SNAP 2014: Previous Year Question Paper with Solutions

 Page 1


SNAP 2014
Quantitative Aptitude
1. How many different letter arrangements can be made from the letter of the word EXTRA in such a way that the vowels are
always together?
A    48
B    60
C    40
D    30
A n s w e r : A
Explanation:
Considering two vowels as one unit ,total number of units = 4
Number of way of arranging these 4 units = 4! = 24 ways
2 vowels can be internally arranged in 2! ways 2 ways
Therefore total number of ways = 24*2 =48 ways.
     
2. The radius of the incircle in the given diagram will be
A    1.8 cm
B    2 cm
C    2.5 cm
D    3.6 cm
A n s w e r : B
Explanation:
AC= 
In-radius of right angled triangle = 
Inradius = 
3. If  and , then the value of  is equal to
A    
B    
= 
 A B + B C
2 2
=
 6 + 8 
2 2
10
2
a+ b- h ( )
= 2
6+8-10 ( )
2
tan ? + sin ? = m tan ? - sin ? = n m -
2
n
2
4 m n
2v( m n)
  
.
Page 2


SNAP 2014
Quantitative Aptitude
1. How many different letter arrangements can be made from the letter of the word EXTRA in such a way that the vowels are
always together?
A    48
B    60
C    40
D    30
A n s w e r : A
Explanation:
Considering two vowels as one unit ,total number of units = 4
Number of way of arranging these 4 units = 4! = 24 ways
2 vowels can be internally arranged in 2! ways 2 ways
Therefore total number of ways = 24*2 =48 ways.
     
2. The radius of the incircle in the given diagram will be
A    1.8 cm
B    2 cm
C    2.5 cm
D    3.6 cm
A n s w e r : B
Explanation:
AC= 
In-radius of right angled triangle = 
Inradius = 
3. If  and , then the value of  is equal to
A    
B    
= 
 A B + B C
2 2
=
 6 + 8 
2 2
10
2
a+ b- h ( )
= 2
6+8-10 ( )
2
tan ? + sin ? = m tan ? - sin ? = n m -
2
n
2
4 m n
2v( m n)
  
.
C    
D    
A n s w e r : C
Explanation:
Going by the options you have only mn or m/n
Case 1 : mn
mn=  =  = 
So 
4. If A and B are two mutually exclusive and exhaustive events with , then what is the value of ?
A    
B    
C    
D    
A n s w e r : B
Explanation:
Since P(B) and P(A) are mutually exclusive and exhaustive , thus, P(B)+P(A)=1
But we know that P(B)=3 P(A) , thus substituting in the above equation we get P(B)=3/4 and P(A)=1/4
Now they have asked P(B_) i.e. 1-P(B)=1-(3/4)=1/4 
    
5. A and B entered into a partnership investing `16,000 and `12,000 respectively. After 3 months, A withdrew `5000 while B
invested `5000 more. After 3 more months, C joins the business with a capital of `21,000. The share of B exceeds that of C, out
of a total profit of
`26,400 after one after by:
A    2400
B    3000
C    3600
D    4800
A n s w e r : C
Explanation:
The profit will be shared based on amount and time the money was invested by person
For A :  = 147,000
For B :  = 189,000
For C :  = 126,000
Share of B will be 
4v( m n)
2v( m/ n)
m -
2
n = 
2
m + n m - n = ( ) ( ) 2 tan ? 2 sin ? = ( ) ( ) 4 tan ? sin ? 
tan ? + sin ? tan ? - sin ? ( ) ( ) tan ? -
2
sin ?
2
 - cos ? 
2
sin ?
2
sin ? =
2
sin ? - 1 =
2
( cos ? 
2
1
) 1 - cos ? = cos ? 
2
sin ?
2
(
2
)
tan ? ·
2
sin ? 
2
4 = 
 m n
4 tan ? · sin ? 
P ( B) = 3 P ( A) P ( ) B
4
3
4
1
3
1
3
2
16000 × 3 + ( ) 11000 × 9 ( )
12000 × 3 + ( ) 17000 × 9 ( )
21000 × 6 ( )
× 147+189+126
189
26400 = 10, 800
126
  
.
Page 3


SNAP 2014
Quantitative Aptitude
1. How many different letter arrangements can be made from the letter of the word EXTRA in such a way that the vowels are
always together?
A    48
B    60
C    40
D    30
A n s w e r : A
Explanation:
Considering two vowels as one unit ,total number of units = 4
Number of way of arranging these 4 units = 4! = 24 ways
2 vowels can be internally arranged in 2! ways 2 ways
Therefore total number of ways = 24*2 =48 ways.
     
2. The radius of the incircle in the given diagram will be
A    1.8 cm
B    2 cm
C    2.5 cm
D    3.6 cm
A n s w e r : B
Explanation:
AC= 
In-radius of right angled triangle = 
Inradius = 
3. If  and , then the value of  is equal to
A    
B    
= 
 A B + B C
2 2
=
 6 + 8 
2 2
10
2
a+ b- h ( )
= 2
6+8-10 ( )
2
tan ? + sin ? = m tan ? - sin ? = n m -
2
n
2
4 m n
2v( m n)
  
.
C    
D    
A n s w e r : C
Explanation:
Going by the options you have only mn or m/n
Case 1 : mn
mn=  =  = 
So 
4. If A and B are two mutually exclusive and exhaustive events with , then what is the value of ?
A    
B    
C    
D    
A n s w e r : B
Explanation:
Since P(B) and P(A) are mutually exclusive and exhaustive , thus, P(B)+P(A)=1
But we know that P(B)=3 P(A) , thus substituting in the above equation we get P(B)=3/4 and P(A)=1/4
Now they have asked P(B_) i.e. 1-P(B)=1-(3/4)=1/4 
    
5. A and B entered into a partnership investing `16,000 and `12,000 respectively. After 3 months, A withdrew `5000 while B
invested `5000 more. After 3 more months, C joins the business with a capital of `21,000. The share of B exceeds that of C, out
of a total profit of
`26,400 after one after by:
A    2400
B    3000
C    3600
D    4800
A n s w e r : C
Explanation:
The profit will be shared based on amount and time the money was invested by person
For A :  = 147,000
For B :  = 189,000
For C :  = 126,000
Share of B will be 
4v( m n)
2v( m/ n)
m -
2
n = 
2
m + n m - n = ( ) ( ) 2 tan ? 2 sin ? = ( ) ( ) 4 tan ? sin ? 
tan ? + sin ? tan ? - sin ? ( ) ( ) tan ? -
2
sin ?
2
 - cos ? 
2
sin ?
2
sin ? =
2
sin ? - 1 =
2
( cos ? 
2
1
) 1 - cos ? = cos ? 
2
sin ?
2
(
2
)
tan ? ·
2
sin ? 
2
4 = 
 m n
4 tan ? · sin ? 
P ( B) = 3 P ( A) P ( ) B
4
3
4
1
3
1
3
2
16000 × 3 + ( ) 11000 × 9 ( )
12000 × 3 + ( ) 17000 × 9 ( )
21000 × 6 ( )
× 147+189+126
189
26400 = 10, 800
126
  
.
Share of C will be 
Difference is 3,600
6. An aeroplane takes off 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time, it
has to increase its speed by 250 km/h from its usual speed. Find its usual speed.
A    1000 km/h
B    750 km/h
C    850 km/h
D    650 km/h
A n s w e r : B
Explanation:
Given t1 - t2 = 1/2 hours
So, 
On solving S=750kmph
7. What smallest number should be added to 4456 so that the sum is completely divisible by 6?
A    4
B    3
C    2
D    1
A n s w e r : C
Explanation:
For divisibility by 6, number should be divide by 3 and even.
Sum of number = 4 + 4 + 5 + 6 = 19
For divisible by 3, 2 number should be added so,
Number = 4456 + 2 = 4458 
    
8. If two tangents inclined at an angle  are drawn to a circle of radius 3 cm, then length of each tangent is equal to
A    
× 147+189+126
126
26400 = 7, 200
t i m e = 
s p e e d
d i s tan c e
t1 = S
1500
t2 = S+250
1500
 - S
1500
= S+250
1500
2
1
60
°
v2 c m 2
3
  
.
Page 4


SNAP 2014
Quantitative Aptitude
1. How many different letter arrangements can be made from the letter of the word EXTRA in such a way that the vowels are
always together?
A    48
B    60
C    40
D    30
A n s w e r : A
Explanation:
Considering two vowels as one unit ,total number of units = 4
Number of way of arranging these 4 units = 4! = 24 ways
2 vowels can be internally arranged in 2! ways 2 ways
Therefore total number of ways = 24*2 =48 ways.
     
2. The radius of the incircle in the given diagram will be
A    1.8 cm
B    2 cm
C    2.5 cm
D    3.6 cm
A n s w e r : B
Explanation:
AC= 
In-radius of right angled triangle = 
Inradius = 
3. If  and , then the value of  is equal to
A    
B    
= 
 A B + B C
2 2
=
 6 + 8 
2 2
10
2
a+ b- h ( )
= 2
6+8-10 ( )
2
tan ? + sin ? = m tan ? - sin ? = n m -
2
n
2
4 m n
2v( m n)
  
.
C    
D    
A n s w e r : C
Explanation:
Going by the options you have only mn or m/n
Case 1 : mn
mn=  =  = 
So 
4. If A and B are two mutually exclusive and exhaustive events with , then what is the value of ?
A    
B    
C    
D    
A n s w e r : B
Explanation:
Since P(B) and P(A) are mutually exclusive and exhaustive , thus, P(B)+P(A)=1
But we know that P(B)=3 P(A) , thus substituting in the above equation we get P(B)=3/4 and P(A)=1/4
Now they have asked P(B_) i.e. 1-P(B)=1-(3/4)=1/4 
    
5. A and B entered into a partnership investing `16,000 and `12,000 respectively. After 3 months, A withdrew `5000 while B
invested `5000 more. After 3 more months, C joins the business with a capital of `21,000. The share of B exceeds that of C, out
of a total profit of
`26,400 after one after by:
A    2400
B    3000
C    3600
D    4800
A n s w e r : C
Explanation:
The profit will be shared based on amount and time the money was invested by person
For A :  = 147,000
For B :  = 189,000
For C :  = 126,000
Share of B will be 
4v( m n)
2v( m/ n)
m -
2
n = 
2
m + n m - n = ( ) ( ) 2 tan ? 2 sin ? = ( ) ( ) 4 tan ? sin ? 
tan ? + sin ? tan ? - sin ? ( ) ( ) tan ? -
2
sin ?
2
 - cos ? 
2
sin ?
2
sin ? =
2
sin ? - 1 =
2
( cos ? 
2
1
) 1 - cos ? = cos ? 
2
sin ?
2
(
2
)
tan ? ·
2
sin ? 
2
4 = 
 m n
4 tan ? · sin ? 
P ( B) = 3 P ( A) P ( ) B
4
3
4
1
3
1
3
2
16000 × 3 + ( ) 11000 × 9 ( )
12000 × 3 + ( ) 17000 × 9 ( )
21000 × 6 ( )
× 147+189+126
189
26400 = 10, 800
126
  
.
Share of C will be 
Difference is 3,600
6. An aeroplane takes off 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time, it
has to increase its speed by 250 km/h from its usual speed. Find its usual speed.
A    1000 km/h
B    750 km/h
C    850 km/h
D    650 km/h
A n s w e r : B
Explanation:
Given t1 - t2 = 1/2 hours
So, 
On solving S=750kmph
7. What smallest number should be added to 4456 so that the sum is completely divisible by 6?
A    4
B    3
C    2
D    1
A n s w e r : C
Explanation:
For divisibility by 6, number should be divide by 3 and even.
Sum of number = 4 + 4 + 5 + 6 = 19
For divisible by 3, 2 number should be added so,
Number = 4456 + 2 = 4458 
    
8. If two tangents inclined at an angle  are drawn to a circle of radius 3 cm, then length of each tangent is equal to
A    
× 147+189+126
126
26400 = 7, 200
t i m e = 
s p e e d
d i s tan c e
t1 = S
1500
t2 = S+250
1500
 - S
1500
= S+250
1500
2
1
60
°
v2 c m 2
3
  
.
B    
C    
D    
A n s w e r : D
Explanation:
TPO is a right angled triangle .
So 
PT= 3
9. Find the value of 
A    5
B    3
C    4
D    2
A n s w e r : C
Explanation:
So given equation becomes   = 4
10. Find the value of 1% of 1% of 25% of 1000 is
A    0.025
B    0.0025
C    0.25
D    0.000025
A n s w e r : A
Explanation:
    
11. C is the mid-point of PQ, if P is (4, x), C is (y, -1) and Q is (-2, 4), then x and y respectively are
A    -6 and 1
B    -6 and 2
C    
6 and -1
D    
6 and -2
A n s w e r : A
6 c m
3 c m
3v3 c m
sin 30 = ( ) = T O
O P
 = T O
3
> T O = 6
P T =
2
T O -
2
O P =
2
36 - 9 = 27
 3
log 5 × 3
2
4
log 3 5
2
4
log a = b
n
(
m
) log a = n
m
b · n
m
log b ( )
log a ( )
· 2
4
· 2
4
·
log 2 ( )
log 3 ( )
log 3 ( )
log 2 ( )
· 100
1
· 100
1
· 100
25
1000 = 0.025
  
.
Page 5


SNAP 2014
Quantitative Aptitude
1. How many different letter arrangements can be made from the letter of the word EXTRA in such a way that the vowels are
always together?
A    48
B    60
C    40
D    30
A n s w e r : A
Explanation:
Considering two vowels as one unit ,total number of units = 4
Number of way of arranging these 4 units = 4! = 24 ways
2 vowels can be internally arranged in 2! ways 2 ways
Therefore total number of ways = 24*2 =48 ways.
     
2. The radius of the incircle in the given diagram will be
A    1.8 cm
B    2 cm
C    2.5 cm
D    3.6 cm
A n s w e r : B
Explanation:
AC= 
In-radius of right angled triangle = 
Inradius = 
3. If  and , then the value of  is equal to
A    
B    
= 
 A B + B C
2 2
=
 6 + 8 
2 2
10
2
a+ b- h ( )
= 2
6+8-10 ( )
2
tan ? + sin ? = m tan ? - sin ? = n m -
2
n
2
4 m n
2v( m n)
  
.
C    
D    
A n s w e r : C
Explanation:
Going by the options you have only mn or m/n
Case 1 : mn
mn=  =  = 
So 
4. If A and B are two mutually exclusive and exhaustive events with , then what is the value of ?
A    
B    
C    
D    
A n s w e r : B
Explanation:
Since P(B) and P(A) are mutually exclusive and exhaustive , thus, P(B)+P(A)=1
But we know that P(B)=3 P(A) , thus substituting in the above equation we get P(B)=3/4 and P(A)=1/4
Now they have asked P(B_) i.e. 1-P(B)=1-(3/4)=1/4 
    
5. A and B entered into a partnership investing `16,000 and `12,000 respectively. After 3 months, A withdrew `5000 while B
invested `5000 more. After 3 more months, C joins the business with a capital of `21,000. The share of B exceeds that of C, out
of a total profit of
`26,400 after one after by:
A    2400
B    3000
C    3600
D    4800
A n s w e r : C
Explanation:
The profit will be shared based on amount and time the money was invested by person
For A :  = 147,000
For B :  = 189,000
For C :  = 126,000
Share of B will be 
4v( m n)
2v( m/ n)
m -
2
n = 
2
m + n m - n = ( ) ( ) 2 tan ? 2 sin ? = ( ) ( ) 4 tan ? sin ? 
tan ? + sin ? tan ? - sin ? ( ) ( ) tan ? -
2
sin ?
2
 - cos ? 
2
sin ?
2
sin ? =
2
sin ? - 1 =
2
( cos ? 
2
1
) 1 - cos ? = cos ? 
2
sin ?
2
(
2
)
tan ? ·
2
sin ? 
2
4 = 
 m n
4 tan ? · sin ? 
P ( B) = 3 P ( A) P ( ) B
4
3
4
1
3
1
3
2
16000 × 3 + ( ) 11000 × 9 ( )
12000 × 3 + ( ) 17000 × 9 ( )
21000 × 6 ( )
× 147+189+126
189
26400 = 10, 800
126
  
.
Share of C will be 
Difference is 3,600
6. An aeroplane takes off 30 minutes later than the scheduled time and in order to reach its destination 1500 km away in time, it
has to increase its speed by 250 km/h from its usual speed. Find its usual speed.
A    1000 km/h
B    750 km/h
C    850 km/h
D    650 km/h
A n s w e r : B
Explanation:
Given t1 - t2 = 1/2 hours
So, 
On solving S=750kmph
7. What smallest number should be added to 4456 so that the sum is completely divisible by 6?
A    4
B    3
C    2
D    1
A n s w e r : C
Explanation:
For divisibility by 6, number should be divide by 3 and even.
Sum of number = 4 + 4 + 5 + 6 = 19
For divisible by 3, 2 number should be added so,
Number = 4456 + 2 = 4458 
    
8. If two tangents inclined at an angle  are drawn to a circle of radius 3 cm, then length of each tangent is equal to
A    
× 147+189+126
126
26400 = 7, 200
t i m e = 
s p e e d
d i s tan c e
t1 = S
1500
t2 = S+250
1500
 - S
1500
= S+250
1500
2
1
60
°
v2 c m 2
3
  
.
B    
C    
D    
A n s w e r : D
Explanation:
TPO is a right angled triangle .
So 
PT= 3
9. Find the value of 
A    5
B    3
C    4
D    2
A n s w e r : C
Explanation:
So given equation becomes   = 4
10. Find the value of 1% of 1% of 25% of 1000 is
A    0.025
B    0.0025
C    0.25
D    0.000025
A n s w e r : A
Explanation:
    
11. C is the mid-point of PQ, if P is (4, x), C is (y, -1) and Q is (-2, 4), then x and y respectively are
A    -6 and 1
B    -6 and 2
C    
6 and -1
D    
6 and -2
A n s w e r : A
6 c m
3 c m
3v3 c m
sin 30 = ( ) = T O
O P
 = T O
3
> T O = 6
P T =
2
T O -
2
O P =
2
36 - 9 = 27
 3
log 5 × 3
2
4
log 3 5
2
4
log a = b
n
(
m
) log a = n
m
b · n
m
log b ( )
log a ( )
· 2
4
· 2
4
·
log 2 ( )
log 3 ( )
log 3 ( )
log 2 ( )
· 100
1
· 100
1
· 100
25
1000 = 0.025
  
.
Explanation:
Midpoint of P(x1,y1) , Q(x2,y2) = C( )
So  
On solving x=-6 and y=1
12. In a given race the odds in favour of three horses A, B, C are 1:3; 1:4; 1:5 respectively. Assuming that dead heat is impossible
the probability that one of them wins is
A    
B    
C    
D    
A n s w e r : B
Explanation:
Odds in favour of A = 1:3, thus P(A wins) = 
Odds in favour of B= 1:4, thus P(A wins) = 
Odds in favour of C = 1:5, thus P(A wins) = 
Since deadheat is not possible only 1 will win.
P(A or B or C wins) = 
13. A and B rent a pasture for 10 months; A puts in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he
pays half as much again as A?
A    120
B    180
C    200
D    280
A n s w e r : D
Explanation:
It is given that B pays 1.5 times that of A
Let B put N number of cows for 3 month
    
14. A property dealer sells a house for ` 6,30,000 and in the bargain makes a profit of 5%. Had he sold it for ` 5,00,000, then what
percentage of loss or gain he would have made?
A    
 gain
B     loss
, 2
x1+ x2
2
y1+ y2
y = , -1 = 2
4-2
2
x+4
60
7
60
37
5
1
8
1
= 1+3
1
4
1
= 1+4
1
5
1
= 1+5
1
6
1
+ 4
1
+ 5
1
= 6
1
60
37
= 
M o n e y p a i d b y A
M o n e y p a i d b y B
 = 2
3
80× 7
3× N
N = 280
2 % 4
1
10%
1
  
.