CMAT 2019: Previous Year Question Paper with Solutions

 Page 1


CMAT 2019 Question Paper
Quant
1. How much time does Mr.Surya take to cover a distance of 500 m if he runs at a speed of 25 km/hr?
A    35 sec
B    80 sec
C    60 sec
D    72 sec
A n s w e r : D
Explanation:
Given Speed of surya = 25 km/hr =  m/s.
Time taken(T) = Distance Travelled/ Speed
 sec 
Hence the time taken by Mr. Surya is '72 sec' or '1.2 min'. 
2. What is the area covered by a bell-shaped curve from —6 sigma to +6 sigma in normal distribution?
A    99.73%
B    99.99%
C    99.999666%
D    99.9999%
A n s w e r : C
Explanation:
As per the empirical rule, approximately 99.7% of the data in a bell-shaped distribution lies within three standard deviations of the mean,
or .   will have approximately 99.99967% of the data. Hence, option C.
3. The following table lists the marks of  seven students(rows) of a class across six subjects(columns). The Numbers in the
Parenthesis indicate the maximum marks of the subject concerned. Use the data in the table to answer the question that follows
:
Who is the topper of the class?
A    Maya
B    Arya
25 × = 18
5
18
125
? T = =
18
125
500
72
µ ± 3 s µ ± 6 s
  
.
Page 2


CMAT 2019 Question Paper
Quant
1. How much time does Mr.Surya take to cover a distance of 500 m if he runs at a speed of 25 km/hr?
A    35 sec
B    80 sec
C    60 sec
D    72 sec
A n s w e r : D
Explanation:
Given Speed of surya = 25 km/hr =  m/s.
Time taken(T) = Distance Travelled/ Speed
 sec 
Hence the time taken by Mr. Surya is '72 sec' or '1.2 min'. 
2. What is the area covered by a bell-shaped curve from —6 sigma to +6 sigma in normal distribution?
A    99.73%
B    99.99%
C    99.999666%
D    99.9999%
A n s w e r : C
Explanation:
As per the empirical rule, approximately 99.7% of the data in a bell-shaped distribution lies within three standard deviations of the mean,
or .   will have approximately 99.99967% of the data. Hence, option C.
3. The following table lists the marks of  seven students(rows) of a class across six subjects(columns). The Numbers in the
Parenthesis indicate the maximum marks of the subject concerned. Use the data in the table to answer the question that follows
:
Who is the topper of the class?
A    Maya
B    Arya
25 × = 18
5
18
125
? T = =
18
125
500
72
µ ± 3 s µ ± 6 s
  
.
C    
Roopesh
D    Riya
A n s w e r : B
Explanation:
The topper of the class is the one who gets a highest overall score. Let us check the options, who has got the overall score.
Option A:
The overall score of Maya = 90 + 50 + 90 + 60 + 70 + 80 = 440 marks 
Option B:
The overall score of Arya = 100 + 80 + 88 + 60 + 80 + 70 = 478 marks
Option C:
The overall score of Rupesh = 80 + 55 + 85 + 95 + 50 + 90 = 455 marks
Option D:
The overall score of Riya = 90 + 72 + 70 + 72 + 91 + 70 = 465 marks
So, the topper of the class is Arya, with a overall score of 478 marks.
4. Rajesh can check the quality of 1000 items in 5 hours and Rakesh can complete 75% of the same job in 3 hours. How much
time is required for both of them to check 1300 items, if Rakesh stops checking after 2 hours ? 
A    1 hour
B    2 hours
C    4 hours
D    3 hours
A n s w e r : C
Explanation:
Given, Rajesh can check the quality of 1000 items in 5 hours
 Efficiency of Rajesh = 200 items/hr.
Also given, Rakesh can complete the 75% of same job in 3 hours
 time taken by Rakesh to complete 100% of the job =  = 4 hours.
 Efficiency of Rakesh = 250 items/hr.
Given in the process of checking 1300 items, Rakesh spends only 2 hours. Let say time spent by Rajesh be 't' hours, which is also the
total time taken.
Total Work = Efficiency  time taken 
Hence the time taken in the process of checking 1300 items is 4 hours.
5. Two oranges, three bananas and four apples cost Rs. 15. Three oranges, two bananas and one apple cost Rs. 10. I bought 3
oranges, 3 bananas and 3 apples. How much did I pay ?
A    Rs. 10
B    Rs. 8
?
? × 75
100
3
?
×
? 1300 = 250 × 2 + 200 × t
? 200 t = 800
? t = 4
  
.
Page 3


CMAT 2019 Question Paper
Quant
1. How much time does Mr.Surya take to cover a distance of 500 m if he runs at a speed of 25 km/hr?
A    35 sec
B    80 sec
C    60 sec
D    72 sec
A n s w e r : D
Explanation:
Given Speed of surya = 25 km/hr =  m/s.
Time taken(T) = Distance Travelled/ Speed
 sec 
Hence the time taken by Mr. Surya is '72 sec' or '1.2 min'. 
2. What is the area covered by a bell-shaped curve from —6 sigma to +6 sigma in normal distribution?
A    99.73%
B    99.99%
C    99.999666%
D    99.9999%
A n s w e r : C
Explanation:
As per the empirical rule, approximately 99.7% of the data in a bell-shaped distribution lies within three standard deviations of the mean,
or .   will have approximately 99.99967% of the data. Hence, option C.
3. The following table lists the marks of  seven students(rows) of a class across six subjects(columns). The Numbers in the
Parenthesis indicate the maximum marks of the subject concerned. Use the data in the table to answer the question that follows
:
Who is the topper of the class?
A    Maya
B    Arya
25 × = 18
5
18
125
? T = =
18
125
500
72
µ ± 3 s µ ± 6 s
  
.
C    
Roopesh
D    Riya
A n s w e r : B
Explanation:
The topper of the class is the one who gets a highest overall score. Let us check the options, who has got the overall score.
Option A:
The overall score of Maya = 90 + 50 + 90 + 60 + 70 + 80 = 440 marks 
Option B:
The overall score of Arya = 100 + 80 + 88 + 60 + 80 + 70 = 478 marks
Option C:
The overall score of Rupesh = 80 + 55 + 85 + 95 + 50 + 90 = 455 marks
Option D:
The overall score of Riya = 90 + 72 + 70 + 72 + 91 + 70 = 465 marks
So, the topper of the class is Arya, with a overall score of 478 marks.
4. Rajesh can check the quality of 1000 items in 5 hours and Rakesh can complete 75% of the same job in 3 hours. How much
time is required for both of them to check 1300 items, if Rakesh stops checking after 2 hours ? 
A    1 hour
B    2 hours
C    4 hours
D    3 hours
A n s w e r : C
Explanation:
Given, Rajesh can check the quality of 1000 items in 5 hours
 Efficiency of Rajesh = 200 items/hr.
Also given, Rakesh can complete the 75% of same job in 3 hours
 time taken by Rakesh to complete 100% of the job =  = 4 hours.
 Efficiency of Rakesh = 250 items/hr.
Given in the process of checking 1300 items, Rakesh spends only 2 hours. Let say time spent by Rajesh be 't' hours, which is also the
total time taken.
Total Work = Efficiency  time taken 
Hence the time taken in the process of checking 1300 items is 4 hours.
5. Two oranges, three bananas and four apples cost Rs. 15. Three oranges, two bananas and one apple cost Rs. 10. I bought 3
oranges, 3 bananas and 3 apples. How much did I pay ?
A    Rs. 10
B    Rs. 8
?
? × 75
100
3
?
×
? 1300 = 250 × 2 + 200 × t
? 200 t = 800
? t = 4
  
.
C    
Rs. 15
D    Cannot be determined
A n s w e r : C
Explanation:
Let the cost of each orange, banana and apple be Rs. 'o' , 'b' , and 'a' respectively.
Given, Two oranges, three bananas and four apples cost Rs. 15
 2o + 3b + 4a = 15..........(1)
Also given, Three oranges, two bananas and one apple cost Rs. 10
 3o + 2b + a = 10............(2)
Adding (1) and (2), we get,
5o + 5b + 5a = 25
 o + b + a = 5
Then the cost of three oranges, three bananas and three apples is given as
3o + 3b + 3a = 3 [o + b + a] = 3 5 = Rs. 15 
6. What value should come in place of question mark(?) in the following equation?
 + 4500 = 19700 - 9800
A    395
B    295
C    225
D    215
A n s w e r : C
Explanation:
 + 4500 = 19700 - 9800
7. In a building there are 30 cylindrical pillars. The radius of each pillar is 35 cm and height is 5 m. Find out the cost of painting
the curved surface of half the number of pillars. The rate of painting is Rs. 10 per .
A    Rs. 16,500
B    Rs. 8250
C    Rs. 1650
D    Rs. 4125
A n s w e r : C
Explanation:
Curved surface area of cylindrical pillar is given as A = 2 rh, where 'r' is base radius and 'h' is height of the cylinder.
?
?
?
×
360 ?
360 ?
? 360 + ? 4500 = 9900
? 360 = ? 5400
? = ? 15
?? = 15
2
?? = 225
m
2
p
2
  
.
Page 4


CMAT 2019 Question Paper
Quant
1. How much time does Mr.Surya take to cover a distance of 500 m if he runs at a speed of 25 km/hr?
A    35 sec
B    80 sec
C    60 sec
D    72 sec
A n s w e r : D
Explanation:
Given Speed of surya = 25 km/hr =  m/s.
Time taken(T) = Distance Travelled/ Speed
 sec 
Hence the time taken by Mr. Surya is '72 sec' or '1.2 min'. 
2. What is the area covered by a bell-shaped curve from —6 sigma to +6 sigma in normal distribution?
A    99.73%
B    99.99%
C    99.999666%
D    99.9999%
A n s w e r : C
Explanation:
As per the empirical rule, approximately 99.7% of the data in a bell-shaped distribution lies within three standard deviations of the mean,
or .   will have approximately 99.99967% of the data. Hence, option C.
3. The following table lists the marks of  seven students(rows) of a class across six subjects(columns). The Numbers in the
Parenthesis indicate the maximum marks of the subject concerned. Use the data in the table to answer the question that follows
:
Who is the topper of the class?
A    Maya
B    Arya
25 × = 18
5
18
125
? T = =
18
125
500
72
µ ± 3 s µ ± 6 s
  
.
C    
Roopesh
D    Riya
A n s w e r : B
Explanation:
The topper of the class is the one who gets a highest overall score. Let us check the options, who has got the overall score.
Option A:
The overall score of Maya = 90 + 50 + 90 + 60 + 70 + 80 = 440 marks 
Option B:
The overall score of Arya = 100 + 80 + 88 + 60 + 80 + 70 = 478 marks
Option C:
The overall score of Rupesh = 80 + 55 + 85 + 95 + 50 + 90 = 455 marks
Option D:
The overall score of Riya = 90 + 72 + 70 + 72 + 91 + 70 = 465 marks
So, the topper of the class is Arya, with a overall score of 478 marks.
4. Rajesh can check the quality of 1000 items in 5 hours and Rakesh can complete 75% of the same job in 3 hours. How much
time is required for both of them to check 1300 items, if Rakesh stops checking after 2 hours ? 
A    1 hour
B    2 hours
C    4 hours
D    3 hours
A n s w e r : C
Explanation:
Given, Rajesh can check the quality of 1000 items in 5 hours
 Efficiency of Rajesh = 200 items/hr.
Also given, Rakesh can complete the 75% of same job in 3 hours
 time taken by Rakesh to complete 100% of the job =  = 4 hours.
 Efficiency of Rakesh = 250 items/hr.
Given in the process of checking 1300 items, Rakesh spends only 2 hours. Let say time spent by Rajesh be 't' hours, which is also the
total time taken.
Total Work = Efficiency  time taken 
Hence the time taken in the process of checking 1300 items is 4 hours.
5. Two oranges, three bananas and four apples cost Rs. 15. Three oranges, two bananas and one apple cost Rs. 10. I bought 3
oranges, 3 bananas and 3 apples. How much did I pay ?
A    Rs. 10
B    Rs. 8
?
? × 75
100
3
?
×
? 1300 = 250 × 2 + 200 × t
? 200 t = 800
? t = 4
  
.
C    
Rs. 15
D    Cannot be determined
A n s w e r : C
Explanation:
Let the cost of each orange, banana and apple be Rs. 'o' , 'b' , and 'a' respectively.
Given, Two oranges, three bananas and four apples cost Rs. 15
 2o + 3b + 4a = 15..........(1)
Also given, Three oranges, two bananas and one apple cost Rs. 10
 3o + 2b + a = 10............(2)
Adding (1) and (2), we get,
5o + 5b + 5a = 25
 o + b + a = 5
Then the cost of three oranges, three bananas and three apples is given as
3o + 3b + 3a = 3 [o + b + a] = 3 5 = Rs. 15 
6. What value should come in place of question mark(?) in the following equation?
 + 4500 = 19700 - 9800
A    395
B    295
C    225
D    215
A n s w e r : C
Explanation:
 + 4500 = 19700 - 9800
7. In a building there are 30 cylindrical pillars. The radius of each pillar is 35 cm and height is 5 m. Find out the cost of painting
the curved surface of half the number of pillars. The rate of painting is Rs. 10 per .
A    Rs. 16,500
B    Rs. 8250
C    Rs. 1650
D    Rs. 4125
A n s w e r : C
Explanation:
Curved surface area of cylindrical pillar is given as A = 2 rh, where 'r' is base radius and 'h' is height of the cylinder.
?
?
?
×
360 ?
360 ?
? 360 + ? 4500 = 9900
? 360 = ? 5400
? = ? 15
?? = 15
2
?? = 225
m
2
p
2
  
.
So curved surface area of each pillar A = 
Given there are 30 cylindrical pillars.
The curved surface area of half the number of pillars = 15 * A = 165 .
Given rate of painting is Rs. 10 per 
The cost of painting curved surface of half the number of pillars = Curved surface area * rate of painting
= 
= Rs. 1650. 
    
8. A management institute has 6 senior professors and 4 junior professors, 3 professors are selected at random for a government
project. The probability that at least one of the junior professors would get selected is :
A    2/3
B    1/5
C    5/6
D    1/6
A n s w e r : C
Explanation:
Probability = Expected number of outcomes/ Total number of outcomes.
Total number of outcomes =  The number of ways of selecting 3 professors at random from a total of 10 professors.
= 10C3 = 120 ways.
Expected number of outcomes = Selecting 3 professors so that at least one of the junior professor is selected.
The possible cases are,
Case(1): Selecting 1 junior professor out of 4 and Selecting 2 senior professor out of 6 = 4C1 * 6C2.
Case(2): Selecting 2 junior professor out of 4 and Selecting 1 senior professor out of 6 = 4C2 * 6C1.
Case (3): Selecting 3 junior professor out of 4  = 4C3.
So Expected number of outcomes = 4C1 * 6C2 + 4C2 * 6C1 + 4C3 =  = 100 ways.
Probability =  
  
9. The angle created by two hands of a clock when the clock shows 5.20 P.M. is :
A    40°
B    60°
C    35°
D    40
A n s w e r : D
Explanation:
In a clock, 
In one revolution the minute hand covers 60°
 60 minutes = 360°
2 × p × 0.35 × 5 = 11 m
2
m
2
m
2
165 × 10
4 × 15 + 6 × 6 + 4
= 120
100
6
5
?
  
.
Page 5


CMAT 2019 Question Paper
Quant
1. How much time does Mr.Surya take to cover a distance of 500 m if he runs at a speed of 25 km/hr?
A    35 sec
B    80 sec
C    60 sec
D    72 sec
A n s w e r : D
Explanation:
Given Speed of surya = 25 km/hr =  m/s.
Time taken(T) = Distance Travelled/ Speed
 sec 
Hence the time taken by Mr. Surya is '72 sec' or '1.2 min'. 
2. What is the area covered by a bell-shaped curve from —6 sigma to +6 sigma in normal distribution?
A    99.73%
B    99.99%
C    99.999666%
D    99.9999%
A n s w e r : C
Explanation:
As per the empirical rule, approximately 99.7% of the data in a bell-shaped distribution lies within three standard deviations of the mean,
or .   will have approximately 99.99967% of the data. Hence, option C.
3. The following table lists the marks of  seven students(rows) of a class across six subjects(columns). The Numbers in the
Parenthesis indicate the maximum marks of the subject concerned. Use the data in the table to answer the question that follows
:
Who is the topper of the class?
A    Maya
B    Arya
25 × = 18
5
18
125
? T = =
18
125
500
72
µ ± 3 s µ ± 6 s
  
.
C    
Roopesh
D    Riya
A n s w e r : B
Explanation:
The topper of the class is the one who gets a highest overall score. Let us check the options, who has got the overall score.
Option A:
The overall score of Maya = 90 + 50 + 90 + 60 + 70 + 80 = 440 marks 
Option B:
The overall score of Arya = 100 + 80 + 88 + 60 + 80 + 70 = 478 marks
Option C:
The overall score of Rupesh = 80 + 55 + 85 + 95 + 50 + 90 = 455 marks
Option D:
The overall score of Riya = 90 + 72 + 70 + 72 + 91 + 70 = 465 marks
So, the topper of the class is Arya, with a overall score of 478 marks.
4. Rajesh can check the quality of 1000 items in 5 hours and Rakesh can complete 75% of the same job in 3 hours. How much
time is required for both of them to check 1300 items, if Rakesh stops checking after 2 hours ? 
A    1 hour
B    2 hours
C    4 hours
D    3 hours
A n s w e r : C
Explanation:
Given, Rajesh can check the quality of 1000 items in 5 hours
 Efficiency of Rajesh = 200 items/hr.
Also given, Rakesh can complete the 75% of same job in 3 hours
 time taken by Rakesh to complete 100% of the job =  = 4 hours.
 Efficiency of Rakesh = 250 items/hr.
Given in the process of checking 1300 items, Rakesh spends only 2 hours. Let say time spent by Rajesh be 't' hours, which is also the
total time taken.
Total Work = Efficiency  time taken 
Hence the time taken in the process of checking 1300 items is 4 hours.
5. Two oranges, three bananas and four apples cost Rs. 15. Three oranges, two bananas and one apple cost Rs. 10. I bought 3
oranges, 3 bananas and 3 apples. How much did I pay ?
A    Rs. 10
B    Rs. 8
?
? × 75
100
3
?
×
? 1300 = 250 × 2 + 200 × t
? 200 t = 800
? t = 4
  
.
C    
Rs. 15
D    Cannot be determined
A n s w e r : C
Explanation:
Let the cost of each orange, banana and apple be Rs. 'o' , 'b' , and 'a' respectively.
Given, Two oranges, three bananas and four apples cost Rs. 15
 2o + 3b + 4a = 15..........(1)
Also given, Three oranges, two bananas and one apple cost Rs. 10
 3o + 2b + a = 10............(2)
Adding (1) and (2), we get,
5o + 5b + 5a = 25
 o + b + a = 5
Then the cost of three oranges, three bananas and three apples is given as
3o + 3b + 3a = 3 [o + b + a] = 3 5 = Rs. 15 
6. What value should come in place of question mark(?) in the following equation?
 + 4500 = 19700 - 9800
A    395
B    295
C    225
D    215
A n s w e r : C
Explanation:
 + 4500 = 19700 - 9800
7. In a building there are 30 cylindrical pillars. The radius of each pillar is 35 cm and height is 5 m. Find out the cost of painting
the curved surface of half the number of pillars. The rate of painting is Rs. 10 per .
A    Rs. 16,500
B    Rs. 8250
C    Rs. 1650
D    Rs. 4125
A n s w e r : C
Explanation:
Curved surface area of cylindrical pillar is given as A = 2 rh, where 'r' is base radius and 'h' is height of the cylinder.
?
?
?
×
360 ?
360 ?
? 360 + ? 4500 = 9900
? 360 = ? 5400
? = ? 15
?? = 15
2
?? = 225
m
2
p
2
  
.
So curved surface area of each pillar A = 
Given there are 30 cylindrical pillars.
The curved surface area of half the number of pillars = 15 * A = 165 .
Given rate of painting is Rs. 10 per 
The cost of painting curved surface of half the number of pillars = Curved surface area * rate of painting
= 
= Rs. 1650. 
    
8. A management institute has 6 senior professors and 4 junior professors, 3 professors are selected at random for a government
project. The probability that at least one of the junior professors would get selected is :
A    2/3
B    1/5
C    5/6
D    1/6
A n s w e r : C
Explanation:
Probability = Expected number of outcomes/ Total number of outcomes.
Total number of outcomes =  The number of ways of selecting 3 professors at random from a total of 10 professors.
= 10C3 = 120 ways.
Expected number of outcomes = Selecting 3 professors so that at least one of the junior professor is selected.
The possible cases are,
Case(1): Selecting 1 junior professor out of 4 and Selecting 2 senior professor out of 6 = 4C1 * 6C2.
Case(2): Selecting 2 junior professor out of 4 and Selecting 1 senior professor out of 6 = 4C2 * 6C1.
Case (3): Selecting 3 junior professor out of 4  = 4C3.
So Expected number of outcomes = 4C1 * 6C2 + 4C2 * 6C1 + 4C3 =  = 100 ways.
Probability =  
  
9. The angle created by two hands of a clock when the clock shows 5.20 P.M. is :
A    40°
B    60°
C    35°
D    40
A n s w e r : D
Explanation:
In a clock, 
In one revolution the minute hand covers 60°
 60 minutes = 360°
2 × p × 0.35 × 5 = 11 m
2
m
2
m
2
165 × 10
4 × 15 + 6 × 6 + 4
= 120
100
6
5
?
  
.
 1 minute = 6°.
 for every minute the minute hand covers 6°.
Similarly In one revolution the hour hand covers 12 hours.
 12 hours = 360°
 1 hour = 30°.
 for every hour, the hour hand covers 30°.
So at 5.20 P.M. the hour hand must have covered 5 * 30° = 150° + 20*1/2 = 160
and minute hand must have covered 20 * 6° = 120°.
So the angle created by two hands of the clock when the time is 5.20 P.M. = 160 - 120 = 40°.
10. The total volume of soaps sold is 680 lakhs units. The volume of Lux sold is 136 lakh units. If the percentage of Lifebuoy sold is
30%, Camay 10%, Liril 15% and Mysore Sandal 10%, answer the following questions.
What is the market share of others in percentage points?
A    15
B    13.5
C    16.8
D    16
A n s w e r : A
Explanation:
Given, Total volume of soaps sold = 680 lakh units.
Volume of Lux sold = 136 lakh units.
 Percentage of Lux sold =  = 20% 
Also given,
percentage of Lifebuoy sold is 30%,
 percentage of Camay 10%,
 percentage of Liril 15% and 
percentage of Mysore Sandal 10% 
From the pie chart
The percentage of Lux + Lifeboy + Camay + Liril + Mysore Sandal + Others  sold = 100%
 The market share of others = 100 - 20 - 30 - 10 - 15 - 10 = 15%
     
11. In a triangle ABC, AD is the bisector of angle A. If AC =4.2 cm, DC = 6 cm, BC =10 cm, find AB.
A    2.7 cm
?
?
?
?
?
? × 680
136
100
?
  
.