Arithmetic Reasoning Practice Test Questions - Verbal Reasoning -- Free Practice

Question 1

A group of friends planned to spend Rs. 240 on food for a trip. Five of them did not turn up. As a result, the remaining friends had to pay Rs. 4 each extra. How many friends went on the trip?

A

10✓✗

B

12✓✗

C

15✓✗

D

20✓✗

Explanation

Let n friends go on the trip, so n + 5 had planned to go.
240/n - 240/(n + 5) = 4
240 × 5 = 4n(n + 5), so n² + 5n - 300 = 0, which gives (n - 15)(n + 20) = 0 and n = 15.
Check: the planned share is 240/20 = Rs. 12 and the actual share is 240/15 = Rs. 16, a difference of Rs. 4.

Question 2

In a college, 14 of the girls and 13 of the boys joined the debate club. If there are 60 girls and 90 boys, what fraction of all the students joined the club?

A

712✓✗

B

310✓✗

C

27✓✗

D

Data inadequate✓✗

Explanation

Girls who joined = 14 × 60 = 15.
Boys who joined = 13 × 90 = 30.
Total students = 60 + 90 = 150, and 15 + 30 = 45 of them joined.
Required fraction = 45150 = 310.

Question 3

Two notebooks and three pens cost Rs. 61, but three notebooks and two pens cost Rs. 64. What are the prices of a notebook and a pen?

A

Rs. 16, Rs. 9✓✗

B

Rs. 11, Rs. 14✓✗

C

Rs. 12, Rs. 13✓✗

D

Rs. 14, Rs. 11✓✗

Explanation

Let a notebook cost Rs. x and a pen cost Rs. y.
2x + 3y = 61 ...(i)
3x + 2y = 64 ...(ii)
Multiplying (i) by 3 and (ii) by 2 and subtracting: 9y - 4y = 183 - 128, so 5y = 55 and y = 11.
Putting y = 11 in (i): 2x = 61 - 33 = 28, so x = 14.
A notebook costs Rs. 14 and a pen costs Rs. 11.

Question 4

The total of the ages of Ravi, Sunil and Tarun is 90 years. What will be the total of their ages four years from now?

A

98 years✓✗

B

94 years✓✗

C

102 years✓✗

D

106 years✓✗

Explanation

Each of the 3 people will be 4 years older, so the total increases by 4 × 3 = 12 years.
Required sum = 90 + 12 = 102 years.

Question 5

P, Q, R, S and T play a game of marbles. P says to Q, "If you give me four marbles, you will have as many as T has, and if I give you four marbles, you will have as many as S has." P and Q together have 12 marbles more than S and T together. If R has 3 fewer marbles than Q and the total number of marbles is 119, how many marbles does Q have?

A

20✓✗

B

22✓✗

C

24✓✗

D

26✓✗

Explanation

The clues give:
Q - 4 = T ...(i)
Q + 4 = S ...(ii)
P + Q = S + T + 12 ...(iii)
R = Q - 3 ...(iv)
From (i) and (ii), S + T = 2Q. From (iii), P = Q + 12.
Total: (Q + 12) + Q + (Q - 3) + 2Q = 119, so 5Q + 9 = 119, 5Q = 110 and Q = 22.

Question 6

The number of boys in a class is four times the number of girls. Which one of the following numbers cannot be the total number of students in the class?

A

72✓✗

B

60✓✗

C

45✓✗

D

85✓✗

Explanation

Let the number of girls be x, so the number of boys is 4x.
Total = x + 4x = 5x, so the total must be a multiple of 5.
45, 60 and 85 are multiples of 5, but 72 is not. So 72 cannot be the total.

Question 7

In a hostel, the number of girls is twice the number of boys. Which one of the following cannot be the total number of students in the hostel?

A

48✓✗

B

36✓✗

C

52✓✗

D

60✓✗

Explanation

Let the number of boys be x, so the number of girls is 2x.
Total = x + 2x = 3x, so the total must be a multiple of 3.
36, 48 and 60 are multiples of 3, but 52 is not. So 52 cannot be the total.

Question 8

A farmer had 25 hens. All but 7 were sold. How many hens does he have left?

A

Nil✓✗

B

25✓✗

C

18✓✗

D

7✓✗

Explanation

"All but 7 were sold" means that every hen except 7 was sold. So 7 hens are left.

Question 9

A boy had 12 pencils. He lost all but 5 of them. How many pencils did he lose?

A

5✓✗

B

7✓✗

C

12✓✗

D

17✓✗

Explanation

"Lost all but 5" means that he kept 5 pencils and lost the rest.
Pencils lost = 12 − 5 = 7.

Question 10

In a family, the mother took 13 of a pizza, and her share was 4 times the share of each of the other members. How many members are there in the family?

A

9✓✗

B

8✓✗

C

7✓✗

D

12✓✗

Explanation

Mother's share = 13, so each of the other members got 13 ÷ 4 = 112.
The rest of the pizza = 1 − 13 = 23 = 812, which is shared by 8 other members.
Total members = 8 + 1 = 9.

Question 11

A grandfather took 25 of a box of sweets, which was twice the share of each of the other family members. How many members are there in the family?

A

3✓✗

B

5✓✗

C

4✓✗

D

6✓✗

Explanation

Grandfather's share = 25, so each of the others got 25 ÷ 2 = 15.
The rest of the box = 1 − 25 = 35, which is shared by 3 other members.
Total members = 3 + 1 = 4.

Question 12

In three jars A, B and C, 120 marbles are placed. Jar C has twice as many marbles as jars A and B combined, and jar B has three times as many marbles as jar A. How many marbles are there in jar C?

A

30✓✗

B

60✓✗

C

90✓✗

D

80✓✗

Explanation

A + B + C = 120 and C = 2(A + B).
So 3(A + B) = 120, which gives A + B = 40 and C = 80.
(Also B = 3A, so A = 10 and B = 30.)

Question 13

A bookcase holds 150 books on three shelves. The middle and bottom shelves together hold four times as many books as the top shelf, and the bottom shelf holds twice as many books as the middle shelf. How many books are there on the middle shelf?

A

30✓✗

B

40✓✗

C

60✓✗

D

None of these✓✗

Explanation

Let the top shelf hold T books, so the middle and bottom together hold 4T.
T + 4T = 150, so T = 30, and the middle and bottom shelves hold 120 books.
Bottom = 2 × middle, so 3 × middle = 120 and middle = 40.

Question 14

Four batsmen P, Q, R and S scored an average of 32 runs in a match. Q scored 6 more than S; P scored as many as Q and S combined; and R scored 4 fewer than P. How many runs did S score?

A

19✓✗

B

25✓✗

C

21✓✗

D

17✓✗

Explanation

Total runs = 32 × 4 = 128.
Let S score x. Then Q = x + 6, P = Q + S = 2x + 6, and R = P − 4 = 2x + 2.
x + (x + 6) + (2x + 6) + (2x + 2) = 128, so 6x + 14 = 128 and x = 19.
So S scored 19 runs.

Question 15

Five students A, B, C, D and E scored an average of 60 marks in a test. B scored 10 more than E; A scored 5 less than B; and C and D scored 129 marks between them. How many marks did E score?

A

48✓✗

B

57✓✗

C

52✓✗

D

62✓✗

Explanation

Total marks = 60 × 5 = 300, so A + B + E = 300 − 129 = 171.
Let E score x. Then B = x + 10 and A = B − 5 = x + 5.
(x + 5) + (x + 10) + x = 171, so 3x + 15 = 171 and x = 52.
So E scored 52 marks.

Question 16

Three friends shared a taxi fare. Ravi paid 34 as much as Sam, and Sam paid 23 as much as Tom. What fraction of the fare did Sam pay?

A

613✓✗

B

29✓✗

C

313✓✗

D

413✓✗

Explanation

Let Tom pay Rs. 6x. Then Sam pays 23 × 6x = 4x, and Ravi pays 34 × 4x = 3x.
Total fare = 6x + 4x + 3x = 13x.
Sam's fraction = 4x13x = 413.

Question 17

Three sisters bought a gift together. Meera paid half as much as Nina, and Nina paid 45 as much as Lata. What fraction of the cost did Lata pay?

A

411✓✗

B

511✓✗

C

211✓✗

D

12✓✗

Explanation

Let Lata pay Rs. 5x. Then Nina pays 45 × 5x = 4x, and Meera pays half of 4x = 2x.
Total cost = 5x + 4x + 2x = 11x.
Lata's fraction = 5x11x = 511.

Question 18

In a club, 30% of the members have exactly two phones each, 50% of the remaining members have three phones each, and the rest have only one phone each. Which of the following statements is definitely true?

A

35% of the members have only one phone each.✓✗

B

40% of the members have three phones each.✓✗

C

70% of the members have at least two phones.✓✗

D

30% of the members have three phones each.✓✗

E

None of these✓✗

Explanation

Let there be 100 members. Then 30 have two phones.
Members with three phones = 50% of (100 − 30) = 35.
Members with only one phone = 100 − (30 + 35) = 35.
So 35% of the members have only one phone each. (At least two phones: 30 + 35 = 65%, not 70%.)

Question 19

In an office, 25% of the employees travel by car, 60% of the remaining employees travel by bus, and the rest walk. Which of the following statements is definitely true?

A

60% of the employees travel by bus.✓✗

B

35% of the employees walk.✓✗

C

45% of the employees travel by bus.✓✗

D

50% of the employees travel by car or walk.✓✗

E

None of these✓✗

Explanation

Let there be 100 employees. Then 25 travel by car.
By bus = 60% of (100 − 25) = 45.
Walk = 100 − (25 + 45) = 30.
So 45% of the employees travel by bus. (Car or walk: 25 + 30 = 55%, not 50%.)

Question 20

When Neha was born, her father was 30 years older than her brother, and her mother was 26 years older than her sister. If Neha's brother is 4 years older than Neha and her mother is 5 years younger than her father, how old was Neha's sister when Neha was born?

A

7 years✓✗

B

4 years✓✗

C

5 years✓✗

D

3 years✓✗

Explanation

When Neha was born: brother = 4 years, father = 4 + 30 = 34 years, mother = 34 − 5 = 29 years, and sister = 29 − 26 = 3 years.

Question 21

When Arjun was born, his mother was 28 years older than his sister, and his father was 33 years older than his brother. If Arjun's sister is 5 years older than Arjun and his father is 4 years older than his mother, how old was Arjun's brother when Arjun was born?

A

2 years✓✗

B

4 years✓✗

C

6 years✓✗

D

8 years✓✗

Explanation

When Arjun was born: sister = 5 years, mother = 5 + 28 = 33 years, father = 33 + 4 = 37 years, and brother = 37 − 33 = 4 years.

Question 22

A certain number of camels and an equal number of men are travelling together. One-fourth of the men are walking and leading their camels, while the rest are riding. If the number of legs touching the ground is 90, how many camels are there?

A

20✓✗

B

18✓✗

C

22✓✗

D

24✓✗

Explanation

Let the number of camels = number of men = x.
All 4x camel legs touch the ground. Only the walking men, x4 of them, have their 2 legs on the ground: 2 × x4 = x2.
4x + x2 = 90, so 9x2 = 90 and x = 20.

Question 23

On a farm, the number of cows is twice the number of farmers. If the total number of legs of the cows and the farmers is 100, how many cows are there?

A

10✓✗

B

25✓✗

C

20✓✗

D

30✓✗

Explanation

Let the number of farmers be x, so there are 2x cows.
Legs = 4 × 2x + 2 × x = 10x = 100, so x = 10.
Number of cows = 2 × 10 = 20.

Question 24

Kiran's sister is 4 years older than him. Their father was 30 years old when their brother was born, and their mother was 27 years old when Kiran was born. If the brother was 3 years old when the sister was born, what were the ages of the father and the mother when the sister was born?

A

30 years, 23 years✓✗

B

30 years, 27 years✓✗

C

33 years, 27 years✓✗

D

33 years, 23 years✓✗

Explanation

The sister was born 3 years after the brother, so the father was 30 + 3 = 33 years old then.
Kiran was born 4 years after the sister, and the mother was 27 then, so she was 27 − 4 = 23 years old when the sister was born.

Question 25

Meena's brother is 5 years older than her. Their father was 27 years old when their elder sister was born, and their mother was 25 years old when Meena was born. If the sister was 6 years old when the brother was born, what were the ages of the father and the mother when the brother was born?

A

33 years, 25 years✓✗

B

33 years, 20 years✓✗

C

31 years, 20 years✓✗

D

27 years, 20 years✓✗

Explanation

The brother was born 6 years after the sister, so the father was 27 + 6 = 33 years old then.
Meena was born 5 years after the brother, and the mother was 25 then, so she was 25 − 5 = 20 years old when the brother was born.

Question 26

The sum of three consecutive even numbers is 150. What is the second number?

A

50✓✗

B

48✓✗

C

52✓✗

D

54✓✗

Explanation

Let the numbers be x, x + 2 and x + 4.
3x + 6 = 150, so x = 48.
The second number = 48 + 2 = 50.

Question 27

The sum of four consecutive even numbers is 100. What is the smallest of them?

A

20✓✗

B

24✓✗

C

22✓✗

D

26✓✗

Explanation

Let the numbers be x, x + 2, x + 4 and x + 6.
4x + 12 = 100, so 4x = 88 and x = 22.

Question 28

A car travels at a constant speed of 72 km per hour. How long will it take to cover 288 km?

A

3 hours✓✗

B

6 hours✓✗

C

5 hours✓✗

D

4 hours✓✗

Explanation

Time = distance ÷ speed = 288 ÷ 72 = 4 hours.

Question 29

A cyclist rides at 15 km per hour for 2.5 hours. How far does she travel?

A

30 km✓✗

B

37.5 km✓✗

C

40 km✓✗

D

35 km✓✗

Explanation

Distance = speed × time = 15 × 2.5 = 37.5 km.

Question 30

A recipe needs 3 cups of flour to make 18 pancakes. How many cups of flour are needed to make 30 pancakes?

A

5 cups✓✗

B

4 cups✓✗

C

6 cups✓✗

D

7 cups✓✗

Explanation

Flour per pancake = 318 = 16 cup.
For 30 pancakes: 30 × 16 = 5 cups.

Question 31

A cook uses 4 kg of rice to serve 30 people. How much rice is needed to serve 45 people?

A

5 kg✓✗

B

7.5 kg✓✗

C

6 kg✓✗

D

8 kg✓✗

Explanation

Rice needed = 4 × 4530 = 4 × 1.5 = 6 kg.

Question 32

A notebook costs Rs. 35. How much will you pay for 6 notebooks?

A

Rs. 180✓✗

B

Rs. 200✓✗

C

Rs. 240✓✗

D

Rs. 210✓✗

Explanation

Cost = 6 × 35 = Rs. 210.

Question 33

You buy 4 pens at Rs. 25 each and 2 erasers at Rs. 8 each. How much do you pay in total?

A

Rs. 108✓✗

B

Rs. 116✓✗

C

Rs. 124✓✗

D

Rs. 132✓✗

Explanation

Cost = 4 × 25 + 2 × 8 = 100 + 16 = Rs. 116.

Question 34

A rectangular hall is 12 m long and 7 m wide. What is its floor area?

A

84 m²✓✗

B

72 m²✓✗

C

96 m²✓✗

D

38 m²✓✗

Explanation

Area = length × width = 12 × 7 = 84 m².

Question 35

A square tile has a side of 9 cm. What is its area?

A

36 cm²✓✗

B

72 cm²✓✗

C

81 cm²✓✗

D

90 cm²✓✗

Explanation

Area of a square = side × side = 9 × 9 = 81 cm².

Question 36

After a 25% increase, the price of a shirt is Rs. 150. What was the original price?

A

Rs. 112.50✓✗

B

Rs. 130✓✗

C

Rs. 125✓✗

D

Rs. 120✓✗

Explanation

New price = 125% of the original price.
Original price = 150 ÷ 1.25 = Rs. 120.

Question 37

After a 10% discount, a pair of shoes costs Rs. 360. What was the price before the discount?

A

Rs. 324✓✗

B

Rs. 400✓✗

C

Rs. 410✓✗

D

Rs. 396✓✗

Explanation

Price after discount = 90% of the original price.
Original price = 360 ÷ 0.9 = Rs. 400.

Question 38

The sum of three consecutive odd numbers is 81. What is the largest of these numbers?

A

29✓✗

B

27✓✗

C

25✓✗

D

31✓✗

Explanation

Let the numbers be x, x + 2 and x + 4.
3x + 6 = 81, so x = 25.
The largest number = 25 + 4 = 29.

Question 39

The sum of five consecutive whole numbers is 100. What is the largest of them?

A

20✓✗

B

21✓✗

C

22✓✗

D

24✓✗

Explanation

Let the numbers be x, x + 1, x + 2, x + 3 and x + 4.
5x + 10 = 100, so x = 18.
The largest number = 18 + 4 = 22.

Question 40

If 6 apples cost Rs. 90, what is the cost of 10 apples?

A

Rs. 120✓✗

B

Rs. 160✓✗

C

Rs. 140✓✗

D

Rs. 150✓✗

Explanation

Cost of 1 apple = 90 ÷ 6 = Rs. 15.
Cost of 10 apples = 10 × 15 = Rs. 150.

Question 41

A dozen eggs cost Rs. 78. What do 18 eggs cost?

A

Rs. 104✓✗

B

Rs. 117✓✗

C

Rs. 126✓✗

D

Rs. 130✓✗

Explanation

Cost of 1 egg = 78 ÷ 12 = Rs. 6.50.
Cost of 18 eggs = 18 × 6.50 = Rs. 117.

Question 42

A machine prints 320 pages in an hour. How many pages will it print in 7 hours?

A

2,240 pages✓✗

B

2,140 pages✓✗

C

2,340 pages✓✗

D

2,440 pages✓✗

Explanation

Pages = 320 × 7 = 2,240 pages.

Question 43

A bakery bakes 175 loaves of bread every day. How many loaves does it bake in a week?

A

1,050 loaves✓✗

B

1,125 loaves✓✗

C

1,225 loaves✓✗

D

1,325 loaves✓✗

Explanation

Loaves in a week = 175 × 7 = 1,225 loaves.

Question 44

A bus travels at 48 km per hour. How long will it take to cover 216 km?

A

4 hours✓✗

B

5.5 hours✓✗

C

5 hours✓✗

D

4.5 hours✓✗

Explanation

Time = distance ÷ speed = 216 ÷ 48 = 4.5 hours.

Question 45

A car covers 270 km in 4.5 hours. What is its average speed?

A

54 km per hour✓✗

B

60 km per hour✓✗

C

64 km per hour✓✗

D

72 km per hour✓✗

Explanation

Speed = distance ÷ time = 270 ÷ 4.5 = 60 km per hour.