Page 1
CMAT 2018 Slot 2
Quant
1. What is the probability of getting a ‘nine’ or ‘ten’ on a single throw of two dice?
A 2/9
B 7/36
C 1/5
D 2/7
A n s w e r : B
Explanation:
Probability = Expected number of outcomes/ Total number of outcomes.
Total number of outcomes we get in a single throw of two dice = = 36.
Possible cases of getting 'nine' in a single throw of two dice:
dice 1 dice 2
three six..................(1)
six three................(2)
four five..................(3)
five four...................(4)
So, total of 4 cases.
Possible cases of getting 'ten' in a single throw of two dice:
dice 1 dice 2
four six.....................(1)
six four....................(2)
five five....................(3)
So, total of 3 cases.
Expected number of outcomes = Total possible cases of getting 'nine' or 'ten' in a single throw of two dice = 4 + 3 = 7 .
So, Probability =
2. The length of a room exceeds its breadth by 2 meters. If the length be increased by 4 meters and the breadth decreased by 2
meters, the area remains the same. Find the surface area of its walls if the height is 3 meters.
A
B
C
D
A n s w e r : D
Explanation:
Let the breadth(b) of the room be 'x' metres.
6 × 6
36
7
248 m
2
424 m
2
112 m
2
84 m
2
.
Page 2
CMAT 2018 Slot 2
Quant
1. What is the probability of getting a ‘nine’ or ‘ten’ on a single throw of two dice?
A 2/9
B 7/36
C 1/5
D 2/7
A n s w e r : B
Explanation:
Probability = Expected number of outcomes/ Total number of outcomes.
Total number of outcomes we get in a single throw of two dice = = 36.
Possible cases of getting 'nine' in a single throw of two dice:
dice 1 dice 2
three six..................(1)
six three................(2)
four five..................(3)
five four...................(4)
So, total of 4 cases.
Possible cases of getting 'ten' in a single throw of two dice:
dice 1 dice 2
four six.....................(1)
six four....................(2)
five five....................(3)
So, total of 3 cases.
Expected number of outcomes = Total possible cases of getting 'nine' or 'ten' in a single throw of two dice = 4 + 3 = 7 .
So, Probability =
2. The length of a room exceeds its breadth by 2 meters. If the length be increased by 4 meters and the breadth decreased by 2
meters, the area remains the same. Find the surface area of its walls if the height is 3 meters.
A
B
C
D
A n s w e r : D
Explanation:
Let the breadth(b) of the room be 'x' metres.
6 × 6
36
7
248 m
2
424 m
2
112 m
2
84 m
2
.
then, length(l) of the room = x+2 metres.
Area(A) = = x(x+2)
Given, length is increased by 4 meters and the breadth decreased by 2 meters
Then, new length(l') of the room = x+6 metres
new breadth(b') of the room = x-2 metres
New Area(A') of the room = = (x+6)(x-2)
Also given that, A = A'
Therefore the length of the room (l) = 8 metres
and breadth of the room (b) = 6 metres
and given height of the room (h) = 3 metres
Since the room will be in the shape of a cuboid, Surface area = 2 ( )
But the Surface area of Walls = Total Surface area - Area of Roof and Floor = 2 (
Hence, Surface Area of walls = 84 .
3. A bus covers a distance of first 50 km in 40 minutes, next 50 km at a speed of 2 km per minute and the next 30 km at a speed
of 1.0 km per minute. What is its average speed during the entire journey?
A 61.5 kmph
B 55.06 kmph
C 82.1 kmph
D 80 kmph
A n s w e r : C
Explanation:
Average Speed = Total distance covered Total time taken
Total distance travelled = 50 + 50 + 30 = 130 km.
Total time taken = Time taken to travel first 50 km + Time taken to travel next 50 km + Time taken to travel next 30 km =
minutes = hours.
Average Speed = kmph
4. Three wheels making 60, 36 and 24 revolutions in a minute start with a certain point in their circumference ownwards. Find
when they will again come together in the same position.
A 4 seconds
B 5 seconds
C 10 seconds
D Never
l × b m
2
l ×
'
b
'
m
2
? x( x + 2) = ( x + 6)( x - 2)
? x +
2
2 x = x +
2
4 x - 12
? 2 x = 12
? x = 6
l × b + b × h + l × h
l × b + b × h + l × h) - 2( l × b) = 2(8 × 3 +
6 × 3) = 84 m
2
m
2
÷
40 + 50 ÷
2 + 30 ÷ 1 = 95 60
95
? 130 ÷ = 60
95
82.1
.
Page 3
CMAT 2018 Slot 2
Quant
1. What is the probability of getting a ‘nine’ or ‘ten’ on a single throw of two dice?
A 2/9
B 7/36
C 1/5
D 2/7
A n s w e r : B
Explanation:
Probability = Expected number of outcomes/ Total number of outcomes.
Total number of outcomes we get in a single throw of two dice = = 36.
Possible cases of getting 'nine' in a single throw of two dice:
dice 1 dice 2
three six..................(1)
six three................(2)
four five..................(3)
five four...................(4)
So, total of 4 cases.
Possible cases of getting 'ten' in a single throw of two dice:
dice 1 dice 2
four six.....................(1)
six four....................(2)
five five....................(3)
So, total of 3 cases.
Expected number of outcomes = Total possible cases of getting 'nine' or 'ten' in a single throw of two dice = 4 + 3 = 7 .
So, Probability =
2. The length of a room exceeds its breadth by 2 meters. If the length be increased by 4 meters and the breadth decreased by 2
meters, the area remains the same. Find the surface area of its walls if the height is 3 meters.
A
B
C
D
A n s w e r : D
Explanation:
Let the breadth(b) of the room be 'x' metres.
6 × 6
36
7
248 m
2
424 m
2
112 m
2
84 m
2
.
then, length(l) of the room = x+2 metres.
Area(A) = = x(x+2)
Given, length is increased by 4 meters and the breadth decreased by 2 meters
Then, new length(l') of the room = x+6 metres
new breadth(b') of the room = x-2 metres
New Area(A') of the room = = (x+6)(x-2)
Also given that, A = A'
Therefore the length of the room (l) = 8 metres
and breadth of the room (b) = 6 metres
and given height of the room (h) = 3 metres
Since the room will be in the shape of a cuboid, Surface area = 2 ( )
But the Surface area of Walls = Total Surface area - Area of Roof and Floor = 2 (
Hence, Surface Area of walls = 84 .
3. A bus covers a distance of first 50 km in 40 minutes, next 50 km at a speed of 2 km per minute and the next 30 km at a speed
of 1.0 km per minute. What is its average speed during the entire journey?
A 61.5 kmph
B 55.06 kmph
C 82.1 kmph
D 80 kmph
A n s w e r : C
Explanation:
Average Speed = Total distance covered Total time taken
Total distance travelled = 50 + 50 + 30 = 130 km.
Total time taken = Time taken to travel first 50 km + Time taken to travel next 50 km + Time taken to travel next 30 km =
minutes = hours.
Average Speed = kmph
4. Three wheels making 60, 36 and 24 revolutions in a minute start with a certain point in their circumference ownwards. Find
when they will again come together in the same position.
A 4 seconds
B 5 seconds
C 10 seconds
D Never
l × b m
2
l ×
'
b
'
m
2
? x( x + 2) = ( x + 6)( x - 2)
? x +
2
2 x = x +
2
4 x - 12
? 2 x = 12
? x = 6
l × b + b × h + l × h
l × b + b × h + l × h) - 2( l × b) = 2(8 × 3 +
6 × 3) = 84 m
2
m
2
÷
40 + 50 ÷
2 + 30 ÷ 1 = 95 60
95
? 130 ÷ = 60
95
82.1
.
A n s w e r : B
Explanation:
First wheel makes 60 revolutions in 1 minute
It makes 60 revolutions in 60 seconds
It makes 1 revolution in 1 second.
This implies, after every 1 second the certain point at which the wheel started its revolution reaches its initial position.
Similarly, Second wheel and Third wheel makes 36 and 24 revolutions in 1 minute respectively.
Second and Third wheel makes 1 revolution in seconds respectively.
So for all the multiples of seconds the certain point of second wheel and third wheel reaches its initial position respectively.
After LCM {1, } seconds all the three wheels will come together in the same position.
LCM of fractions = LCM of numerators/ HCF of denominators
LCM {1, } = LCM {1,5,5} HCF {1,3,2} = 5 1 = 5.
Hence, after 5 seconds all the wheels will come again together in the same position.
5. A certain amount of money invested at 10% per annum compound interest for two years became Rs. 2000.
What is the initial investment?
A Rs. 856
B Rs. 1,625
C Rs. 1,653
D Rs. 1,275
A n s w e r : C
Explanation:
If the principle amount 'P' when compounded annually for 'n' years at 'R%" interest rate per annum becomes P'.
Then
Given P' = 2000, n = 2 years, R = 10%
Hence the initial amount P = Rs. 1,653.
6. If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the
cone.
A Remains unaltered
B Decreases by 25%
C Increases by 25%
D Increases by 50%
A n s w e r : B
?
?
? a n d 3
5
2
5
a n d 3
5
2
5
, 3
5
2
5
? , 3
5
2
5
÷ ÷
P =
'
P [1 + ] 100
R
n
? P = P ÷
'
[1 + ] 100
R
n
? P = 2000 ÷ [1 + ] 100
10
2
? P = 2000 ÷ 1.21
? P = 1653
.
Page 4
CMAT 2018 Slot 2
Quant
1. What is the probability of getting a ‘nine’ or ‘ten’ on a single throw of two dice?
A 2/9
B 7/36
C 1/5
D 2/7
A n s w e r : B
Explanation:
Probability = Expected number of outcomes/ Total number of outcomes.
Total number of outcomes we get in a single throw of two dice = = 36.
Possible cases of getting 'nine' in a single throw of two dice:
dice 1 dice 2
three six..................(1)
six three................(2)
four five..................(3)
five four...................(4)
So, total of 4 cases.
Possible cases of getting 'ten' in a single throw of two dice:
dice 1 dice 2
four six.....................(1)
six four....................(2)
five five....................(3)
So, total of 3 cases.
Expected number of outcomes = Total possible cases of getting 'nine' or 'ten' in a single throw of two dice = 4 + 3 = 7 .
So, Probability =
2. The length of a room exceeds its breadth by 2 meters. If the length be increased by 4 meters and the breadth decreased by 2
meters, the area remains the same. Find the surface area of its walls if the height is 3 meters.
A
B
C
D
A n s w e r : D
Explanation:
Let the breadth(b) of the room be 'x' metres.
6 × 6
36
7
248 m
2
424 m
2
112 m
2
84 m
2
.
then, length(l) of the room = x+2 metres.
Area(A) = = x(x+2)
Given, length is increased by 4 meters and the breadth decreased by 2 meters
Then, new length(l') of the room = x+6 metres
new breadth(b') of the room = x-2 metres
New Area(A') of the room = = (x+6)(x-2)
Also given that, A = A'
Therefore the length of the room (l) = 8 metres
and breadth of the room (b) = 6 metres
and given height of the room (h) = 3 metres
Since the room will be in the shape of a cuboid, Surface area = 2 ( )
But the Surface area of Walls = Total Surface area - Area of Roof and Floor = 2 (
Hence, Surface Area of walls = 84 .
3. A bus covers a distance of first 50 km in 40 minutes, next 50 km at a speed of 2 km per minute and the next 30 km at a speed
of 1.0 km per minute. What is its average speed during the entire journey?
A 61.5 kmph
B 55.06 kmph
C 82.1 kmph
D 80 kmph
A n s w e r : C
Explanation:
Average Speed = Total distance covered Total time taken
Total distance travelled = 50 + 50 + 30 = 130 km.
Total time taken = Time taken to travel first 50 km + Time taken to travel next 50 km + Time taken to travel next 30 km =
minutes = hours.
Average Speed = kmph
4. Three wheels making 60, 36 and 24 revolutions in a minute start with a certain point in their circumference ownwards. Find
when they will again come together in the same position.
A 4 seconds
B 5 seconds
C 10 seconds
D Never
l × b m
2
l ×
'
b
'
m
2
? x( x + 2) = ( x + 6)( x - 2)
? x +
2
2 x = x +
2
4 x - 12
? 2 x = 12
? x = 6
l × b + b × h + l × h
l × b + b × h + l × h) - 2( l × b) = 2(8 × 3 +
6 × 3) = 84 m
2
m
2
÷
40 + 50 ÷
2 + 30 ÷ 1 = 95 60
95
? 130 ÷ = 60
95
82.1
.
A n s w e r : B
Explanation:
First wheel makes 60 revolutions in 1 minute
It makes 60 revolutions in 60 seconds
It makes 1 revolution in 1 second.
This implies, after every 1 second the certain point at which the wheel started its revolution reaches its initial position.
Similarly, Second wheel and Third wheel makes 36 and 24 revolutions in 1 minute respectively.
Second and Third wheel makes 1 revolution in seconds respectively.
So for all the multiples of seconds the certain point of second wheel and third wheel reaches its initial position respectively.
After LCM {1, } seconds all the three wheels will come together in the same position.
LCM of fractions = LCM of numerators/ HCF of denominators
LCM {1, } = LCM {1,5,5} HCF {1,3,2} = 5 1 = 5.
Hence, after 5 seconds all the wheels will come again together in the same position.
5. A certain amount of money invested at 10% per annum compound interest for two years became Rs. 2000.
What is the initial investment?
A Rs. 856
B Rs. 1,625
C Rs. 1,653
D Rs. 1,275
A n s w e r : C
Explanation:
If the principle amount 'P' when compounded annually for 'n' years at 'R%" interest rate per annum becomes P'.
Then
Given P' = 2000, n = 2 years, R = 10%
Hence the initial amount P = Rs. 1,653.
6. If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the
cone.
A Remains unaltered
B Decreases by 25%
C Increases by 25%
D Increases by 50%
A n s w e r : B
?
?
? a n d 3
5
2
5
a n d 3
5
2
5
, 3
5
2
5
? , 3
5
2
5
÷ ÷
P =
'
P [1 + ] 100
R
n
? P = P ÷
'
[1 + ] 100
R
n
? P = 2000 ÷ [1 + ] 100
10
2
? P = 2000 ÷ 1.21
? P = 1653
.
Explanation:
The Volume of the right circular cone of base radius 'r' and height 'h' is given by 'V' =
Given 'h' has been increased by 200%
New height h' = h[1 + ] = 3h
also,radius of the base is reduced by 50%
New base radius r' = r[1 - ] =
New Volume of the cone with new base radius r' and new height h' is given by V' = = .
Change in Volume =
Hence the new volume decreased by 25 %.
7. An electric appliance is priced at Rs. 600 initially. Because of market recession, price was successively reduced three times,
each time by 10% of the price after the earlier reduction. What is the current price?
A Rs. 420
B Rs. 437.40
C Rs. 444.30
D Rs. 478
A n s w e r : B
Explanation:
Initial price is given as 'I' = Rs. 600
After the first reduction, the initial price is reduced by 10%
the new price I' =
After second reduction, I' is reduced by 10%
the new price I'' =
After third reduction, I'' is reduced by 10%
the new price I''' =
Hence the Current price after three successive reductions is Rs. 437.4
8. Below given is the Table showing Age-wise Ownership of mobiles:
If 1 crore mobiles were sold last year, how many LG sets were sold?
A 10, 000
B 12,500
p r h 3
1
2
? 100
200
? 100
50
2
r
p r h 3
1
'2 '
p( ) (3 h) = 3
1
2
r
2
4
3 V
× O l d V o l u m e
N e w V o l u m e- O l d V o l u m e
100 = × V
- V 4
3 V
100 = -25
? 600[1 - ] = 100
10
540
? 540[1 - ] = 100
10
486
? 486[1 - ] = 100
10
437.4
.
Page 5
CMAT 2018 Slot 2
Quant
1. What is the probability of getting a ‘nine’ or ‘ten’ on a single throw of two dice?
A 2/9
B 7/36
C 1/5
D 2/7
A n s w e r : B
Explanation:
Probability = Expected number of outcomes/ Total number of outcomes.
Total number of outcomes we get in a single throw of two dice = = 36.
Possible cases of getting 'nine' in a single throw of two dice:
dice 1 dice 2
three six..................(1)
six three................(2)
four five..................(3)
five four...................(4)
So, total of 4 cases.
Possible cases of getting 'ten' in a single throw of two dice:
dice 1 dice 2
four six.....................(1)
six four....................(2)
five five....................(3)
So, total of 3 cases.
Expected number of outcomes = Total possible cases of getting 'nine' or 'ten' in a single throw of two dice = 4 + 3 = 7 .
So, Probability =
2. The length of a room exceeds its breadth by 2 meters. If the length be increased by 4 meters and the breadth decreased by 2
meters, the area remains the same. Find the surface area of its walls if the height is 3 meters.
A
B
C
D
A n s w e r : D
Explanation:
Let the breadth(b) of the room be 'x' metres.
6 × 6
36
7
248 m
2
424 m
2
112 m
2
84 m
2
.
then, length(l) of the room = x+2 metres.
Area(A) = = x(x+2)
Given, length is increased by 4 meters and the breadth decreased by 2 meters
Then, new length(l') of the room = x+6 metres
new breadth(b') of the room = x-2 metres
New Area(A') of the room = = (x+6)(x-2)
Also given that, A = A'
Therefore the length of the room (l) = 8 metres
and breadth of the room (b) = 6 metres
and given height of the room (h) = 3 metres
Since the room will be in the shape of a cuboid, Surface area = 2 ( )
But the Surface area of Walls = Total Surface area - Area of Roof and Floor = 2 (
Hence, Surface Area of walls = 84 .
3. A bus covers a distance of first 50 km in 40 minutes, next 50 km at a speed of 2 km per minute and the next 30 km at a speed
of 1.0 km per minute. What is its average speed during the entire journey?
A 61.5 kmph
B 55.06 kmph
C 82.1 kmph
D 80 kmph
A n s w e r : C
Explanation:
Average Speed = Total distance covered Total time taken
Total distance travelled = 50 + 50 + 30 = 130 km.
Total time taken = Time taken to travel first 50 km + Time taken to travel next 50 km + Time taken to travel next 30 km =
minutes = hours.
Average Speed = kmph
4. Three wheels making 60, 36 and 24 revolutions in a minute start with a certain point in their circumference ownwards. Find
when they will again come together in the same position.
A 4 seconds
B 5 seconds
C 10 seconds
D Never
l × b m
2
l ×
'
b
'
m
2
? x( x + 2) = ( x + 6)( x - 2)
? x +
2
2 x = x +
2
4 x - 12
? 2 x = 12
? x = 6
l × b + b × h + l × h
l × b + b × h + l × h) - 2( l × b) = 2(8 × 3 +
6 × 3) = 84 m
2
m
2
÷
40 + 50 ÷
2 + 30 ÷ 1 = 95 60
95
? 130 ÷ = 60
95
82.1
.
A n s w e r : B
Explanation:
First wheel makes 60 revolutions in 1 minute
It makes 60 revolutions in 60 seconds
It makes 1 revolution in 1 second.
This implies, after every 1 second the certain point at which the wheel started its revolution reaches its initial position.
Similarly, Second wheel and Third wheel makes 36 and 24 revolutions in 1 minute respectively.
Second and Third wheel makes 1 revolution in seconds respectively.
So for all the multiples of seconds the certain point of second wheel and third wheel reaches its initial position respectively.
After LCM {1, } seconds all the three wheels will come together in the same position.
LCM of fractions = LCM of numerators/ HCF of denominators
LCM {1, } = LCM {1,5,5} HCF {1,3,2} = 5 1 = 5.
Hence, after 5 seconds all the wheels will come again together in the same position.
5. A certain amount of money invested at 10% per annum compound interest for two years became Rs. 2000.
What is the initial investment?
A Rs. 856
B Rs. 1,625
C Rs. 1,653
D Rs. 1,275
A n s w e r : C
Explanation:
If the principle amount 'P' when compounded annually for 'n' years at 'R%" interest rate per annum becomes P'.
Then
Given P' = 2000, n = 2 years, R = 10%
Hence the initial amount P = Rs. 1,653.
6. If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the
cone.
A Remains unaltered
B Decreases by 25%
C Increases by 25%
D Increases by 50%
A n s w e r : B
?
?
? a n d 3
5
2
5
a n d 3
5
2
5
, 3
5
2
5
? , 3
5
2
5
÷ ÷
P =
'
P [1 + ] 100
R
n
? P = P ÷
'
[1 + ] 100
R
n
? P = 2000 ÷ [1 + ] 100
10
2
? P = 2000 ÷ 1.21
? P = 1653
.
Explanation:
The Volume of the right circular cone of base radius 'r' and height 'h' is given by 'V' =
Given 'h' has been increased by 200%
New height h' = h[1 + ] = 3h
also,radius of the base is reduced by 50%
New base radius r' = r[1 - ] =
New Volume of the cone with new base radius r' and new height h' is given by V' = = .
Change in Volume =
Hence the new volume decreased by 25 %.
7. An electric appliance is priced at Rs. 600 initially. Because of market recession, price was successively reduced three times,
each time by 10% of the price after the earlier reduction. What is the current price?
A Rs. 420
B Rs. 437.40
C Rs. 444.30
D Rs. 478
A n s w e r : B
Explanation:
Initial price is given as 'I' = Rs. 600
After the first reduction, the initial price is reduced by 10%
the new price I' =
After second reduction, I' is reduced by 10%
the new price I'' =
After third reduction, I'' is reduced by 10%
the new price I''' =
Hence the Current price after three successive reductions is Rs. 437.4
8. Below given is the Table showing Age-wise Ownership of mobiles:
If 1 crore mobiles were sold last year, how many LG sets were sold?
A 10, 000
B 12,500
p r h 3
1
2
? 100
200
? 100
50
2
r
p r h 3
1
'2 '
p( ) (3 h) = 3
1
2
r
2
4
3 V
× O l d V o l u m e
N e w V o l u m e- O l d V o l u m e
100 = × V
- V 4
3 V
100 = -25
? 600[1 - ] = 100
10
540
? 540[1 - ] = 100
10
486
? 486[1 - ] = 100
10
437.4
.
C
15,000
D Cannot be determined
A n s w e r : D
Explanation:
Let say,
The number mobiles sold in last year of the brands LG, SAMSUNG, NOKIA, SONY, MICRO-MAX be A, B, C, D, and E respectively.
Given that A+B+C+D+E = 1 crore.
Out of these 1 crore mobiles, the number of mobile sets of LG sold are 15% of A = .
But from the given data, the values of A, B, C, D, and E cannot be found out.
So the number of LG sets sold last year cannot be determined.
Note that the 15% does not represent the percentage of LG mobiles among the ones that are 1 yr old, but the percentage of 1 yr old
mobiles among LG mobiles.
9. = ?
A 16.4
B 14.4
C 16
D 14
A n s w e r : D
Explanation:
= = = = = 14
10. In what time will Rs. 6,250 amount to Rs. 6,632.55 at 4% compound interest payable half-yearly?
A 1 year
B
years
C 3 years
D
years
A n s w e r : B
Explanation:
If the principle amount 'P' when compounded half-yearly at R% interest rate per annum for 'n' years, the new amount is P'.
then
Given P' = 6,632.55, P = 6,250 and R = 4%
Taking logarithm on both sides we get,
n = log(1.061) log(1.02) = 3
Since n refers to half a year in this case, the number of years will be years.
× 100
15
A
188 +
51 +
169
188 +
51 +
169
188 +
51 + 13
188 +
64
188 + 8 196
2
3
2
5
P =
'
P [1 + ] 2×100
R
n
? 6, 632.55 = 6, 250[1 + ] 2×100
4
n
? 1.061 = 1.02
n
÷
2
3
.
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