CMAT 2018 Slot - 1: Previous Year Question Paper with Solutions

 Page 1


CMAT 2018 Slot 1
Quant
1. How many iron balls, each of radius 1 cm, can be made from a sphere whose radius is 8 cm?
A    64
B    256
C    512
D    124
A n s w e r : C
Explanation:
Volume(V)  of the sphere with radius R=8 cm is given by V= .
                                                                                                       = = .                                                                                                 
and Volume (v) of each iron ball with radius r= 1cm is given by v= .
                                                                                                              = = .
Let say 'n' iron balls each of volume 'v' are required to form a sphere of volume 'V'.
=> Total volume of 'n' iron balls = Volume of the sphere
=>  = V
=> n=  =  = 512. 
Hence 512 iron balls are required in total to form the sphere.
 
2. If a is between 0 and 1, which of the following statements is (are) true?
(i)  - 1> 0
(ii)  + 1 > 0
(iii)  - a > 0
A    only (ii)
B    (i) & (ii)
C    (iii) only
D    All three
A n s w e r : A
Explanation:
Given      0<a<1..............................................(1)
Let us go with the verification of options
Option (i):
squaring on both sides of (1), we get
0< <1
Subtracting '1' in the above equation, we get
-1< -1<0....................(2)
-1< 0, Hence option (i) is false.
Option (ii):
p R 3
4
3
p(8 ) 3
4
3
p(512) c m 3
4
3
p r 3
4
3
p(1 ) 3
4
3
p c m 3
4
3
n × v
V ÷ v p(512) ÷ 3
4
 p 3
4
a
2
a
2
a
2
a
2
a
2
? a
2
  
.
Page 2


CMAT 2018 Slot 1
Quant
1. How many iron balls, each of radius 1 cm, can be made from a sphere whose radius is 8 cm?
A    64
B    256
C    512
D    124
A n s w e r : C
Explanation:
Volume(V)  of the sphere with radius R=8 cm is given by V= .
                                                                                                       = = .                                                                                                 
and Volume (v) of each iron ball with radius r= 1cm is given by v= .
                                                                                                              = = .
Let say 'n' iron balls each of volume 'v' are required to form a sphere of volume 'V'.
=> Total volume of 'n' iron balls = Volume of the sphere
=>  = V
=> n=  =  = 512. 
Hence 512 iron balls are required in total to form the sphere.
 
2. If a is between 0 and 1, which of the following statements is (are) true?
(i)  - 1> 0
(ii)  + 1 > 0
(iii)  - a > 0
A    only (ii)
B    (i) & (ii)
C    (iii) only
D    All three
A n s w e r : A
Explanation:
Given      0<a<1..............................................(1)
Let us go with the verification of options
Option (i):
squaring on both sides of (1), we get
0< <1
Subtracting '1' in the above equation, we get
-1< -1<0....................(2)
-1< 0, Hence option (i) is false.
Option (ii):
p R 3
4
3
p(8 ) 3
4
3
p(512) c m 3
4
3
p r 3
4
3
p(1 ) 3
4
3
p c m 3
4
3
n × v
V ÷ v p(512) ÷ 3
4
 p 3
4
a
2
a
2
a
2
a
2
a
2
? a
2
  
.
Squaring on both sides of (1), we get
0< <1
Adding '1' on both sides of above equation, we get
1< +1<2....................(3)
+1>0, Hence Option (ii) is true.
Option (iii):
As 0<a<1, .............(4)
Subtracting 'a' on both sides of (4), we get
, Hence Option (iii) is also false.
                        
3. The following pie chart provides information about the revenue share of six companies P, Q, R, S,T, U as a percentage of the total car
market(in Rs.)in the year 2010. These are the only six companies producing car in the market.
         Revenue share
If the revenue share of company T increases by 20% in the year 2011, then find the percentage increase in the
revenue share of these six companies in the year 2011 assuming that all the other companies except T
generated the same revenue as they did in the year 2010.
A    2.8%
B    3.2%
C    1.8%
D    2.6%
A n s w e r : A
Explanation:
Let, us assume the total revenue for 2010 as 100.
Since, all the companies except T have generated the same revenue in 2011, the percentage increase in revenue for all companies will be only
due to the increase in revenue of T.
Increase in revenue of T(2011) = 20% * 14 = 2.8
Total revenue(2011) = 102.8
 % increase in revenue =  * 100% = 2.8 %
Hence, option A.
4. In how many years will Rs. 2 lakh double itself at 11.5% per annum simple interest?
a
2
a
2
? a
2
a <
2
a
a -
2
a < 0
? 100
102.8-100
  
.
Page 3


CMAT 2018 Slot 1
Quant
1. How many iron balls, each of radius 1 cm, can be made from a sphere whose radius is 8 cm?
A    64
B    256
C    512
D    124
A n s w e r : C
Explanation:
Volume(V)  of the sphere with radius R=8 cm is given by V= .
                                                                                                       = = .                                                                                                 
and Volume (v) of each iron ball with radius r= 1cm is given by v= .
                                                                                                              = = .
Let say 'n' iron balls each of volume 'v' are required to form a sphere of volume 'V'.
=> Total volume of 'n' iron balls = Volume of the sphere
=>  = V
=> n=  =  = 512. 
Hence 512 iron balls are required in total to form the sphere.
 
2. If a is between 0 and 1, which of the following statements is (are) true?
(i)  - 1> 0
(ii)  + 1 > 0
(iii)  - a > 0
A    only (ii)
B    (i) & (ii)
C    (iii) only
D    All three
A n s w e r : A
Explanation:
Given      0<a<1..............................................(1)
Let us go with the verification of options
Option (i):
squaring on both sides of (1), we get
0< <1
Subtracting '1' in the above equation, we get
-1< -1<0....................(2)
-1< 0, Hence option (i) is false.
Option (ii):
p R 3
4
3
p(8 ) 3
4
3
p(512) c m 3
4
3
p r 3
4
3
p(1 ) 3
4
3
p c m 3
4
3
n × v
V ÷ v p(512) ÷ 3
4
 p 3
4
a
2
a
2
a
2
a
2
a
2
? a
2
  
.
Squaring on both sides of (1), we get
0< <1
Adding '1' on both sides of above equation, we get
1< +1<2....................(3)
+1>0, Hence Option (ii) is true.
Option (iii):
As 0<a<1, .............(4)
Subtracting 'a' on both sides of (4), we get
, Hence Option (iii) is also false.
                        
3. The following pie chart provides information about the revenue share of six companies P, Q, R, S,T, U as a percentage of the total car
market(in Rs.)in the year 2010. These are the only six companies producing car in the market.
         Revenue share
If the revenue share of company T increases by 20% in the year 2011, then find the percentage increase in the
revenue share of these six companies in the year 2011 assuming that all the other companies except T
generated the same revenue as they did in the year 2010.
A    2.8%
B    3.2%
C    1.8%
D    2.6%
A n s w e r : A
Explanation:
Let, us assume the total revenue for 2010 as 100.
Since, all the companies except T have generated the same revenue in 2011, the percentage increase in revenue for all companies will be only
due to the increase in revenue of T.
Increase in revenue of T(2011) = 20% * 14 = 2.8
Total revenue(2011) = 102.8
 % increase in revenue =  * 100% = 2.8 %
Hence, option A.
4. In how many years will Rs. 2 lakh double itself at 11.5% per annum simple interest?
a
2
a
2
? a
2
a <
2
a
a -
2
a < 0
? 100
102.8-100
  
.
A    Less than 8
B    Between 8 and 9
C    9.3
D    10.5
A n s w e r : B
Explanation:
Let say after a Time period (T) 'x'  years the amount Rs. 2 lakh gets doubled at a rate of interest (R) = 11.5% per annum 
Initial principle amount (P) = 2,00,000 Rs.
Simple Interest (I)  for 'x' years is given by I =  = 
                       => I = .
Final Principle amount (P') = P + I =  (as given)  
                                               => I =  = P
                                              =>  = 200000
                                              => x = 
                                              => x = 8.695 = between 8 and 9.                                                                   
5. If AB + C = D, find A and C given that when B = 6, D = 30 and when B = 8, D = 36.
A    A = 2, C = 6
B    A = 3, C = 12
C    A = 6, C = 3
D    A = 4, C = 3
A n s w e r : B
Explanation:
Given AB + C = D................................(1
If B = 6 and D = 30,  then from (1), 
6A + C = 30........................(2)
and If B = 8 and D = 36, 
8A + C = 36........................(3)
(3)-(2) => 2A = 6
=> A= 3
Substituting the value of A in equation (2) we get,
18 + C = 30
=> C = 12.
6. If  + 3y - 18 = 0, which of the following is true?
A    y = 3 or y = 0
B    y > - 6 or y < 3
C    -6 = y = 3
D    y = 3 or y = - 6
A n s w e r : D
P T R ÷ 100 200000 × x × 11.5 ÷ 100
23000 × x
2 × P
2 × P - P
23000 × x
200000 ÷ 23000
y
2
  
.
Page 4


CMAT 2018 Slot 1
Quant
1. How many iron balls, each of radius 1 cm, can be made from a sphere whose radius is 8 cm?
A    64
B    256
C    512
D    124
A n s w e r : C
Explanation:
Volume(V)  of the sphere with radius R=8 cm is given by V= .
                                                                                                       = = .                                                                                                 
and Volume (v) of each iron ball with radius r= 1cm is given by v= .
                                                                                                              = = .
Let say 'n' iron balls each of volume 'v' are required to form a sphere of volume 'V'.
=> Total volume of 'n' iron balls = Volume of the sphere
=>  = V
=> n=  =  = 512. 
Hence 512 iron balls are required in total to form the sphere.
 
2. If a is between 0 and 1, which of the following statements is (are) true?
(i)  - 1> 0
(ii)  + 1 > 0
(iii)  - a > 0
A    only (ii)
B    (i) & (ii)
C    (iii) only
D    All three
A n s w e r : A
Explanation:
Given      0<a<1..............................................(1)
Let us go with the verification of options
Option (i):
squaring on both sides of (1), we get
0< <1
Subtracting '1' in the above equation, we get
-1< -1<0....................(2)
-1< 0, Hence option (i) is false.
Option (ii):
p R 3
4
3
p(8 ) 3
4
3
p(512) c m 3
4
3
p r 3
4
3
p(1 ) 3
4
3
p c m 3
4
3
n × v
V ÷ v p(512) ÷ 3
4
 p 3
4
a
2
a
2
a
2
a
2
a
2
? a
2
  
.
Squaring on both sides of (1), we get
0< <1
Adding '1' on both sides of above equation, we get
1< +1<2....................(3)
+1>0, Hence Option (ii) is true.
Option (iii):
As 0<a<1, .............(4)
Subtracting 'a' on both sides of (4), we get
, Hence Option (iii) is also false.
                        
3. The following pie chart provides information about the revenue share of six companies P, Q, R, S,T, U as a percentage of the total car
market(in Rs.)in the year 2010. These are the only six companies producing car in the market.
         Revenue share
If the revenue share of company T increases by 20% in the year 2011, then find the percentage increase in the
revenue share of these six companies in the year 2011 assuming that all the other companies except T
generated the same revenue as they did in the year 2010.
A    2.8%
B    3.2%
C    1.8%
D    2.6%
A n s w e r : A
Explanation:
Let, us assume the total revenue for 2010 as 100.
Since, all the companies except T have generated the same revenue in 2011, the percentage increase in revenue for all companies will be only
due to the increase in revenue of T.
Increase in revenue of T(2011) = 20% * 14 = 2.8
Total revenue(2011) = 102.8
 % increase in revenue =  * 100% = 2.8 %
Hence, option A.
4. In how many years will Rs. 2 lakh double itself at 11.5% per annum simple interest?
a
2
a
2
? a
2
a <
2
a
a -
2
a < 0
? 100
102.8-100
  
.
A    Less than 8
B    Between 8 and 9
C    9.3
D    10.5
A n s w e r : B
Explanation:
Let say after a Time period (T) 'x'  years the amount Rs. 2 lakh gets doubled at a rate of interest (R) = 11.5% per annum 
Initial principle amount (P) = 2,00,000 Rs.
Simple Interest (I)  for 'x' years is given by I =  = 
                       => I = .
Final Principle amount (P') = P + I =  (as given)  
                                               => I =  = P
                                              =>  = 200000
                                              => x = 
                                              => x = 8.695 = between 8 and 9.                                                                   
5. If AB + C = D, find A and C given that when B = 6, D = 30 and when B = 8, D = 36.
A    A = 2, C = 6
B    A = 3, C = 12
C    A = 6, C = 3
D    A = 4, C = 3
A n s w e r : B
Explanation:
Given AB + C = D................................(1
If B = 6 and D = 30,  then from (1), 
6A + C = 30........................(2)
and If B = 8 and D = 36, 
8A + C = 36........................(3)
(3)-(2) => 2A = 6
=> A= 3
Substituting the value of A in equation (2) we get,
18 + C = 30
=> C = 12.
6. If  + 3y - 18 = 0, which of the following is true?
A    y = 3 or y = 0
B    y > - 6 or y < 3
C    -6 = y = 3
D    y = 3 or y = - 6
A n s w e r : D
P T R ÷ 100 200000 × x × 11.5 ÷ 100
23000 × x
2 × P
2 × P - P
23000 × x
200000 ÷ 23000
y
2
  
.
Explanation:
 
 
 
 
7. In how many different ways can 3 red balls, 2 blue balls and 4 yellow balls be arranged so that the balls of the same color come
together?
A    1742
B    1732
C    1728
D    1750
A n s w e r : C
Explanation:
Since balls of same color should come together, let us consider 3 red balls as one unit and 2 blue balls as one unit and 4 yellow balls as
another unit.
So, we have a total of 3 different units which can be arranged in '3!' ways.
these 3 red balls can internally be arranged in '3!' ways.
Similarly the blue balls and yellow balls can be arranged internally in '2!' and '4!' ways respectively.
So, total number ways = = 1728 ways
    
8. The following table shows the courier charges (in Rs.) for sending 1 kg parcel from one city to another.
Among the following, the charges will be the least for sending a parcel from:-
A    Ahmedabad to Jaipur
B    
Mumbai to Bangalore
C    Jaipur to Bangalore
D    Kolkata to Mumbai
A n s w e r : D
Explanation:
By carefully observing the given data and by observing the given options,
The charges will be least for the parcel from Kolkata to Mumbai which is Rs. 7,
Hence option (D) is the answer.
y +
2
3 y - 18 = 0
? y +
2
6 y - 3 y - 18 = 0
? y( y + 6) - 3( y + 6) = 0
? ( y - 3)( y + 6) = 0
? y = 3 a n d y = -6
3! × 3! × 2! × 4! = 6 × 6 × 2 × 24
  
.
Page 5


CMAT 2018 Slot 1
Quant
1. How many iron balls, each of radius 1 cm, can be made from a sphere whose radius is 8 cm?
A    64
B    256
C    512
D    124
A n s w e r : C
Explanation:
Volume(V)  of the sphere with radius R=8 cm is given by V= .
                                                                                                       = = .                                                                                                 
and Volume (v) of each iron ball with radius r= 1cm is given by v= .
                                                                                                              = = .
Let say 'n' iron balls each of volume 'v' are required to form a sphere of volume 'V'.
=> Total volume of 'n' iron balls = Volume of the sphere
=>  = V
=> n=  =  = 512. 
Hence 512 iron balls are required in total to form the sphere.
 
2. If a is between 0 and 1, which of the following statements is (are) true?
(i)  - 1> 0
(ii)  + 1 > 0
(iii)  - a > 0
A    only (ii)
B    (i) & (ii)
C    (iii) only
D    All three
A n s w e r : A
Explanation:
Given      0<a<1..............................................(1)
Let us go with the verification of options
Option (i):
squaring on both sides of (1), we get
0< <1
Subtracting '1' in the above equation, we get
-1< -1<0....................(2)
-1< 0, Hence option (i) is false.
Option (ii):
p R 3
4
3
p(8 ) 3
4
3
p(512) c m 3
4
3
p r 3
4
3
p(1 ) 3
4
3
p c m 3
4
3
n × v
V ÷ v p(512) ÷ 3
4
 p 3
4
a
2
a
2
a
2
a
2
a
2
? a
2
  
.
Squaring on both sides of (1), we get
0< <1
Adding '1' on both sides of above equation, we get
1< +1<2....................(3)
+1>0, Hence Option (ii) is true.
Option (iii):
As 0<a<1, .............(4)
Subtracting 'a' on both sides of (4), we get
, Hence Option (iii) is also false.
                        
3. The following pie chart provides information about the revenue share of six companies P, Q, R, S,T, U as a percentage of the total car
market(in Rs.)in the year 2010. These are the only six companies producing car in the market.
         Revenue share
If the revenue share of company T increases by 20% in the year 2011, then find the percentage increase in the
revenue share of these six companies in the year 2011 assuming that all the other companies except T
generated the same revenue as they did in the year 2010.
A    2.8%
B    3.2%
C    1.8%
D    2.6%
A n s w e r : A
Explanation:
Let, us assume the total revenue for 2010 as 100.
Since, all the companies except T have generated the same revenue in 2011, the percentage increase in revenue for all companies will be only
due to the increase in revenue of T.
Increase in revenue of T(2011) = 20% * 14 = 2.8
Total revenue(2011) = 102.8
 % increase in revenue =  * 100% = 2.8 %
Hence, option A.
4. In how many years will Rs. 2 lakh double itself at 11.5% per annum simple interest?
a
2
a
2
? a
2
a <
2
a
a -
2
a < 0
? 100
102.8-100
  
.
A    Less than 8
B    Between 8 and 9
C    9.3
D    10.5
A n s w e r : B
Explanation:
Let say after a Time period (T) 'x'  years the amount Rs. 2 lakh gets doubled at a rate of interest (R) = 11.5% per annum 
Initial principle amount (P) = 2,00,000 Rs.
Simple Interest (I)  for 'x' years is given by I =  = 
                       => I = .
Final Principle amount (P') = P + I =  (as given)  
                                               => I =  = P
                                              =>  = 200000
                                              => x = 
                                              => x = 8.695 = between 8 and 9.                                                                   
5. If AB + C = D, find A and C given that when B = 6, D = 30 and when B = 8, D = 36.
A    A = 2, C = 6
B    A = 3, C = 12
C    A = 6, C = 3
D    A = 4, C = 3
A n s w e r : B
Explanation:
Given AB + C = D................................(1
If B = 6 and D = 30,  then from (1), 
6A + C = 30........................(2)
and If B = 8 and D = 36, 
8A + C = 36........................(3)
(3)-(2) => 2A = 6
=> A= 3
Substituting the value of A in equation (2) we get,
18 + C = 30
=> C = 12.
6. If  + 3y - 18 = 0, which of the following is true?
A    y = 3 or y = 0
B    y > - 6 or y < 3
C    -6 = y = 3
D    y = 3 or y = - 6
A n s w e r : D
P T R ÷ 100 200000 × x × 11.5 ÷ 100
23000 × x
2 × P
2 × P - P
23000 × x
200000 ÷ 23000
y
2
  
.
Explanation:
 
 
 
 
7. In how many different ways can 3 red balls, 2 blue balls and 4 yellow balls be arranged so that the balls of the same color come
together?
A    1742
B    1732
C    1728
D    1750
A n s w e r : C
Explanation:
Since balls of same color should come together, let us consider 3 red balls as one unit and 2 blue balls as one unit and 4 yellow balls as
another unit.
So, we have a total of 3 different units which can be arranged in '3!' ways.
these 3 red balls can internally be arranged in '3!' ways.
Similarly the blue balls and yellow balls can be arranged internally in '2!' and '4!' ways respectively.
So, total number ways = = 1728 ways
    
8. The following table shows the courier charges (in Rs.) for sending 1 kg parcel from one city to another.
Among the following, the charges will be the least for sending a parcel from:-
A    Ahmedabad to Jaipur
B    
Mumbai to Bangalore
C    Jaipur to Bangalore
D    Kolkata to Mumbai
A n s w e r : D
Explanation:
By carefully observing the given data and by observing the given options,
The charges will be least for the parcel from Kolkata to Mumbai which is Rs. 7,
Hence option (D) is the answer.
y +
2
3 y - 18 = 0
? y +
2
6 y - 3 y - 18 = 0
? y( y + 6) - 3( y + 6) = 0
? ( y - 3)( y + 6) = 0
? y = 3 a n d y = -6
3! × 3! × 2! × 4! = 6 × 6 × 2 × 24
  
.
9. Three numbers X, Y and Z are in the ratio of 12: 15: 25. If the sum of twice of these numbers is 614, the ratio between the difference
of Y and X and the difference of Z and Y is:-
A    3:7
B    5:1
C    3:10
D    10:3
A n s w e r : C
Explanation:
Given X, Y and Z are in the ratio 12: 15: 25
Let say X = 12k, Y = 15k and Z = 25k, where k is any constant.
Difference between Y and X = 15k - 12k = 3k..............................(1)
and Difference between Z and Y = 25k - 15k = 10k.....................(2)
Ratio of (1) and (2) = .
10. Ankush and Babulal walk around circular track.They start at 9 a.m. from the same point in the opposite directions.Ankush and Babulal
walk at a speed of 3 rounds per hour and 5 rounds per hour respectively. How many times shall they cross each other until 10.30
a.m.?
A    9
B    10
C    12
D    11
A n s w e r : C
Explanation:
Given speed of Ankush = 3 rounds per hour = 1  round per 20 min
Whereas speed of Babulal = 5 rounds per hour = 1 round per 12 min.
Let us consider Ankush as stationery at the starting point.
The relative speed of Babulal with respect to Ankush = 3 rounds per hour + 5 rounds per hour = 8 rounds per hour 
This implies, In one hour Babulal crosses Ankush 8 times. 
So, starting from 9.00 am to 10.30 am i.e., 1.5 hours or 90 min, Babulal crosses Ankush 12 times.
     
11. The monthly incomes of Amit and Bharat are in the ratio of 5:4, their monthly expenses are in the ratio of 19:21, and their monthly
savings are in the ratio of 37:18. If the total annual savings of Amit and Bharat is Rs.1,32,000, Amit’s monthly income is:-
A    Rs. 12,000
B    Rs. 15,000
C    Rs. 18,000
D    Rs. 16,000
A n s w e r : B
Explanation:
Given monthly savings of Amit and Bharat are in the ration 37:18. Let the savings of Amit and Bharat be 37k and 18k, where 'k' is a constant.
3 k ÷ 10 k = 3 : 10
  
.