SNAP 2009: Previous Year Question Paper with Solutions

 Page 1


SNAP 2009
Quantitative Aptitude
1. A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was
a four is
A    
B    
C    
D    None of these
A n s w e r : B
Explanation:
There are three possibilities for sum of uppermost faces of dice is equal to 15. They are
5, 5, 5 - only 1 arrangement
4, 5, 6 - 3! = 6 arrangements
3, 6, 6 -  = 3 arrangements
Out of these 10 arrangements, there are 2 cases in which 4 occurs in first roll ( 4,5,6 or 4,6,5)
Therefore, probability =  = 
Answer is option B.
     
2. A boat covers a distance of 30 kms downstream in 2 hours while it takes 6 hours to cover the same distance upstream. What is
the speed of the boat in kms per hour?
A    5
B    7.5
C    13
D    10
A n s w e r : D
Explanation:
Let speed of boat be V and speed of stream be U 
so as per case 1 
Downstream i.e V+U = 30/2 =15
And Upstream i.e V-U = 30/6 = 5 
Now adding 
we get 2V =2
V =10
3. A five digit number is formed by using the digits 1, 2, 3, 4 and 5 without repetitions. What is the probability that the number is
divisible by 4?
A    
B    
5
2
5
1
6
1
2
3!
10
2
5
1
5
1
6
5
4
  
.
Page 2


SNAP 2009
Quantitative Aptitude
1. A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was
a four is
A    
B    
C    
D    None of these
A n s w e r : B
Explanation:
There are three possibilities for sum of uppermost faces of dice is equal to 15. They are
5, 5, 5 - only 1 arrangement
4, 5, 6 - 3! = 6 arrangements
3, 6, 6 -  = 3 arrangements
Out of these 10 arrangements, there are 2 cases in which 4 occurs in first roll ( 4,5,6 or 4,6,5)
Therefore, probability =  = 
Answer is option B.
     
2. A boat covers a distance of 30 kms downstream in 2 hours while it takes 6 hours to cover the same distance upstream. What is
the speed of the boat in kms per hour?
A    5
B    7.5
C    13
D    10
A n s w e r : D
Explanation:
Let speed of boat be V and speed of stream be U 
so as per case 1 
Downstream i.e V+U = 30/2 =15
And Upstream i.e V-U = 30/6 = 5 
Now adding 
we get 2V =2
V =10
3. A five digit number is formed by using the digits 1, 2, 3, 4 and 5 without repetitions. What is the probability that the number is
divisible by 4?
A    
B    
5
2
5
1
6
1
2
3!
10
2
5
1
5
1
6
5
4
  
.
C    
D    None of these
A n s w e r : A
Explanation:
For a number to be divisible by 4, last 2 digits must be divisible by 4
Last 2 digits can be 12, 24, 32, 52
_, _, _, _, _
Last 2 digits have 4 possibilities and remaining digits can be arranged in 3! ways
Number of 5 digit numbers divisible by 4 are 3!  4 = 24
Total number of 5 digit numbers that can be formed = 5!
Therefore, probability =  = 
Answer is option A.
4. If the algebraic sum of deviations of 20 observations measured from 23 is 70, mean of these observations would be
A    24
B    25
C    26
D    None of these
A n s w e r : D
Explanation:
Sum of observation is given as = 70
Number of observation = 20
Therefore, Mean = 70/20=3.5
But, here observation starts from 23.
Therefore, Mean = 23 + 3.5 = 26.5
    
5. An alloy of gold and silver weighs 50 gms. It contains 80% gold. How much gold should be added to the alloy so that percentage
of gold is increased to 90?
A    50 gms
B    60 gms
C    30 gms
D    40 gms
A n s w e r : A
Explanation:
Gold in 50g of alloy 
= 80×5010=40g 
Let x g gold must be added. 
5
4
× 
 5!
24
5
1
  
.
Page 3


SNAP 2009
Quantitative Aptitude
1. A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was
a four is
A    
B    
C    
D    None of these
A n s w e r : B
Explanation:
There are three possibilities for sum of uppermost faces of dice is equal to 15. They are
5, 5, 5 - only 1 arrangement
4, 5, 6 - 3! = 6 arrangements
3, 6, 6 -  = 3 arrangements
Out of these 10 arrangements, there are 2 cases in which 4 occurs in first roll ( 4,5,6 or 4,6,5)
Therefore, probability =  = 
Answer is option B.
     
2. A boat covers a distance of 30 kms downstream in 2 hours while it takes 6 hours to cover the same distance upstream. What is
the speed of the boat in kms per hour?
A    5
B    7.5
C    13
D    10
A n s w e r : D
Explanation:
Let speed of boat be V and speed of stream be U 
so as per case 1 
Downstream i.e V+U = 30/2 =15
And Upstream i.e V-U = 30/6 = 5 
Now adding 
we get 2V =2
V =10
3. A five digit number is formed by using the digits 1, 2, 3, 4 and 5 without repetitions. What is the probability that the number is
divisible by 4?
A    
B    
5
2
5
1
6
1
2
3!
10
2
5
1
5
1
6
5
4
  
.
C    
D    None of these
A n s w e r : A
Explanation:
For a number to be divisible by 4, last 2 digits must be divisible by 4
Last 2 digits can be 12, 24, 32, 52
_, _, _, _, _
Last 2 digits have 4 possibilities and remaining digits can be arranged in 3! ways
Number of 5 digit numbers divisible by 4 are 3!  4 = 24
Total number of 5 digit numbers that can be formed = 5!
Therefore, probability =  = 
Answer is option A.
4. If the algebraic sum of deviations of 20 observations measured from 23 is 70, mean of these observations would be
A    24
B    25
C    26
D    None of these
A n s w e r : D
Explanation:
Sum of observation is given as = 70
Number of observation = 20
Therefore, Mean = 70/20=3.5
But, here observation starts from 23.
Therefore, Mean = 23 + 3.5 = 26.5
    
5. An alloy of gold and silver weighs 50 gms. It contains 80% gold. How much gold should be added to the alloy so that percentage
of gold is increased to 90?
A    50 gms
B    60 gms
C    30 gms
D    40 gms
A n s w e r : A
Explanation:
Gold in 50g of alloy 
= 80×5010=40g 
Let x g gold must be added. 
5
4
× 
 5!
24
5
1
  
.
Now, according to the question, 
40+x50+x=90100
=>100(40+x)=90(50+x)
=>10(40+x)=9(50+x)
=>400+10x=45+9x
=>80×5010=40g
=>x=450-400=>x=50g
Thus, 50 g of gold must be added to it 90%.
6. Weekly incomes of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves
Rs. 300 per week, then the weekly income of the first person is
A    Rs. 7500
B    Rs. 4500
C    Rs. 6300
D    Rs. 5400
A n s w e r : C
Explanation:
Let the incomes of two persons are 7x and 3x 
Expenditure of first person = 7x - 300 
Expenditure of second person = 3x - 300 
According to the question, 
7x-300/3x-300=5/2
=> 14x-600 = 15x-1500 
x = 900 
Income of first person 
= 7x = 7×900=RS.6300
7. Wheat is now being sold at Rs. 27 per kg. During last month its cost was Rs. 24 per kg. Find by how much per cent a family
reduces its consumption so as to keep the expenditure fixed.
A    10.2%
B    12.1%
C    12.3%
D    11.1%
A n s w e r : D
Explanation:
Old price of rice = Rs.24/k 
New price of rice = Rs.27 per/kg 
Therefore, Increase in price of rice = New price - Old price = 27 - 24 = Rs.3/kg 
Therefore, Increased percentage in price 
= 3/24×100=12.5 %
Now, reduction in consumption, so as to keep the expenditure fixed. 
According to the formula, 
a
  
.
Page 4


SNAP 2009
Quantitative Aptitude
1. A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was
a four is
A    
B    
C    
D    None of these
A n s w e r : B
Explanation:
There are three possibilities for sum of uppermost faces of dice is equal to 15. They are
5, 5, 5 - only 1 arrangement
4, 5, 6 - 3! = 6 arrangements
3, 6, 6 -  = 3 arrangements
Out of these 10 arrangements, there are 2 cases in which 4 occurs in first roll ( 4,5,6 or 4,6,5)
Therefore, probability =  = 
Answer is option B.
     
2. A boat covers a distance of 30 kms downstream in 2 hours while it takes 6 hours to cover the same distance upstream. What is
the speed of the boat in kms per hour?
A    5
B    7.5
C    13
D    10
A n s w e r : D
Explanation:
Let speed of boat be V and speed of stream be U 
so as per case 1 
Downstream i.e V+U = 30/2 =15
And Upstream i.e V-U = 30/6 = 5 
Now adding 
we get 2V =2
V =10
3. A five digit number is formed by using the digits 1, 2, 3, 4 and 5 without repetitions. What is the probability that the number is
divisible by 4?
A    
B    
5
2
5
1
6
1
2
3!
10
2
5
1
5
1
6
5
4
  
.
C    
D    None of these
A n s w e r : A
Explanation:
For a number to be divisible by 4, last 2 digits must be divisible by 4
Last 2 digits can be 12, 24, 32, 52
_, _, _, _, _
Last 2 digits have 4 possibilities and remaining digits can be arranged in 3! ways
Number of 5 digit numbers divisible by 4 are 3!  4 = 24
Total number of 5 digit numbers that can be formed = 5!
Therefore, probability =  = 
Answer is option A.
4. If the algebraic sum of deviations of 20 observations measured from 23 is 70, mean of these observations would be
A    24
B    25
C    26
D    None of these
A n s w e r : D
Explanation:
Sum of observation is given as = 70
Number of observation = 20
Therefore, Mean = 70/20=3.5
But, here observation starts from 23.
Therefore, Mean = 23 + 3.5 = 26.5
    
5. An alloy of gold and silver weighs 50 gms. It contains 80% gold. How much gold should be added to the alloy so that percentage
of gold is increased to 90?
A    50 gms
B    60 gms
C    30 gms
D    40 gms
A n s w e r : A
Explanation:
Gold in 50g of alloy 
= 80×5010=40g 
Let x g gold must be added. 
5
4
× 
 5!
24
5
1
  
.
Now, according to the question, 
40+x50+x=90100
=>100(40+x)=90(50+x)
=>10(40+x)=9(50+x)
=>400+10x=45+9x
=>80×5010=40g
=>x=450-400=>x=50g
Thus, 50 g of gold must be added to it 90%.
6. Weekly incomes of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves
Rs. 300 per week, then the weekly income of the first person is
A    Rs. 7500
B    Rs. 4500
C    Rs. 6300
D    Rs. 5400
A n s w e r : C
Explanation:
Let the incomes of two persons are 7x and 3x 
Expenditure of first person = 7x - 300 
Expenditure of second person = 3x - 300 
According to the question, 
7x-300/3x-300=5/2
=> 14x-600 = 15x-1500 
x = 900 
Income of first person 
= 7x = 7×900=RS.6300
7. Wheat is now being sold at Rs. 27 per kg. During last month its cost was Rs. 24 per kg. Find by how much per cent a family
reduces its consumption so as to keep the expenditure fixed.
A    10.2%
B    12.1%
C    12.3%
D    11.1%
A n s w e r : D
Explanation:
Old price of rice = Rs.24/k 
New price of rice = Rs.27 per/kg 
Therefore, Increase in price of rice = New price - Old price = 27 - 24 = Rs.3/kg 
Therefore, Increased percentage in price 
= 3/24×100=12.5 %
Now, reduction in consumption, so as to keep the expenditure fixed. 
According to the formula, 
a
  
.
= 
=11.1 %
    
8. There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities is
A    92
B    90
C    91
D    None of these
A n s w e r : B
Explanation:
The number of different journey tickets that are required by the authorities = The number of selecting 2 stations × \times\ × 2 (For every
pair stations say A and B, there are two tickets required A to B and B to A)
=  = 90
9. The radius of circle is so increased that its circumference increased by 5%. The area of the circle then increases by
A    12.5%
B    10.25%
C    10.5%
D    11.25%
A n s w e r : B
Explanation:
We know that Circumference is dependent linearly on radius 
so if circumference is increased by 5% , we can conclude radius is increased by 5%
Now Area varies directly with square of radius 
Now if r is changed to 1.05 r 
so r^2 will change to (1.05r)(1.05r) = 1.1025 r^2
So we can conclude area will change by 10.25%
10. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
A    
B    
C    
D    
A n s w e r : D
Explanation:
ABACUS 
Vowels = AAU 
Remaining BCS
× 100+ a
a
100
× 100+12.5
12.5
100
C × 
10
2 2
2!
6!
3! * 3!
2!
(3!*3!)
2!
(4!*3!)
  
.
Page 5


SNAP 2009
Quantitative Aptitude
1. A dice is rolled three times and sum of three numbers appearing on the uppermost face is 15. The chance that the first roll was
a four is
A    
B    
C    
D    None of these
A n s w e r : B
Explanation:
There are three possibilities for sum of uppermost faces of dice is equal to 15. They are
5, 5, 5 - only 1 arrangement
4, 5, 6 - 3! = 6 arrangements
3, 6, 6 -  = 3 arrangements
Out of these 10 arrangements, there are 2 cases in which 4 occurs in first roll ( 4,5,6 or 4,6,5)
Therefore, probability =  = 
Answer is option B.
     
2. A boat covers a distance of 30 kms downstream in 2 hours while it takes 6 hours to cover the same distance upstream. What is
the speed of the boat in kms per hour?
A    5
B    7.5
C    13
D    10
A n s w e r : D
Explanation:
Let speed of boat be V and speed of stream be U 
so as per case 1 
Downstream i.e V+U = 30/2 =15
And Upstream i.e V-U = 30/6 = 5 
Now adding 
we get 2V =2
V =10
3. A five digit number is formed by using the digits 1, 2, 3, 4 and 5 without repetitions. What is the probability that the number is
divisible by 4?
A    
B    
5
2
5
1
6
1
2
3!
10
2
5
1
5
1
6
5
4
  
.
C    
D    None of these
A n s w e r : A
Explanation:
For a number to be divisible by 4, last 2 digits must be divisible by 4
Last 2 digits can be 12, 24, 32, 52
_, _, _, _, _
Last 2 digits have 4 possibilities and remaining digits can be arranged in 3! ways
Number of 5 digit numbers divisible by 4 are 3!  4 = 24
Total number of 5 digit numbers that can be formed = 5!
Therefore, probability =  = 
Answer is option A.
4. If the algebraic sum of deviations of 20 observations measured from 23 is 70, mean of these observations would be
A    24
B    25
C    26
D    None of these
A n s w e r : D
Explanation:
Sum of observation is given as = 70
Number of observation = 20
Therefore, Mean = 70/20=3.5
But, here observation starts from 23.
Therefore, Mean = 23 + 3.5 = 26.5
    
5. An alloy of gold and silver weighs 50 gms. It contains 80% gold. How much gold should be added to the alloy so that percentage
of gold is increased to 90?
A    50 gms
B    60 gms
C    30 gms
D    40 gms
A n s w e r : A
Explanation:
Gold in 50g of alloy 
= 80×5010=40g 
Let x g gold must be added. 
5
4
× 
 5!
24
5
1
  
.
Now, according to the question, 
40+x50+x=90100
=>100(40+x)=90(50+x)
=>10(40+x)=9(50+x)
=>400+10x=45+9x
=>80×5010=40g
=>x=450-400=>x=50g
Thus, 50 g of gold must be added to it 90%.
6. Weekly incomes of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves
Rs. 300 per week, then the weekly income of the first person is
A    Rs. 7500
B    Rs. 4500
C    Rs. 6300
D    Rs. 5400
A n s w e r : C
Explanation:
Let the incomes of two persons are 7x and 3x 
Expenditure of first person = 7x - 300 
Expenditure of second person = 3x - 300 
According to the question, 
7x-300/3x-300=5/2
=> 14x-600 = 15x-1500 
x = 900 
Income of first person 
= 7x = 7×900=RS.6300
7. Wheat is now being sold at Rs. 27 per kg. During last month its cost was Rs. 24 per kg. Find by how much per cent a family
reduces its consumption so as to keep the expenditure fixed.
A    10.2%
B    12.1%
C    12.3%
D    11.1%
A n s w e r : D
Explanation:
Old price of rice = Rs.24/k 
New price of rice = Rs.27 per/kg 
Therefore, Increase in price of rice = New price - Old price = 27 - 24 = Rs.3/kg 
Therefore, Increased percentage in price 
= 3/24×100=12.5 %
Now, reduction in consumption, so as to keep the expenditure fixed. 
According to the formula, 
a
  
.
= 
=11.1 %
    
8. There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities is
A    92
B    90
C    91
D    None of these
A n s w e r : B
Explanation:
The number of different journey tickets that are required by the authorities = The number of selecting 2 stations × \times\ × 2 (For every
pair stations say A and B, there are two tickets required A to B and B to A)
=  = 90
9. The radius of circle is so increased that its circumference increased by 5%. The area of the circle then increases by
A    12.5%
B    10.25%
C    10.5%
D    11.25%
A n s w e r : B
Explanation:
We know that Circumference is dependent linearly on radius 
so if circumference is increased by 5% , we can conclude radius is increased by 5%
Now Area varies directly with square of radius 
Now if r is changed to 1.05 r 
so r^2 will change to (1.05r)(1.05r) = 1.1025 r^2
So we can conclude area will change by 10.25%
10. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
A    
B    
C    
D    
A n s w e r : D
Explanation:
ABACUS 
Vowels = AAU 
Remaining BCS
× 100+ a
a
100
× 100+12.5
12.5
100
C × 
10
2 2
2!
6!
3! * 3!
2!
(3!*3!)
2!
(4!*3!)
  
.
Now AAU will be considered 1 and B,C,S separate 
so these can be arranged in 4! ways 
Vowels AAU can be arranged in 3!/2! ways 
so total arrangements = 
    
11. In 4 years, Rs. 6000 amounts to Rs. 8000. In what time at the same rate will Rs. 525 amount to Rs. 700?
A    2 years
B    3 years
C    4 years
D    5 years
A n s w e r : C
Explanation:
A=P+SI
We get SI =2000
2000 = (6000*R*4)/100
we get R=25/3 %
Now 
P =525
A =700
So SI = 175
175 = (525*25/3*T)/100
We get T = 4 years
Instructions [12 - 14 ]
At the start of a game of cards, J and B together had four times as much money as T, while T and B together had three times as much
as J. At the end of the evening, J and B together had three times as much money as T, while T and B together had twice as much as J. B
lost Rs. 200
12. What fraction of the total money did T have at the beginning of the game?
A    
B    
C    
D    
A n s w e r : D
Explanation: Money J had with respect to total = 300/1500 = 1/5
13. What fraction of the total money did J win/lose?
A    
Won 
B    
Lost 
C    
Lost 
D    
Won 
2!
4!× 3!
3
1
8
1
9
2
5
1
12
1
6
1
3
1
5
1
  
.