Home Questions & Answer Aptitude Questions & Answers Analytical Reasoning Questions & Answers

Analytical Reasoning Questions & Answers (Compiled from UPSC, SSC ,PSC ,IBPS previous question papers)

Directions (next five questions) : In these questions, relationship between different elements is shown in the statement. These statements are followed by two conclusions.

Statements : R≤C A<M≥T≥Y;M≤S

Conclusions : I. S >R

II . Y ≤ S
AIf only conclusion I follows
BIf only conclusion II follows
CIf either conclusion I or II follows
DIf neither conclusion I nor II follows
EIf both conclusions I and II follow

Explanation:

Statements : R≤C A<M≥T≥Y

M≤S

R≤A<M≤S

S≥M≥T≥Y

Conclusions : I. S > R → True

II. Y≤S → True

Statements : D > W ≥ C≤X; C≥L; W<K

Conclusions : I. X > K

II L ≤ W
AIf only conclusion I follows
BIf only conclusion II follows

CIf either conclusion I or II follows
DIf neither conclusion I nor II follows
EIf both conclusions I and II follow
Explanation:

Statements : D > W ≥ C≤X

C≥L

W<K

K>W≥C≤X

W≥C≥L

Conclusions : I. X > K → True

II. L ≤W → True

Statements : K ≥ S=U≤R; L<U≤J

Conclusions : I. R > J

II . L= K
AIf only conclusion I follows
BIf only conclusion II follows
CIf either conclusion I or II follows
DIf neither conclusion I nor II follows

EIf both conclusions I and II follow
Explanation:

Statements : K ≥ S=U≤R

L<U≤J

R≥U≤J

K≥S=U>L

Conclusions : I. R>J → False

II. L = K → False

Directions (next five questions) : Study the following information to answer the given questions.

Eight friends P,Q,R,S,T,U,V and W are sitting around a square table in such a way that four of them sit at four corners while four sit in the middle of each of the four sides. The ones who sit at the four corners face the centre while those who sit in the middle of the sides face outside (i.e., opposite to the centre).

V sits second to the right of R. R sits in the middle of one of the sides of the table.
Only two people sit between V and Q. S is one of the immediate neighbours of Q.
T sits second to the left of S.
P sits second to the left of U.
V is not an immediate neighbor of U.

Who sits second to the left of W
AT
BU
CV
DS
EQ

Explanation:

Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group
AQ

What is the position of V with respect to Q
ASecond to the left
BThird to the left
CSecond to the right
DFifth to the right
EFifth to the right

Explanation:

Which of the following is true regarding P
ABoth T and R are immediate neighbours of P.
BOnly three people sit between P and S.
CP sits at middle of one of the sides.
DW sits second to the left of P.

ENone of the given options is true
Explanation:

How many people sit between R and T when counted from the right of R
ANone
BFour
COne
DThree

ETwo
Explanation:

Directions (next 5 questions) : In each question below are two/three statements followed by two conclusions numbered I and II. You have to take the two/three given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements : All crafts are projects.

Some projects are missions.

No mission is a guide.

Conclusions : I. No guide is a craft.

II Atleast some missions are crafts.
AIf only conclusion I follows
BIf only conclusion II follows
CIf either conclusion I or conclusion II follows
DIf neither conclusion I nor conclusion II follows

EIf both conclusion I and conclusion II follow
Explanation:

Statements : No price is a rate.

All rates are expenses.

Conclusions : I. No expense is a price.

II All prices being expenses is a possibility.
AIf only conclusion I follows
BIf only conclusion II follows
CIf either conclusion I or conclusion II follows
DIf neither conclusion I nor conclusion II follows
EIf both conclusion I and conclusion II follow

Explanation:

Statements : Some outputs are results.

All outputs are products.

All products are yields.

Conclusions: I. All outputs are yields.

II All results being yields is a possibility
AIf only conclusion I follows
BIf only conclusion II follows
CIf either conclusion I or conclusion II follows
DIf neither conclusion I nor conclusion II follows
EIf both conclusion I and conclusion II follow

Explanation:

Statements : Some outputs are results.

All outputs are products.

All products are yields.

Conclusions : I. No product is a result.

II All yields are products.
AIf only conclusion I follows
BIf only conclusion II follows
CIf either conclusion I or conclusion II follows
DIf neither conclusion I nor conclusion II follows

EIf both conclusion I and conclusion II follow
Explanation:

Statements : All crafts are projects.

Some projects are missions.

No mission is a guide.

Conclusions: I. Some projects are guides.

II No project is a guide.
AIf only conclusion I follows
BIf only conclusion II follows
CIf either conclusion I or conclusion II follows

DIf neither conclusion I nor conclusion II follows
EIf both conclusion I and conclusion II follow
Explanation:

Directions (next 2 questions) : These questions consist of a question and two statements numbered I and II given below. You have to decide whether the data given in the statements are sufficient to answer the questions. Read both the statements and choose the most appropriate option.

How far is point M from point S

I.Point S is 7m to the south of point M. Point T is 4m to the east of point S. Point P is 4m to the north of point T. Point Q is to the west of point P.

II.Point R is 4m to the west of point Q. Point S is 4m to the north of point Q. Point X is 4m to the north of point R. Point M is 11 m to the east of point X.
AIf the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
BIf the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
CIf the data either in statement I alone or in statement II alone are sufficient to answer the question.

DIf the data in both statement I and II together are not sufficient to answer the question.
EIf the data in both statements I and II together are necessary to answer the question.
Explanation:

From statement I.

From statement II.

Two mobile phones were purchased at the same price. One was sold at a profit of 20% and second was sold at a price which was INR 1520/- less than the price at which the first was sold. If the overall profit earned by selling both the mobile phones was 1%, what was the cost price of one mobile phone
AINR 6000
BINR 5200
CINR 4800
DINR 4000

EINR 5000
Explanation:

Let the cost price of one mobile = INR x

According to question,

x×120/100+(x×120/100-1520)=2x×101/100

6x/5+6x/5-1520=202/100x

12x/5-202x/100=1520

38/100x=1520

x=INR4000/-

A jar has 40 litre milk. From the jar, 8 litre of milk was taken out and replaced by an equal quantity of water. If 8 litre of the newly formed mixture is taken out of the jar. What is the final quantity of milk left in the jar
A32.5 litre
B30 litre
C25.6 litre

D24.2 litre
E24 litre
Explanation:

Final qunatity in the jar = 40×(1-8/40)²

=40×4/5×4/5

=25.6litre

Directions (next 6 questions) : In these questions, two questions numbered I and II are given. You have to solve both the equations and mark the appropriate option.

Give answer :

I. 6x²+11x+3=0

II 20y²+9y+1=0
AIf x >y
BIf x< y

CIf x≥y
DIf x≤y
EIf x=y or the relationship cannot be established.
Explanation:

I. 6x²+11x+3=0

6x²+2x+9x+3=0

2x(3x+1)+3(3x+1)=0

(3x+1)(2x+3)=0

x=1/3,3/2

II. 20y²+9y+1=0

20y²+5y+4y+1=0

5y(4y+1)+1(4y+1)=0

(4y+1)(5Y+1)=0

y=-1/4,-1/5

∴x< y

I. 30x²+17x+2=0

II 3y²+8y+4=0
AIf x >y

BIf x< y
CIf x≥y
DIf x≤y
EIf x=y or the relationship cannot be established. I.
Explanation:

I. 30x²+17x+2=0

30x²+5x+12x+2=0

5x(6x+1)+2(6x+1)=0

(5x+2)(6x+1)=0

x=-2/5,-1/6

II. 3y²+8y+4=0

3y²+6y+2y+4=0

3y(y+2)+2(y+2)=0

(y+2)(3y+2)=0

y=-2,-2/3

∴x >y

I. 4x²-13x+10=0

II 2y²-15y+22=0
AIf x >y
BIf x< y
CIf x≥y
DIf x≤y

EIf x=y or the relationship cannot be established.
Explanation:

I. 4x²-13x+10=0

4x²-8x-5x+10=0

4x(x-2)-5(x-2)=0

(x-2)(4x-5)=0

x=2,5/4

II. 2y²-15y+22=0

2y²-4y-11y+22=0

2y(y-2)-11(y-2)=0

(y-2)(2y-11)=0

y=2,11/2

∴x≤y

I. x²-10x+25=0

II y²-9y+20=0
AIf x >y
BIf x< y
CIf x≥y

DIf x≤y
EIf x=y or the relationship cannot be established.
Explanation:

I. x²-10x+25=0

x²-5x-5x+25=0

x(x-5)-5(x-5)=0

(x-5)²=0

x=5

II. y²-9y+20=0

y²-4y-5y+20=0

y(y-4)-5(y-4)=0

(y-4)(y-5)=0

y=4,5

∴x≥y

I. 2x²-9x+4=0

II y²-14y+40=0
AIf x >y
BIf x< y
CIf x≥y
DIf x≤y

EIf x=y or the relationship cannot be established.
Explanation:

I.

2x²-9x+4=0

2x²-8x-x+4=0

2x(x-4)-1(x-4)=0

(x-4)(2x-1)=0

x=4,1/2

II.

y²-14y+40=0

y²-10y-4y+40=0

y(y-10)-4(y-10)=0

(y-4)(y-10)=0

y=4,10

∴x≤y

The speed of a boat in still water is 16km/h and the speed of the current is 2 km/h. The distance travelled by the boat from point A to point B downstream is 12 km more than the distance covered by the same boat from point B to point C upstream in the same time. How much time will the boat take to travel from C to B downstream
A3 hour
B2 hour 30 min
C3 hour 20 min
D2 hour 20 min

E2 hour
Explanation:

Downstream speed of boat = (16+2) = 18 km/h

Upstream speed of boat = (16-2) = 14 km/h

Let BC = x km

and AB = (x+12)km

According to question,

x+12/18=x/14

14x+168 = 18x

4x=168

x= 42km

Time taken to travel 42 km downstream

= 42/18 = 7/3

= 2 hour 20 min

Directions (next five questions ) : In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement are sufficient to answer the question. Read both the statements and

Give answer :

How much money did Ms. Malini receive as retirement funds

Out of the total money received Ms. Shalini gave 25% to her husband and 10% to her daughter. Out of the remaining she invested 30% in Mutual funds, 60% in Pension fund scheme and remaining INR 2,60,000/-, she spent on miscellaneous items.

Out of the total money received Ms. Shalini invested 58.5% in various schemes, gave 35% of the total money received to her husband and daughter and remaining money she spent on miscellaneous items.
AIf the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

BIf the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
CIf the data either in statement I alone or in statement II alone are sufficient to answer the question.
DIf the data given in both statements I and II together are not sufficient to answer the question.
EIf the data in both statements I and II together are necessary to answer the question.
Explanation:

I.Let Ms. Malini received as retirement funds

= INR x

Amount given to her husband and daughter

x×35/100= (7/20)x

Remaining amount =x-7x/20

=13/20x

Amount invested from remaining amount

= 13x/20×90/100

=117/200x

Final remaining amount = 13x/20-(117/200)x

=130x-117x/200

=13x/200

Now, according to statement,

13x/200=260000

x=INR 40,00,000/-

In how many days can ‘B’ alone complete the work

A,B, and C together can complete the work in 4 ³²/₃₇ days.

A and B together can complete the work in 6 ²/₃ days, B and C together can complete the work together in 8 2/11 days and A and C together can complete the work in 7 ¹/₃ days.
AIf the data in both statements I and II together are necessary to answer the question.

BIf the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
CIf the data either in statement I alone or in statement II alone are sufficient to answer the question.
DIf the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
EIf the data given in both statements I and II together are not sufficient to answer the question.
Explanation:

I. (A+B+C)'S 1day's work = 37/180

II. (A+C)'s 1 day's work-(A+C)'s 1day's work

=37/180-3/22

(A+B+C-A-C)'s 1 day's work = 814-540/180×22

B's 1day's work = 274/180×22

B's 1da's work = 137/1980

∴B can complete the work = 1980/37

=53 19/37 days

Hence, the data in both statements I and II together are necessary to answer the question.

What is the curved surface area of the right circular cylinder

I.Area of the base of the cylinder is 616 cm²

II.Volume of the cylinder is 9240 cm²,
AIf the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
BIf the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
CIf the data either in statement I alone or in statement II alone are sufficient to answer the question.
DIf the data given in both statements I and II together are not sufficient to answer the question.
EIf the data in both statements I and II together are necessary to answer the question.

Explanation:

I. Given,

πr²= 616 cm²

22/7×r²=616

r²=616×7/22

r=14cm

II. Given, πr²h=9240

22/7×14×14×h = 9240

h = 420/28

h = 15 cm

Now, curved surface area of the cylinder = 2πrh

= 2×22/7×14×15 = 1320 cm²

Hence, the data in both statement I and II together are necessary to answer the question.

What was the initial quantity of mixture of juice and water

I.Juice and water were in the ratio 6:1 respectively in the mixture initially.

II.When 7 litre of mixture is taken out and 5 litre of water is added, the ratio between juice and water becomes 8:3 respectively
AIf the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
BIf the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
CIf the data either in statement I alone or in statement II alone are sufficient to answer the question.
DIf the data given in both statements I and II together are not sufficient to answer the question.
EIf the data in both statements I and II together are necessary to answer the question.

Explanation:

Let the initial quantity of the mixture = 7x litre

I. Quantity of juice =6x

Quantity of water = x

II. According to statement,

6x-7×6/7=8/3

x-7×1/7+5

18x-18=8x+32

10x=50

x=5 litre

∴Initial quantity of the mixture = 7x =7×5

=35 litre

Hence, the data in both the statement I and II together are necessary to answer the question.

What is the area of the circular field

I.Area of the largest square that can be inscribed in the given circular field is 392 cm²

II.Area of the smallest square in which the given circular field can be inscribed is 784 cm²
AIf the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
BIf the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
CIf the data either in statement I alone or in statement II alone are sufficient to answer the question.

DIf the data given in both statements I and II together are not sufficient to answer the question.
EIf the data in both statements I and II together are necessary to answer the question.
Explanation:

I.

Let the side of the square = acm

According to statement,

a²= 392 cm²

a= 19.79cm

Diagonal of the square = a√2

=19.79√2 cm

Radius of the circle = Diagonal/2

= 19.79×√2/2

=13.99=14 cm

∴ Are of the circle =πr²

=22/7×(14)²

=22×14×14/7

=616cm²

II.

Let the side of the square = acm

and the radius of the circle = a/2 cm

According to statement,

a²= 784 cm²

a=28cm

∴Area of the circle =π(a/2)²

=22/7×14×14= 616cm²

Hence, the data either in statement I alone or in statement II alone are sufficient to answer the question.

Directions (next six questions) : Refer to the table and answer the given questions.

Data regarding number of books sold in either hard bounds or paperback editions and also the categories of books sold in Fiction and Non-Fiction categories of books sold in Fiction and Non-Fiction category, by four different shops, in a particular month (January 2014)

Book Shops	Respective ratio between hard bounds sold and number of paperbacks sold	Number of paperbacks sold out of total number of books sold	Percentage of fictions (hardbound + paperback) sold out of total books sold
A	2;3	600	45
B	3:5	450	75
C	1:3	450	50
D	2:7	1400	60

[Please note : Total books sold = Number of hardbounds sold + Number of paperbacks sold]

Number of hardbound editions sold by shop B is what percent less than sold by shop D
A30%
B36.75%
C25%
D32.5%

E40.25%

Explanation:

Required percentage = 400-270×100

400

=130=32.5%

Required ratio = 300=5:3

180

Book shop	Total number of books	Number of paper back books	Number of hard bound books	Number of fiction books	Number of Non-fiction books
A	600×5/3=1000	600	1000-600 =400	1000×45/100=450	1000-450=550
B	450×8/5=720	450	720-450=270	720×75/100=540	720-540=180
C	450×4/3=600	450	600-450=150	600×50/100=300	600-300=300
D	1400×9/7=1800	1400	1800-1400=400	1800×60/100=1080	1800-1080=720

What is the average number of fictions sold by shops A and B
A475
B470
C495

D480
E490

Explanation:

Required average = 450+540=990=495

2 2

Required ratio = 300=5:3

180

Book shop	Total number of books	Number of paper back books	Number of hard bound books	Number of fiction books	Number of Non-fiction books
A	600×5/3=1000	600	1000-600 =400	1000×45/100=450	1000-450=550
B	450×8/5=720	450	720-450=270	720×75/100=540	720-540=180
C	450×4/3=600	450	600-450=150	600×50/100=300	600-300=300
D	1400×9/7=1800	1400	1800-1400=400	1800×60/100=1080	1800-1080=720

Total number of books sold by shop B is what percent more than sold by shop C
A50%
B25 1/3%
C15 1/3%
D30%
E20%

Explanation:

Required percentage = 720-600×100

600

=120/6=20%

Required ratio = 300=5:3

180

Book shop	Total number of books	Number of paper back books	Number of hard bound books	Number of fiction books	Number of Non-fiction books
A	600×5/3=1000	600	1000-600 =400	1000×45/100=450	1000-450=550
B	450×8/5=720	450	720-450=270	720×75/100=540	720-540=180
C	450×4/3=600	450	600-450=150	600×50/100=300	600-300=300
D	1400×9/7=1800	1400	1800-1400=400	1800×60/100=1080	1800-1080=720