XAT 2024: Past Year Question Paper with Answer Key | Mock Test Series for XAT - CAT PDF Download

 Page 1


Quant
1. In a small college, students are allowed to take only one specialization. Traditionally, only two specializations
are offered: Science and Arts. Students enrolled to specialize in Science must take Physics and Mathematics
subjects, while students enrolled to specialize in Arts must take Economics and Political Science subjects.
Students enrolled in Science are not allowed to take either Economics or Political Science, while students
enrolled in Arts are not allowed to take either Physics or Mathematics.
Recently, the college has started a third specialization called MatEco that requires students to take
Economics and Mathematics. However, MatEco students would not be allowed to take either Physics or
Political Science. When the college opens this new specialization for enrolment, it allows students, originally
enrolled in Science or Arts, to switch to MatEco.
From among the students originally enrolled in Arts, 20 students switch to MatEco. This makes the number
of Science students twice the number of Arts students. After this, from among the students who originally
enrolled in Science, 45 students switch to MatEco. This makes the number of Arts students twice the
number of Science students.
In total, how many students, from among those originally enrolled in Science or Arts, are now taking
Economics?
A    45
B    65
C    80
D    95
E    None of the remaining options is correct.
2. In a school, the number of students in each class, from Class I to X, in that order, are in an arithmetic
progression. The total number of students from Class I to V is twice the total number of students from Class
VI to X.
If the total number of students from Class I to IV is 462, how many students are there in Class VI?
A    93
B    88
C    83
D    77
E    None of the remaining options is correct.
3. A ight, tr aveling to a destination 11,200 kms away, was supposed to take off at 6:30 AM. Due to bad
weather, the departure of the ight got dela yed by three hours. The pilot increased the average speed of the
airplane by 100 km/hr from the initially planned average speed, to reduce the overall delay to one hour.
Had the pilot increased the average speed by 350 km/hr from the initially planned average speed, when
would have the ight r eached its destination?
Page 2


Quant
1. In a small college, students are allowed to take only one specialization. Traditionally, only two specializations
are offered: Science and Arts. Students enrolled to specialize in Science must take Physics and Mathematics
subjects, while students enrolled to specialize in Arts must take Economics and Political Science subjects.
Students enrolled in Science are not allowed to take either Economics or Political Science, while students
enrolled in Arts are not allowed to take either Physics or Mathematics.
Recently, the college has started a third specialization called MatEco that requires students to take
Economics and Mathematics. However, MatEco students would not be allowed to take either Physics or
Political Science. When the college opens this new specialization for enrolment, it allows students, originally
enrolled in Science or Arts, to switch to MatEco.
From among the students originally enrolled in Arts, 20 students switch to MatEco. This makes the number
of Science students twice the number of Arts students. After this, from among the students who originally
enrolled in Science, 45 students switch to MatEco. This makes the number of Arts students twice the
number of Science students.
In total, how many students, from among those originally enrolled in Science or Arts, are now taking
Economics?
A    45
B    65
C    80
D    95
E    None of the remaining options is correct.
2. In a school, the number of students in each class, from Class I to X, in that order, are in an arithmetic
progression. The total number of students from Class I to V is twice the total number of students from Class
VI to X.
If the total number of students from Class I to IV is 462, how many students are there in Class VI?
A    93
B    88
C    83
D    77
E    None of the remaining options is correct.
3. A ight, tr aveling to a destination 11,200 kms away, was supposed to take off at 6:30 AM. Due to bad
weather, the departure of the ight got dela yed by three hours. The pilot increased the average speed of the
airplane by 100 km/hr from the initially planned average speed, to reduce the overall delay to one hour.
Had the pilot increased the average speed by 350 km/hr from the initially planned average speed, when
would have the ight r eached its destination?
A    11:30 PM
B    7:50 PM
C    5:10 PM
D    8:10 PM
E    10:36 PM
4. 
Consider the equation , where x is a real number.
For how many different values of x does the given equation hold?
A    0
B    1
C    2
D    4
E    Innitely many
5. The cost of running a movie theatre is Rs. 10,000 per day, plus additional Rs. 5000 per show. The theatre has
200 seats. A new movie released on Friday. There were three shows, where the ticket price was Rs. 250 each
for the rst two shows and Rs. 200 for the late-night show .
For all shows together, total occupancy was 80%. What was the maximum amount of prot possible?
A    Rs. 1,20,000
B    Rs. 87,000
C    Rs. 95,000
D    Rs. 91,000
E    Rs. 1,16,000
6. FS food stall sells only chicken biryani. If FS x es a selling price of Rs. 160 per plate, 300 plates of biriyani
are sold. For each increase in the selling price by Rs. 10 per plate, 10 fewer plates are sold. Similarly, for each
decrease in the selling price by Rs. 10 per plate, 10 more plates are sold. FS incurs a cost of Rs. 120 per plate
of biriyani, and has decided that the selling price will never be less than the cost price. Moreover, due to
capacity constraints, more than 400 plates cannot be produced in a day.
If the selling price on any given day is the same for all the plates and can only be a multiple of Rs. 10, then
what is the maximum prot that FS can achie ve in a day?
A    Rs. 25,300
B    Rs. 28,900
C    Rs. 41,400
D    Rs. 52,900
E    None of the remaining options is correct.
log ( x -
5
2) = 2 log (2 x -
25
4)
Page 3


Quant
1. In a small college, students are allowed to take only one specialization. Traditionally, only two specializations
are offered: Science and Arts. Students enrolled to specialize in Science must take Physics and Mathematics
subjects, while students enrolled to specialize in Arts must take Economics and Political Science subjects.
Students enrolled in Science are not allowed to take either Economics or Political Science, while students
enrolled in Arts are not allowed to take either Physics or Mathematics.
Recently, the college has started a third specialization called MatEco that requires students to take
Economics and Mathematics. However, MatEco students would not be allowed to take either Physics or
Political Science. When the college opens this new specialization for enrolment, it allows students, originally
enrolled in Science or Arts, to switch to MatEco.
From among the students originally enrolled in Arts, 20 students switch to MatEco. This makes the number
of Science students twice the number of Arts students. After this, from among the students who originally
enrolled in Science, 45 students switch to MatEco. This makes the number of Arts students twice the
number of Science students.
In total, how many students, from among those originally enrolled in Science or Arts, are now taking
Economics?
A    45
B    65
C    80
D    95
E    None of the remaining options is correct.
2. In a school, the number of students in each class, from Class I to X, in that order, are in an arithmetic
progression. The total number of students from Class I to V is twice the total number of students from Class
VI to X.
If the total number of students from Class I to IV is 462, how many students are there in Class VI?
A    93
B    88
C    83
D    77
E    None of the remaining options is correct.
3. A ight, tr aveling to a destination 11,200 kms away, was supposed to take off at 6:30 AM. Due to bad
weather, the departure of the ight got dela yed by three hours. The pilot increased the average speed of the
airplane by 100 km/hr from the initially planned average speed, to reduce the overall delay to one hour.
Had the pilot increased the average speed by 350 km/hr from the initially planned average speed, when
would have the ight r eached its destination?
A    11:30 PM
B    7:50 PM
C    5:10 PM
D    8:10 PM
E    10:36 PM
4. 
Consider the equation , where x is a real number.
For how many different values of x does the given equation hold?
A    0
B    1
C    2
D    4
E    Innitely many
5. The cost of running a movie theatre is Rs. 10,000 per day, plus additional Rs. 5000 per show. The theatre has
200 seats. A new movie released on Friday. There were three shows, where the ticket price was Rs. 250 each
for the rst two shows and Rs. 200 for the late-night show .
For all shows together, total occupancy was 80%. What was the maximum amount of prot possible?
A    Rs. 1,20,000
B    Rs. 87,000
C    Rs. 95,000
D    Rs. 91,000
E    Rs. 1,16,000
6. FS food stall sells only chicken biryani. If FS x es a selling price of Rs. 160 per plate, 300 plates of biriyani
are sold. For each increase in the selling price by Rs. 10 per plate, 10 fewer plates are sold. Similarly, for each
decrease in the selling price by Rs. 10 per plate, 10 more plates are sold. FS incurs a cost of Rs. 120 per plate
of biriyani, and has decided that the selling price will never be less than the cost price. Moreover, due to
capacity constraints, more than 400 plates cannot be produced in a day.
If the selling price on any given day is the same for all the plates and can only be a multiple of Rs. 10, then
what is the maximum prot that FS can achie ve in a day?
A    Rs. 25,300
B    Rs. 28,900
C    Rs. 41,400
D    Rs. 52,900
E    None of the remaining options is correct.
log ( x -
5
2) = 2 log (2 x -
25
4)
7. A farmer has a triangular plot of land. One side of the plot, henceforth called the base, is 300 feet long and
the other two sides are equal. The perpendicular distance, from the corner of the plot, where the two equal
sides meet, to the base, is 200 feet. To counter the adverse effect of climate change, the farmer wants to dig
a circular pond. He plans that half of the circular area will be inside the triangular plot and the other half will
be outside, which he will purchase at the market rate from his neighbour. The diameter of the circular plot is
entirely contained in the base and the circumference of the pond touches the two equal sides of the triangle
from inside.
If the market rate per square feet of land is Rs. 1400, how much does the farmer must pay to buy the land
from his neighbour for the pond? (Choose the closest option.)
A    Rs. 3,16,80,000
B    Rs. 4,25,60,000
C    Rs. 6,33,60,000
D    Rs. 7,42,80,000
E    Rs. 2,98,20,000
8. A group of boys is practising football in a rectangular ground. Raju and Ratan are standing at the two
opposite mid-points of the two shorter sides. Raju has the ball, who passes it to Rivu, who is standing
somewhere on one of the longer sides. Rivu holds the ball for 3 seconds and passes it to Ratan. Ratan holds
the ball for 2 seconds and passes it back to Raju. The path of the ball from Raju to Rivu makes a right angle
with the path of the ball from Rivu to Ratan. The speed of the ball, whenever passed, is always 10 metre per
second, and the ball always moves on straight lines along the ground.
Consider the following two additional pieces of information:
I. The dimension of the ground is 80 metres × 50 metres.
II. The area of the triangle formed by Raju, Rivu and Ratan is 1000 square metres.
Consider the problem of computing the following: how many seconds does it take for Raju to get the ball
back since he passed it to Rivu? Choose the correct option.
A    I alone is sucient to solve the problem.
B    II alone is sucient to solve the problem.
C    Either of I or II, by itself, is sucient to solve the problem.
D    I and II both are required to solve the problem.
E    The problem cannot be solved even with both I and II.
9. The least common multiple of a number and 990 is 6930. The greatest common divisor of that number and
550 is 110.
What is the sum of the digits of the least possible value of that number?
A    6
B    9
C    14
D    18
E    None of the remaining options is correct.
Page 4


Quant
1. In a small college, students are allowed to take only one specialization. Traditionally, only two specializations
are offered: Science and Arts. Students enrolled to specialize in Science must take Physics and Mathematics
subjects, while students enrolled to specialize in Arts must take Economics and Political Science subjects.
Students enrolled in Science are not allowed to take either Economics or Political Science, while students
enrolled in Arts are not allowed to take either Physics or Mathematics.
Recently, the college has started a third specialization called MatEco that requires students to take
Economics and Mathematics. However, MatEco students would not be allowed to take either Physics or
Political Science. When the college opens this new specialization for enrolment, it allows students, originally
enrolled in Science or Arts, to switch to MatEco.
From among the students originally enrolled in Arts, 20 students switch to MatEco. This makes the number
of Science students twice the number of Arts students. After this, from among the students who originally
enrolled in Science, 45 students switch to MatEco. This makes the number of Arts students twice the
number of Science students.
In total, how many students, from among those originally enrolled in Science or Arts, are now taking
Economics?
A    45
B    65
C    80
D    95
E    None of the remaining options is correct.
2. In a school, the number of students in each class, from Class I to X, in that order, are in an arithmetic
progression. The total number of students from Class I to V is twice the total number of students from Class
VI to X.
If the total number of students from Class I to IV is 462, how many students are there in Class VI?
A    93
B    88
C    83
D    77
E    None of the remaining options is correct.
3. A ight, tr aveling to a destination 11,200 kms away, was supposed to take off at 6:30 AM. Due to bad
weather, the departure of the ight got dela yed by three hours. The pilot increased the average speed of the
airplane by 100 km/hr from the initially planned average speed, to reduce the overall delay to one hour.
Had the pilot increased the average speed by 350 km/hr from the initially planned average speed, when
would have the ight r eached its destination?
A    11:30 PM
B    7:50 PM
C    5:10 PM
D    8:10 PM
E    10:36 PM
4. 
Consider the equation , where x is a real number.
For how many different values of x does the given equation hold?
A    0
B    1
C    2
D    4
E    Innitely many
5. The cost of running a movie theatre is Rs. 10,000 per day, plus additional Rs. 5000 per show. The theatre has
200 seats. A new movie released on Friday. There were three shows, where the ticket price was Rs. 250 each
for the rst two shows and Rs. 200 for the late-night show .
For all shows together, total occupancy was 80%. What was the maximum amount of prot possible?
A    Rs. 1,20,000
B    Rs. 87,000
C    Rs. 95,000
D    Rs. 91,000
E    Rs. 1,16,000
6. FS food stall sells only chicken biryani. If FS x es a selling price of Rs. 160 per plate, 300 plates of biriyani
are sold. For each increase in the selling price by Rs. 10 per plate, 10 fewer plates are sold. Similarly, for each
decrease in the selling price by Rs. 10 per plate, 10 more plates are sold. FS incurs a cost of Rs. 120 per plate
of biriyani, and has decided that the selling price will never be less than the cost price. Moreover, due to
capacity constraints, more than 400 plates cannot be produced in a day.
If the selling price on any given day is the same for all the plates and can only be a multiple of Rs. 10, then
what is the maximum prot that FS can achie ve in a day?
A    Rs. 25,300
B    Rs. 28,900
C    Rs. 41,400
D    Rs. 52,900
E    None of the remaining options is correct.
log ( x -
5
2) = 2 log (2 x -
25
4)
7. A farmer has a triangular plot of land. One side of the plot, henceforth called the base, is 300 feet long and
the other two sides are equal. The perpendicular distance, from the corner of the plot, where the two equal
sides meet, to the base, is 200 feet. To counter the adverse effect of climate change, the farmer wants to dig
a circular pond. He plans that half of the circular area will be inside the triangular plot and the other half will
be outside, which he will purchase at the market rate from his neighbour. The diameter of the circular plot is
entirely contained in the base and the circumference of the pond touches the two equal sides of the triangle
from inside.
If the market rate per square feet of land is Rs. 1400, how much does the farmer must pay to buy the land
from his neighbour for the pond? (Choose the closest option.)
A    Rs. 3,16,80,000
B    Rs. 4,25,60,000
C    Rs. 6,33,60,000
D    Rs. 7,42,80,000
E    Rs. 2,98,20,000
8. A group of boys is practising football in a rectangular ground. Raju and Ratan are standing at the two
opposite mid-points of the two shorter sides. Raju has the ball, who passes it to Rivu, who is standing
somewhere on one of the longer sides. Rivu holds the ball for 3 seconds and passes it to Ratan. Ratan holds
the ball for 2 seconds and passes it back to Raju. The path of the ball from Raju to Rivu makes a right angle
with the path of the ball from Rivu to Ratan. The speed of the ball, whenever passed, is always 10 metre per
second, and the ball always moves on straight lines along the ground.
Consider the following two additional pieces of information:
I. The dimension of the ground is 80 metres × 50 metres.
II. The area of the triangle formed by Raju, Rivu and Ratan is 1000 square metres.
Consider the problem of computing the following: how many seconds does it take for Raju to get the ball
back since he passed it to Rivu? Choose the correct option.
A    I alone is sucient to solve the problem.
B    II alone is sucient to solve the problem.
C    Either of I or II, by itself, is sucient to solve the problem.
D    I and II both are required to solve the problem.
E    The problem cannot be solved even with both I and II.
9. The least common multiple of a number and 990 is 6930. The greatest common divisor of that number and
550 is 110.
What is the sum of the digits of the least possible value of that number?
A    6
B    9
C    14
D    18
E    None of the remaining options is correct.
10. 
The roots of the polynomial  are the radii of three concentric circles.
The ratio of their area, when arranged from the largest to the smallest, is:
A    6:2:1
B    9:4:1
C    16:6:3
D    36:16:1
E    None of the remaining options is correct.
11. A local restaurant has 16 vegetarian items and 9 non-vegetarian items in their menu. Some items contain
gluten, while the rest are gluten-free.
One evening, Rohit and his friends went to the restaurant. They planned to choose two different vegetarian
items and three different non-vegetarian items from the entire menu. Later, Bela and her friends also went
to the same restaurant: they planned to choose two different vegetarian items and one non-vegetarian item
only from the gluten-free options. The number of item combinations that Rohit and his friends could choose
from, given their plan, was 12 times the number of item combinations that Bela and her friends could
choose from, given their plan.
How many menu items contain gluten?
A    1
B    2
C    3
D    4
E    5
12. 
Consider the system of two linear equations as follows: ; and , where
p, q, and r are real numbers.
Which of the following statements DEFINITELY CONTRADICTS the fact that the lines represented by the two
equations are coinciding?
A    p and q must have opposite signs
B    The smallest among p, q, and r is r
C    The largest among p, q, and r is q
D    r and q must have same signs
E    p cannot be 0
13. Consider a 4-digit number of the form abbb, i.e., the rst digit is a (a > 0) and the last thr ee digits are all b.
Which of the following conditions is both NECESSARY and SUFFICIENT to ensure that the 4-digit number is
divisible by a?
A    b is divisible by a
B    b is equal to 0
P ( x) = 2 x -
3
11 x +
2
17 x - 6
3 x + 21 y + p = 0 q x + r y - 7 = 0
Page 5


Quant
1. In a small college, students are allowed to take only one specialization. Traditionally, only two specializations
are offered: Science and Arts. Students enrolled to specialize in Science must take Physics and Mathematics
subjects, while students enrolled to specialize in Arts must take Economics and Political Science subjects.
Students enrolled in Science are not allowed to take either Economics or Political Science, while students
enrolled in Arts are not allowed to take either Physics or Mathematics.
Recently, the college has started a third specialization called MatEco that requires students to take
Economics and Mathematics. However, MatEco students would not be allowed to take either Physics or
Political Science. When the college opens this new specialization for enrolment, it allows students, originally
enrolled in Science or Arts, to switch to MatEco.
From among the students originally enrolled in Arts, 20 students switch to MatEco. This makes the number
of Science students twice the number of Arts students. After this, from among the students who originally
enrolled in Science, 45 students switch to MatEco. This makes the number of Arts students twice the
number of Science students.
In total, how many students, from among those originally enrolled in Science or Arts, are now taking
Economics?
A    45
B    65
C    80
D    95
E    None of the remaining options is correct.
2. In a school, the number of students in each class, from Class I to X, in that order, are in an arithmetic
progression. The total number of students from Class I to V is twice the total number of students from Class
VI to X.
If the total number of students from Class I to IV is 462, how many students are there in Class VI?
A    93
B    88
C    83
D    77
E    None of the remaining options is correct.
3. A ight, tr aveling to a destination 11,200 kms away, was supposed to take off at 6:30 AM. Due to bad
weather, the departure of the ight got dela yed by three hours. The pilot increased the average speed of the
airplane by 100 km/hr from the initially planned average speed, to reduce the overall delay to one hour.
Had the pilot increased the average speed by 350 km/hr from the initially planned average speed, when
would have the ight r eached its destination?
A    11:30 PM
B    7:50 PM
C    5:10 PM
D    8:10 PM
E    10:36 PM
4. 
Consider the equation , where x is a real number.
For how many different values of x does the given equation hold?
A    0
B    1
C    2
D    4
E    Innitely many
5. The cost of running a movie theatre is Rs. 10,000 per day, plus additional Rs. 5000 per show. The theatre has
200 seats. A new movie released on Friday. There were three shows, where the ticket price was Rs. 250 each
for the rst two shows and Rs. 200 for the late-night show .
For all shows together, total occupancy was 80%. What was the maximum amount of prot possible?
A    Rs. 1,20,000
B    Rs. 87,000
C    Rs. 95,000
D    Rs. 91,000
E    Rs. 1,16,000
6. FS food stall sells only chicken biryani. If FS x es a selling price of Rs. 160 per plate, 300 plates of biriyani
are sold. For each increase in the selling price by Rs. 10 per plate, 10 fewer plates are sold. Similarly, for each
decrease in the selling price by Rs. 10 per plate, 10 more plates are sold. FS incurs a cost of Rs. 120 per plate
of biriyani, and has decided that the selling price will never be less than the cost price. Moreover, due to
capacity constraints, more than 400 plates cannot be produced in a day.
If the selling price on any given day is the same for all the plates and can only be a multiple of Rs. 10, then
what is the maximum prot that FS can achie ve in a day?
A    Rs. 25,300
B    Rs. 28,900
C    Rs. 41,400
D    Rs. 52,900
E    None of the remaining options is correct.
log ( x -
5
2) = 2 log (2 x -
25
4)
7. A farmer has a triangular plot of land. One side of the plot, henceforth called the base, is 300 feet long and
the other two sides are equal. The perpendicular distance, from the corner of the plot, where the two equal
sides meet, to the base, is 200 feet. To counter the adverse effect of climate change, the farmer wants to dig
a circular pond. He plans that half of the circular area will be inside the triangular plot and the other half will
be outside, which he will purchase at the market rate from his neighbour. The diameter of the circular plot is
entirely contained in the base and the circumference of the pond touches the two equal sides of the triangle
from inside.
If the market rate per square feet of land is Rs. 1400, how much does the farmer must pay to buy the land
from his neighbour for the pond? (Choose the closest option.)
A    Rs. 3,16,80,000
B    Rs. 4,25,60,000
C    Rs. 6,33,60,000
D    Rs. 7,42,80,000
E    Rs. 2,98,20,000
8. A group of boys is practising football in a rectangular ground. Raju and Ratan are standing at the two
opposite mid-points of the two shorter sides. Raju has the ball, who passes it to Rivu, who is standing
somewhere on one of the longer sides. Rivu holds the ball for 3 seconds and passes it to Ratan. Ratan holds
the ball for 2 seconds and passes it back to Raju. The path of the ball from Raju to Rivu makes a right angle
with the path of the ball from Rivu to Ratan. The speed of the ball, whenever passed, is always 10 metre per
second, and the ball always moves on straight lines along the ground.
Consider the following two additional pieces of information:
I. The dimension of the ground is 80 metres × 50 metres.
II. The area of the triangle formed by Raju, Rivu and Ratan is 1000 square metres.
Consider the problem of computing the following: how many seconds does it take for Raju to get the ball
back since he passed it to Rivu? Choose the correct option.
A    I alone is sucient to solve the problem.
B    II alone is sucient to solve the problem.
C    Either of I or II, by itself, is sucient to solve the problem.
D    I and II both are required to solve the problem.
E    The problem cannot be solved even with both I and II.
9. The least common multiple of a number and 990 is 6930. The greatest common divisor of that number and
550 is 110.
What is the sum of the digits of the least possible value of that number?
A    6
B    9
C    14
D    18
E    None of the remaining options is correct.
10. 
The roots of the polynomial  are the radii of three concentric circles.
The ratio of their area, when arranged from the largest to the smallest, is:
A    6:2:1
B    9:4:1
C    16:6:3
D    36:16:1
E    None of the remaining options is correct.
11. A local restaurant has 16 vegetarian items and 9 non-vegetarian items in their menu. Some items contain
gluten, while the rest are gluten-free.
One evening, Rohit and his friends went to the restaurant. They planned to choose two different vegetarian
items and three different non-vegetarian items from the entire menu. Later, Bela and her friends also went
to the same restaurant: they planned to choose two different vegetarian items and one non-vegetarian item
only from the gluten-free options. The number of item combinations that Rohit and his friends could choose
from, given their plan, was 12 times the number of item combinations that Bela and her friends could
choose from, given their plan.
How many menu items contain gluten?
A    1
B    2
C    3
D    4
E    5
12. 
Consider the system of two linear equations as follows: ; and , where
p, q, and r are real numbers.
Which of the following statements DEFINITELY CONTRADICTS the fact that the lines represented by the two
equations are coinciding?
A    p and q must have opposite signs
B    The smallest among p, q, and r is r
C    The largest among p, q, and r is q
D    r and q must have same signs
E    p cannot be 0
13. Consider a 4-digit number of the form abbb, i.e., the rst digit is a (a > 0) and the last thr ee digits are all b.
Which of the following conditions is both NECESSARY and SUFFICIENT to ensure that the 4-digit number is
divisible by a?
A    b is divisible by a
B    b is equal to 0
P ( x) = 2 x -
3
11 x +
2
17 x - 6
3 x + 21 y + p = 0 q x + r y - 7 = 0
C    21b is divisible by a
D    9b is divisible by a
E    3b is divisible by a
14. Consider a right-angled triangle ABC, right angled at B. Two circles, each of radius r, are drawn inside the
triangle in such a way that one of them touches AB and BC, while the other one touches AC and BC. The
two circles also touch each other (see the image below).
If AB = 18 cm and BC = 24 cm, then nd the v alue of r.
A    3 cm
B    4 cm
C    3.5 cm
D    4.5 cm
E    None of the remaining options is correct.
15. A king has distributed all his rare jewels in three boxes. The rst bo x contains 1/3 of the rare jewels, while
the second box contains k/5 of the rare jewels, for some positive integer value of k. The third box contains
66 rare jewels.
How many rare jewels does the king have?
A    990
B    660
C    240
D    1080
E    Cannot be determined uniquely from the given information.
Instructions [16 - 17 ]
Read the following scenario and answer the TWO questions that follow.
Aman has come to the market with Rs. 100. If he buys 5 kilograms of cabbage and 4 kilograms of potato, he
will have Rs. 20 left; or else, if he buys 4 kilograms of cabbage and 5 kilograms of onion, he will have Rs. 7 left.
The per kilogram prices of cabbage, onion and potato are positive integers (in rupees), and any type of these
vegetables can only be purchased in positive integer kilogram, or none at all.
16. Aman decides to buy only onion, in whatever maximum quantity possible (in positive integer kilogram), with
the money he has come to the market with. How much money will he be left with after the purchase?
A    Rs. 12