Question – 1
1.
ColumnA  ColumnB 

(a^2ab+b^2)/(a^2+ab+b^2) when a = b  (a^2ab+b^2)/(a^2+ab+b^2) when a = b 
(Note: [a^2=a*a])

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:A
 Answer Explanation:
When a =b
(a^2ab+b^2)/(a^2+ab+b^2)
=[(b)^2(b)b+b^2]/[(b)^2+(b)b+b^2]
=(b^2+b^2+b^2)/(b^2b^2+b^2)
= 3b^2/b^2
= 3When a=b
(a^2ab+b^2)/(a^2+ab+b^2)
=[(b)^2(b)b+b^2]/[(b)^2+(b)b+b^2]
=(b^2b^2+b^2)/(b^2+b^2+b^2)
= b^2/3b^2
= 1/3
Option A is correct.
Question – 2
2. A task was to be completed in 20 days by a team. 12 members of the team were dropped and the remaining completed the work in 32 days.?
ColumnA  ColumnB 

Half of the number of members initially in the team  Number of members dropped from the team 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:A
 Answer Explanation:
Let there be x members in the team initially
x members complete the work in 20 days
Work done by 1 person in 1 day = 1/20x
Work done by 1 person in 32 days = 32/20x = 8/5xNumber of persons after 12 members were dropped = (x12)
Work done by (x12) persons in 32 days = work done by 1 person in 32
days*number of persons
1=(8/5x)*(x12)
5x=8x8*12
5x=8x96
8x5x=96
3x=96
x=32There were 32 persons initially
Half of 32=32/2=16
Number of members dropped from the team = 12
Option A is correct.
Question – 3
3. (a/b)^(x6) = (b/a)^(2x3)?
ColumnA  ColumnB 

x^2.  x 
(Note: [a^2=a*a])

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
(a/b)^(x6) = (a/b)^[(2x3)]
(a/b)^(x6) = (a/b)^(32x)
x6=32x
2x+x=3+6
x=9/3=3
x^2=3^2=9<3x^2
Question – 4
4. The average of x and y is 25. x is 200% of the average of 5, 22, 13 and y.?
ColumnA  ColumnB 

x  (x+y)/3 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:A
 Answer Explanation:
The average of the numbers is (5+22+13+y)/4
= (40+y)/4
200% of this average is x
x = 200/100*(40+y)/4
x = (40+y)/2
2x = 40+y
2xy = 40 …….(1)
Also the average of x and y is 25.
(x+y)/2=25
x+y = 25*2=50 ….(2)Add (1) and (2)
2xy+x+y=40+50=90
3x=90
x=30
Putting x=30 in x+y=50, we get
y=5030=20x=30
(x+y)/3=50/3=16.67x>(x+y)/3
Option A is correct.
Question – 5
5. x+1/y=1 and y+1/z=1.?
ColumnA  ColumnB 

z1/x  y1/z 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:C
 Answer Explanation:
x+1/y=1
x=11/y
=(y1)/y
1/x=y/(y1) …..(1)y+1/z=1
1/z=1y
z=1/(1y) …..(2)Substituting values from (1) and (2), we get
z+1/x = 1/(1y)+y/(y1)
= 1/(1y) – y/(1y)
= (1y)/(1y) = 1z+1/x=y+1/z
Option C is correct.
Question – 6
6. Consider a regular polygon.?
ColumnA  ColumnB 

Number of diagonals  Number of interior angles 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:D
 Answer Explanation:
PConsider a triangle:
Number of diagonals = 0, number of interior angles = 3Consider a quadrilateral:
Number of diagonals = 2, number of interior angles = 4Consider a pentagon:
Number of diagonals = 5, number of interior angles = 5
Hence, a relationship cannot be established.
Option D is correct.
Question – 7
7. A pipe can fill a tank with water in 6 hours. Due to a leak, the tank is filled in 7 hours.?
ColumnA  ColumnB 

Time taken to empty a full tank through the leak  Two days 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
Let the time taken to empty the tank due to the leak be x hours.
Tank filled in one hour = 1/6
Tank emptied in 1 hour = 1/x
1/7=1/61/x
6x=7x42
7x6x=42
x=42
Time taken to empty the tank through the leak = 42 hoursTwo days = 24*2=48 hours
Option B is correct
Question – 8
8. log[(x+y)/5] = 1/2 (logx+logy).?
ColumnA  ColumnB 

x/y  y/x 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:D
 Answer Explanation:
log[(x+y)/5] = 1/2 (logx+logy)
(x+y)/5 = sqrt(xy)
(x+y)=5*sqrt(xy)
Squaring both sides
(x+y)^2 = 5^2*xy
x^2+y^2+2xy = 25xy
x^2+y^2=25xy2xy = 23xy
Dividing both sides by xy
x/y+y/x=23We cannot determine which of x/y and y/x is greater.
Option D is correct.
Question – 9
9. A person covers half of his journey at 30 km/hr and the other half at 20 km/hr.?
ColumnA  ColumnB 

His average speed for the whole journey  His average speed for the first half of his journey 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
Let the distance be 2x km
Time = Distance/speed
Time for first half of journey = x/30
Time for second half of journey = x/20
Total time = x/30+x/20 = (20x+30x)/(20*30)
= 50x/(20*30)
= x/12Average speed = total distance/total time
= (x+x)/(x/12)
= 2x*12/x
= 24 km/hrAverage speed for the first half of his journey = 30 km/hr
Option B is correct.
Question – 10
10.
ColumnA  ColumnB 

The number of chords of a circle formed by joining the vertices of a cyclic pentagon.  The number of diameters of a circle formed by joining 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:A
 Answer Explanation:
Any two points of the pentagon can be joined to form a chord.
The number of points is given by C(5,2)
C(5,2) = 5!/(2!3!)
= 5*4/2 = 10
10 chords can be drawn by joining the vertices of a cyclic pentagon.Of these 10 chords, 5 are the sides of the pentagon and 5 are the diagonals of the pentagon. None of these diagonals passes through the centre of the circle. Hence, the number of diameters is zero.
Option A is true.
Question – 11
11. A stick of length 30cm is at a distance of 8 cm from the centre of a hemispherical urn.?
ColumnA  ColumnB 

Length of the longest stick that can be placed in the urn.  Diameter of the urn 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:C
 Answer Explanation:
The longest stick that can be placed shall be equal to the diameter of the urn.
Trivially option C is correct.
Question – 12
12. $20000 is lent out in two parts at 8% and 15% simple interest respectively. The net interest in a year is $2300.?
ColumnA  ColumnB 

First part  Second part 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:C
 Answer Explanation:
Let the amount lent at 8% be $x and the amount lent at 15% be $(20000x)
Simple interest, SI=PRT/100, where P, R and T are principal, rate and time respectively.
According to the conditions, we have
x*8*1/100+(20000x)*15*1/100=2300
8x+30000015x=230000
7x=70000
x=$10000
First part = $10000 and Second part = $20000$10000=$10000
Option C is correct.
Question – 13
13.
ColumnA  ColumnB 

The number of consecutive multiples of both 2 and 3 that lie between 200 and 350  The number of consecutive multiples of both 2 and 3 that 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:C
 Answer Explanation:
The numbers will be multiples of 6 since they are multiples of both 2 and 3.
The numbers lie between 200 and 350 and form an A.P. with common difference 6.
The first term of the A.P. will be 204 and the last term will be 348.
The nth term of an AP with first term ‘a’ and common difference ‘d’ is given by
Tn=a+(n1)d
348 = 204 +(n1)6
144 = (n1)6
n = 24+1=25
25 such numbers exist.The numbers will be multiples of 6 since they are multiples of both 2 and 3.
The numbers lie between 350 and 500 and form an A.P. with common difference 6.
The first term of the A.P. will be 354 and the last term will be 498.
The nth term of an AP with first term ‘a’ and common difference ‘d’ is given by
Tn=a+(n1)d
498 = 354 +(n1)6
144 = (n1)6
n = 24+1=25
25 such numbers exist.Option C is correct.
Question – 14
14. The difference between the areas of two concentric circles is 500*pi. The sum of the radii of the circles is equal to 50 cm.?
ColumnA  ColumnB 

Difference between the two radii  Radius of the smaller circle 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:B
 Answer Explanation:
Let R and r be the two radii such that R>r
Area of a circle = pi*r^2, where r is the radius
pi*R^2pi*r^2=500*pi
R^2r^2=500
and R+r=50 cm
(R^2r^2) = (R+r)(Rr) = 500
(50)(Rr)=500
Rr=500/50 = 10 cm
The difference between the radii is 10 cm.R+r=50 and Rr=10
Subtracting one relation from the other, we get
R+rR+r=5010=40
2r=40
r=20
Radius of the smaller circle = 20cmOption B is correct.
[pi=22/7]
[r^2=r*r]
Question – 15
15. In a school function, the girls have to raise one hand and the boys have to raise both their hands holding colored pieces of cloth in each. The boys hold three pieces, one green and two red and the girls hold one green piece each.The number of green cloth pieces is 120 and the number of red cloth pieces is 40.?
ColumnA  ColumnB 

Half the number of girls among the group  Twice the number of boys in the group 

A. If the quantity on the left is greater

B. If the quantity on the right is greater

C. If both are equal

D. If the relationship cannot be determined without further information
 Answer:A
 Answer Explanation:
Let the number of boys be x and the number of girls be y.
According to the conditions, we have
x+y = 120 …(1)
2x=40 …(2)
x = 40/2=20
y = 120 – x
= 120 – 20 = 100
Number of girls = 100
Number of boys = 20
Half the number of girls = 100/2=50
Twice the number of boys = 20*2=40
Option A is correct.