and 7x + 2y = 2018 and Q the point of intersection of the lines 3x + 4y = 2018 and 5x + 3y = 1. If the line through P and Q has slope 2, the value of a is:

A.
1/2
B.
1
C.
4035
D.
1009
E.
3026

Answer: Option E

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

P be the point of intersection of the lines 3x + 4y = 2a and 7x + 2y = 2018.

Solving these two equations we get the coordinates of P in terms of a.

∴ P ≡ $(\frac{4036 - 2 a}{11}, \frac{7 a - 3027}{11})$

Q the point of intersection of the lines 3x + 4y = 2018 and 5x + 3y = 1

Solving these two equations we get the coordinates of Q.

∴ Q ≡ (-550, 917)

Now slope of line connecting P and Q is 2

∴ $\frac{\frac{7 a - 3027}{11} - 917}{\frac{4036 - 2 a}{11} + 550}$ = $\frac{2}{1}$

⇒ $\frac{7 a - 13114}{10086 - 2 a}$ = $\frac{2}{1}$

⇒ 11a = 33286

⇒ a = 3026

Hence, option (e).

9. XAT 2019 QADI | Algebra - Number Theory

When opening his fruit shop for the day a shopkeeper found that his stock of apples could be perfectly arranged in a complete triangular array: that is, every row with one apple more than the row immediately above, going all the way up ending with a single apple at the top.

During any sales transaction, apples are always picked from the uppermost row, and going below only when that row is exhausted. When one customer walked in the middle of the day she found an incomplete array in display having 126 apples totally. How many rows of apples (complete and incomplete) were seen by this customer? (Assume that the initial stock did not exceed 150 apples.)

A.
14
B.
13
C.
15
D.
11
E.
12

Answer: Option E

Video Explanation

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

In the given triangular array, 1st row will have 1 apple, 2nd row will have 2 apples and so on.

∴ n^th row will have n apples.

⇒ Total number of apples initially = 1 + 2 + 3 + … + n = $\frac{n (n + 1)}{2}$

Initially total number of apples should be greater than 126 but less than or equal to 150

∴ 126 < $\frac{n (n + 1)}{2}$ ≤ 150

Only integral value of n satisfying this is 16.

⇒ $\frac{16 \times 17}{2}$ = 136

∴ Initially there are 16 rows and 136 apples arranged in a triangular array in these 16 rows.

As the customer observes 126 apples, it would mean that 10 apples were removed.

Now, apples are removed starting from Row 1, which has 1 apple. So apples must have been removed in such a way with 1 apple from Row 1, 2 apples from Row 2, 3 apples from Row 3 and 4 apples from Row 4.

∴ Total 10 apples were removed the first 4 rows.

As out of 16 rows, apples are removed till Row 4, it would mean that only 16 - 4 or 12 rows of apples are visible to the customer.

Hence, option (e).

10. XAT 2019 QADI | Algebra - Logarithms

$\frac{\log (97 - 56 \sqrt{3})}{\log (\sqrt{7 + 4 \sqrt{3}})}$ equals which of the following?

A.
-5
B.
-3
C.
None of the others
D.
-4
E.
-2

Answer: Option D

Video Explanation

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Given $\frac{\log (97 - 56 \sqrt{3})}{\log (\sqrt{7 + 4 \sqrt{3}})}$

= $\frac{\log {(7 - 4 \sqrt{3})}^{2}}{\log {(7 + 4 \sqrt{3})}^{1 / 2}}$

Now, $7 + 4 \sqrt{3}$ = $\frac{1}{7 - 4 \sqrt{3}}$

⇒ $\frac{\log {(7 - 4 \sqrt{3})}^{2}}{\log {(7 + 4 \sqrt{3})}^{1 / 2}}$ = $\frac{\log {(7 - 4 \sqrt{3})}^{2}}{\log {(7 - 4 \sqrt{3})}^{- 1 / 2}}$ = $\frac{2}{- 1 / 2}$ = -4

11. XAT 2019 QADI | Geometry - Quadrilaterals & Polygons

In the trapezium ABCD the sides AB and CD are parallel. The value of $\frac{\sin ∠ B A C}{\sin ∠ B A D}$ is

A.
AD/AC
B.
AB/CD
C.
BC/AD
D.
AC/AD
E.
AC/CD

12. XAT 2019 QADI | Arithmetic - Simple & Compound Interest

A computer is sold either for Rs.19200 cash or for Rs.4800 cash down payment together with five equal monthly installments. If the rate of interest charged is 12% per annum, then the amount of each installment (nearest to a rupee) is

A.
Rs. 2965
B.
Rs. 2990
C.
Rs.3016
D.
Rs. 2896
E.
Rs. 2880

Answer: Option A

Video Explanation

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Price of computer = Rs 19,200

Down payment = Rs. 4,800

∴ Amount borrowed (i.e., loan taken) = 19200 – 4800 = Rs. 14,400.

This amount has to be repaid equally over 5 months at 12% p.a.

Let Rs. x is paid at the end of every month.

Interest charged for 1 month = 12%/12 = 1%

∴ 14400 $(1 + \frac{1 \times 5}{100})$ = x $(1 + \frac{1 \times 4}{100})$ + x $(1 + \frac{1 \times 3}{100})$ + x $(1 + \frac{1 \times 2}{100})$ + x $(1 + \frac{1 \times 1}{100})$ + x

⇒ 15120 = 1.04x + 1.03x + 1.02x + 1.01x + x

⇒ 15120 = 5.1x

⇒ x = 15120/5.1 ≈ 2965.

Hence, option (a).

13. XAT 2019 QADI | Geometry - Quadrilaterals & Polygons

In the picture below, EFGH, ABCD are squares, and ABE, BCF, CDG, DAH are equilateral triangles. What is the ratio of the area of the square EFGH to that of ABCD?

A.
√2 + 2
B.
3 + √2
C.
√2 + √3
D.
√3 + √2
E.
1 + √3

14. XAT 2019 QADI | Geometry - Triangles

The figure below shows two right angled triangles ∆OAB and ∆OQP with right angles at vertex A and P, respectively, having the common vertex O, The lengths of some of the sides are indicated in the figure. (Note that the figure is not drawn to scale.) AB and OP are parallel. What is ∠QOB?

A.
tan^–1(2/3)
B.
45°
C.
60°
D.
30°
E.
tan^–1(3/2)

Answer: Option B

Video Explanation

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Consider the figure given below.

In ∆POQ, OQ = $\sqrt{1^{2} + 2^{2}}$ = √5

In ∆AOB, OB = $\sqrt{1^{2} + 3^{2}}$ = √10

In ∆DQB, QB = $\sqrt{2^{2} + 1^{2}}$ = √5

Now, in ∆QOB, OB² = OQ² + QB²

⇒ ∆QOB is a right isosceles triangle, right angles at Q.

∴ ∠QOB = 45°

Hence, option (b).

15. XAT 2019 QADI | Algebra - Functions & Graphs

Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:

A.
48
B.
26
C.
49
D.
24
E.
23

16. XAT 2019 QADI | Geometry - Triangles

Let ABC be an isosceles triangle. Suppose that the sides AB and AC are equal and let the length of AB be x cm. Let b denote the angle ∠ABC and sin b = 3/5. If the area of the triangle ABC is M sq. cm, then which of the following is true about M?

A.
x²/4 ≤ M < x²/2
B.
3x²/4 ≤ M < x²
C.
M ≥ x²
D.
x²/2 ≤ M < 3x²/4
E.
M < x²/4

Answer: Option A

Video Explanation

Join our Telegram Channel for CAT/MBA Preparation.

Explanation :

Now ∆ABC is an isosceles triangle where AB = AC. Let a perpendicular from A meet BC at D. As ∆ABC is isosceles, AD is a perpendicular bisector and BD = CD.

Given, Sin b = 3/5

⇒ Cos b = 4/5

In ∆ABD,

Sin b = $\frac{3}{5}$ = $\frac{A D}{A B}$

⇒ AD = $\frac{3}{5} A B$ = $\frac{3 x}{5}$

Also, Cos b = $\frac{4}{5}$ = $\frac{B D}{A B}$

BD = $\frac{4}{5} A B$ = $\frac{4 x}{5}$

∆ABC, BD = CD = 4x/5

∴ BC = 8x/5

⇒ Area of ∆ABC = ½ × BC × AD = ½ × 8x/5 × 3x/5 = 12x/25 = 0.48x.

Looking at the options we can see that M lies between x²/4 and x²/2.

Hence, option (a).

17. XAT 2019 QADI | Algebra - Number Theory

If x² + x + 1 = 0, then x²⁰¹⁸+ x²⁰¹⁹ equals which of the following:

A.
-x
B.
x
C.
None of the others
D.
x - 1
E.
x + 1

18. XAT 2019 QADI | Geometry - Circles

What is the maximum number of points that can be placed on a circular disk of radius 1 metre (some of the points could be placed on the bounding circle of the disk) such that no two points are at a distance of less than 1 metre from each other?

A.
5
B.
8
C.
6
D.
9
E.
7

19. XAT 2019 QADI | Modern Math - Permutation & Combination | Data Sufficiency

A bag contains marbles of three colours-red, blue and green. There are 8 blue marbles in the bag. There are two additional statement of facts available:

If we pull out marbles from the bag at random, to guarantee that we have at least 3 green marbles, we need to extract 17 marbles.
If we pull out marbles from the bag at random, to guarantee that we have at least 2 red marbles, we need to extract 19 marbles.

Which of the two statements above, alone or in combination shall be sufficient to answer the question "how many green marbles are there in the bag"?

A.
Both statements taken together are suﬃcient to answer the question, but neither statement alone is suﬃcient.
B.
Each statement alone is suﬃcient to answer the question.
C.
Statements 1 and 2 together are not suﬃcient, and additional data is needed to answer the question.
D.
Statement 2 alone is suﬃcient, but statement 1 alone is not suﬃcient to answer the question.
E.
Statement 1 alone is suﬃcient, but statement 2 alone is not suﬃcient to answer the question.

20. XAT 2019 QADI | Algebra - Number Theory | Data Sufficiency

We have two unknown positive integers m and n, whose product is less than 100.
There are two additional statement of facts available:

mn is divisible by six consecutive integers { j, j + 1,...,j + 5 }
m + n is a perfect square.

Which of the two statements above, alone or in combination shall be sufficient to determine the numbers m and n?

A.
Statements 1 and 2 together are not suﬃcient, and additional data is needed to answer the question.
B.
Both statements taken together are suﬃcient to answer the question, but neither statement alone is suﬃcient.
C.
Each statement alone is suﬃcient to answer the question.
D.
Statement 2 alone is suﬃcient, but statement 1 alone is not suﬃcient to answer the question.
E.
Statement 1 alone is suﬃcient, but statement 2 alone is not suﬃcient to answer the question.

21. XAT 2019 QADI | LR - Mathematical Reasoning

Which of the following pairs of cities are in the same time zone?

A.
Vaq and Sab
B.
No pair of cities are in the same time zone.
C.
Sab and Raz
D.
Sab and Raz
E.
Zut and Yag

22. XAT 2019 QADI | LR - Mathematical Reasoning

What is the total time taken in minutes by the train to go from Zut to Raz?

A.
28 hours, 40 minutes
B.
22 hours, 40 minutes
C.
24 hours, 40 minutes
D.
20 hours, 40 minutes
E.
16 hours, 40 minutes

23. XAT 2019 QADI | LR - Mathematical Reasoning

What time is it at Yag when it is 12:00 noon at Sab?

A.
5:00 pm
B.
7:00 pm
C.
9:30 pm
D.
2:30 pm
E.
12:00 pm

24. XAT 2019 QADI | DI - Tables & Graphs

How many students major in chemistry?

A.
200
B.
180
C.
190
D.
170
E.
175

25. XAT 2019 QADI | DI - Tables & Graphs

12% of all students are from Chennai. What is the largest possible percentage of economics students that can be from Chennai, rounded oﬀ to the nearest integer?

A.
69%
B.
71%
C.
75%
D.
73%
E.
77%

26. XAT 2019 QADI | DI - Tables & Graphs

If the proportion of physics majors who are from Delhi is the same as the proportion of engineering majors who are from Delhi, how many engineering majors are from Delhi?

A.
22
B.
26
C.
18
D.
20
E.
24

27. XAT 2019 QADI N/A

Given that a and b are integers and that 5x + 2√7 is a root of the polynomial x² - ax + b + 2√7 in x, what is the value of b?

A.
14
B.
9
C.
7
D.
2
E.
5

XAT 2019 QADI | Previous Year XAT Paper

Feedback