## ARITHMETIC REASONING

### Introduction

Q. In a tournament each of six players will play every other player exactly once. How many matches will be played during the tournament

A. Player 1=5, player 2=4, player 3=3; player 4=2; player 5=1; player 6=0; 5+4+3+2+1+0=15

Q. A, B, C and D play a game of cards. A says to B, if I give you 8 cards, you will have as many as C has and I shall have 3 less than what C has. Also, if I take 6 cards from C, I shall have twice as many as D has.” If B and D together have 50 cards, how many cards has A got

A. Solving below equations we get A=40. B+8 = C …(i) A-8=C-3 i.e. C = A-5 …(ii) A+6=2*D …..(iii) B+D=50 i.e. D = 50 – B ….(iv) Substituting (ii) in (i) and (iv) in (iii) we get A+2B=94 and A-B=13

Q. A group of 1200 persons consisting of captains and soldiers is traveling in a train. For every 15 soldiers there is one captain. The number of captains in the group is

A. So captains to soldiers is 1:15 so in 1200 soldiers we have 1200/15=80.

Q. Aruna cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight . If she has seven pieces of the cake in all with her, how heavy was the original cake

A. She has 7 pieces where 6 pieces are making one half of the weight of the cake since she cut the half of cake into 6 pieces. 6 * 20 = 120. This is half the

weight of cake so full weight of cake is 2 * 120 = 240 gm.

Each of these questions is followed by two statements, I and II. Mark the answer as

(a) if the question can be answered with the help of statement I alone.

(b) if the question can be answered with the help of statement II alone.

(c) if both statement I and statement II are needed to answer the question.

(d) if the question cannot be answered even with the help of both the statements.

Q.If x, y and z are real numbers, is z – x even or odd?

I. xyz is odd.

II. xy + yz + zx is even.

1.a

2.b

3.c

4.d

Ans.1

Q.What is the value of x, if x and y are consecutive positive even integers?

I. (x – y)2 = 4

II. (x + y)2 < 100

1.a

2.b

3.c

4.d

Ans.d

Q.What is the profit percentage?

I. The cost price is 80% of the selling price.

II. The profit is Rs.50.

1.a

2.b

3.c

4.d

Ans.a

Q.What is the area of the triangle?

I. Two sides are 41 cm each.

II. The altitude to the third side is 9 cm long.

1.a

2.b

3.c

4.d

Ans.c

Each question is followed by two statements, I and II. Mark the answer as

(a) if the question cannot be answered even with the help of both the statements taken together.

(b) if the question can be answered by any one of the two statements.

(c) if each statement alone is sufficient to answer the question, but not the other one (E.g. statement I alone is required to answer the question, but not statement II and vice versa).

(d) if both statements I and II together are needed to answer the question.

Q.A tractor travelled a distance 5 m. What is the radius of the rear wheel?

I. The front wheel rotates ‘N’ times more than the rear wheel over this distance.

II. The circumference of the rear wheel is ‘t’ times that of the front wheel.

1.a

2.b

3.c

4.d

Ans.a

Q.What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together? (The containers are of equal volume.)

I. The ratio of liquid A to liquid B in the first and second vessel is 3 : 5, 2 : 3 respectively.

II. The ratio of liquid A to liquid B in vessel 3 is 4 : 3.

a

b

c

d

Ans.a

Q.If a, b and c are integers, is (a – b + c) > (a + b – c)?

I. b is negative.

II. c is positive.

1.a

2.b

3.c

4.d

Ans.d

Q.If α and β are the roots of the equation ax2+bx+c=0 then what is the value of α2 + β2

I.α + β = -b/a

II.2*α β = c/a

1.a

2.b

3.c

4.d

Ans.d> Q.A tractor travelled a distance 5 m. What is the radius of the rear wheel?

I. The front wheel rotates ‘N’ times more than the rear wheel over this distance.

II. The circumference of the rear wheel is ‘t’ times that of the front wheel.

1.a

2.b

3.c

4.d

Ans.a

Q.What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together? (The containers are of equal volume.)

I. The ratio of liquid A to liquid B in the first and second vessel is 3 : 5, 2 : 3 respectively.

II. The ratio of liquid A to liquid B in vessel 3 is 4 : 3.

1.a

2.b

3.c

4.d

Ans.a

Q.If a, b and c are integers, is (a – b + c) > (a + b – c)?

I. b is negative.

II. c is positive.

1.a

2.b

3.c

4.d

Ans.d

Q.If α and β are the roots of the equation ax2+bx+c=0 then what is the value of α2 + β2

I.α + β = -b/a

II.2*α β = c/a

1.a

2.b

3.c

4.d

Ans.d

Q.A tractor travelled a distance 5 m. What is the radius of the rear wheel?

I. The front wheel rotates ‘N’ times more than the rear wheel over this distance.

II. The circumference of the rear wheel is ‘t’ times that of the front wheel.

1.a

2.b

3.c

4.d

Ans.a

Q.What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together? (The containers are of equal volume.)

I. The ratio of liquid A to liquid B in the first and second vessel is 3 : 5, 2 : 3 respectively.

II. The ratio of liquid A to liquid B in vessel 3 is 4 : 3.

1.a

2.b

3.c

4.d

Ans.a

Q.If a, b and c are integers, is (a – b + c) > (a + b – c)?

I. b is negative.

II. c is positive.

a Ans.d

Q.If α and β are the roots of the equation ax2+bx+c=0 then what is the value of α2 + β2

I.α + β = -b/a

II.2*α β = c/a

1.a

2.b

3.c

4.d

Ans.d

Q.A tractor travelled a distance 5 m. What is the radius of the rear wheel?

I. The front wheel rotates ‘N’ times more than the rear wheel over this distance.

II. The circumference of the rear wheel is ‘t’ times that of the front wheel.

1.a

2.b

3.c

Ans.a

Q.What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together? (The containers are of equal volume.)

I. The ratio of liquid A to liquid B in the first and second vessel is 3 : 5, 2 : 3 respectively.

II. The ratio of liquid A to liquid B in vessel 3 is 4 : 3.

1.a

2.b

3.c

4.d

Ans.a

Q.If a, b and c are integers, is (a – b + c) > (a + b – c)?

I. b is negative.

II. c is positive.

1.a

2.b

3.c

4.d

Ans.d

Q.If α and β are the roots of the equation ax2+bx+c=0 then what is the value of α2 + β2

I.α + β = -b/a

II.2*α β = c/a

1.a

2.b

3.c

4.d

Ans.d

### Read and choose the correct alternative

Each question is followed by two statements, I and II. Answer the questions based on the statements and mark the answer as

(a) if the question can be answered with the help of any one statement alone but not by the other statement.

(b) if the question can be answered with the help of either of the statements taken individually.

(c) if the question can be answered with the help of both statements together.

(d) if the question cannot be answered even with the help of both statements together

Q. Find the length of AB if ∠ YBC = ∠ XOY = ∠ XAC = 90°

Q. Find the length of AB if ∠ YBC = ∠ XOY = ∠ XAC = 90°

I. Radius of the arc is given.

II. OA = 5>I. Radius of the arc is given.

II. OA = 5

1.A

2.B

3.C

4.D

Ans.D

Q. Is n odd?

I. n is divisible by 3, 5, 7 and 9.

II. 0 < n < 400

1.A

2.B

3.C

4.D

Ans . C

Q. Radha and Rani appeared in an examination. What was the total number of questions?

I. Radha and Rani together solved 20% of the paper.

II. Radha alone solved 3/5 of the paper solved by Rani

1.A

2.B

3.C

4.D

Ans . D

Q. What is the price of tea?

I. Price of coffee is Rs. 5 more than that of tea.

II. Price of coffee is Rs. 5 less than the price of a cold drink which cost three times the price of tea.

1.A

2.B

3.C

4.D

Ans.C

Q. In a group of 150 students, find the number of girls.

I. Each girl was given 50 paise, while each boy was given 25 paise to purchase goods totalling Rs. 49.

II. Girls and boys were given 30 paise each to buy goods totalling Rs. 45.

1.A

2.B

3.C

4.D

Ans.A

Q. There are four racks numbered 1, 2, 3, 4 and four books numbered 1, 2, 3, 4. If an even rack has to contain an odd-numbered book and an odd rack contains an even-numbered book, then what is the position of book 4?

I. Second book has been put in third rack.

II. Third book has been put in second rack.

1.A

2.B

3.C

4.D

Ans . A

Each question is followed by two statements, I and II. Answer the questions based on the statements and mark the answer as

(a) if the question can be answered with the help of any one statement alone but not by the other statement.

(b) if the question can be answered with the help of either of the statements taken individually.

(c) if the question can be answered with the help of both statements together.

(d) if the question cannot be answered even with the help of both statements together

Q. Find the length of AB if ∠ YBC = ∠ XOY = ∠ XAC = 90°

Q. Find the length of AB if ∠ YBC = ∠ XOY = ∠ XAC = 90°

I. Radius of the arc is given.

II. OA = 5>I. Radius of the arc is given.

II. OA = 5

1.A

2.B

3.C

4.D

Ans.D

Q. Is n odd?

I. n is divisible by 3, 5, 7 and 9.

II. 0 < n < 400

1.A

2.B

3.C

4.D

Ans . C

Q. Radha and Rani appeared in an examination. What was the total number of questions?

I. Radha and Rani together solved 20% of the paper.

II. Radha alone solved 3/5 of the paper solved by Rani

1.A

2.B

3.C

4.D

Ans . D

Q. What is the price of tea?

I. Price of coffee is Rs. 5 more than that of tea.

II. Price of coffee is Rs. 5 less than the price of a cold drink which cost three times the price of tea.

1.A

2.B

3.C

4.D

Ans.C

Q. In a group of 150 students, find the number of girls.

I. Each girl was given 50 paise, while each boy was given 25 paise to purchase goods totalling Rs. 49.

II. Girls and boys were given 30 paise each to buy goods totalling Rs. 45.

1.A

2.B

3.C

4.D

Ans.A

Q. There are four racks numbered 1, 2, 3, 4 and four books numbered 1, 2, 3, 4. If an even rack has to contain an odd-numbered book and an odd rack contains an even-numbered book, then what is the position of book 4?

I. Second book has been put in third rack.

II. Third book has been put in second rack.

1.A

2.B

3.C

4.D

Ans . A

### Each question is followed by two statements I and II. Mark:

(a) if the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.

(b) if the question can be answered by using either statement alone.

(c) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

(d) if the question cannot be answered even by using both the statements together

Q. The average weight of students in a class is 50 kg. What is the number of students in the class?

I. The heaviest and the lightest members of the class weigh 60 kg and 40 kg respectively.

II. Exclusion of the heaviest and the lightest members from the class does not change the average weight of the students

1.A

2.B

3.C

4.D

Ans . D

Q. A small storage tank is spherical in shape. What is the storage volume of the tank?

I. The wall thickness of the tank is 1 cm.

II. When an empty spherical tank is immersed in a large tank filled with water, 20 l of water overflow from the large tank.

1.A

2.B

3.C

4.D

Ans . C

Q. Mr X starts walking northwards along the boundary of a field from point A on the boundary, and after walking for 150 m reaches B, and then walks westwards, again along the boundary, for another 100 m when he reaches C. What is the maximum distance between any pair of points on the boundary of the field?

I. The field is rectangular in shape.

II. The field is a polygon, with C as one of its vertices and A as the mid-point of a side.

1.A

2.B

3.C

4.D

Ans . C

Q. A line graph on a graph sheet shows the revenue for each year from 1990 through 1998 by points and joins the successive points by straight-line segments. The point for revenue of 1990 is labelled A, that for 1991 as B, and that for 1992 as C. What is the ratio of growth in revenue between 1991-92 and 1990-91?

I. The angle between AB and X-axis when measured with a protractor is 40°, and the angle between CB and X-axis is 80°.

II. The scale of Y-axis is 1 cm = Rs. 100

1.A

2.B

3.C

4.D

Ans . A

Q. There is a circle with centre C at the origin and radius r cm. Two tangents are drawn from an external point D at a distance d cm from the centre. What are the angles between each tangent and the X-axis?

I. The coordinates of D are given.

II. The X-axis bisects one of the tangents.

1.A

2.B

3.C

4.D

Ans . B

Q. Find a pair of real numbers x and y that satisfy the following two equations simultaneously. It is known that the values of a, b, c, d, e and f are non-zero.

ax + by = c

dx + ey = f

I. a = kd and b = ke, c = kf, k ≠ 0

II. a = b = 1, d = e = 2, f ≠ 2c

1.A

2.B

3.C

4.D

Ans . D

Q. Three professors A, B and C are separately given three sets of numbers to add. They were expected to find the answers to 1 + 1, 1 + 1 + 2, and 1 + 1 respectively. Their respective answers were 3, 3 and 2. How many of the professors are mathematicians?

I. A mathematician can never add two numbers correctly, but can always add three numbers correctly.

II. When a mathematician makes a mistake in a sum, the error is +1 or –1.

1.A

2.B

3.C

4.D

Ans . D

Q. How many students among A, B, C and D have passed the examination?

I. The following is a true statement: A and B passed the examination.

II. The following is a false statement: At least one among C and D has passed the examination

1.A

2.B

3.C

4.D

Ans . C

Q. What is the distance x between two cities A and B in integral number of kilometres?

I. x satisfies the equation log2x√x

II. x ≤ 10 km

1.A

2.B

3.C

4.D

Ans . C

Q. Mr Mendel grew 100 flowering plants from black seeds and white seeds, each seed giving rise to one plant. A plant gives flowers of only one colour. From a black seed comes a plant giving red or blue flowers. From a white seed comes a plant giving red or white flowers. How many black seeds were used by Mr Mendel?

I. The number of plants with white flowers was 10.

II. The number of plants with red flowers was 70.

1.A

2.B

3.C

4.D

Ans . D