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Olympiad Test: Mathematical And Analytical Reasoning - 2 - Class 4 MCQ


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20 Questions MCQ Test - Olympiad Test: Mathematical And Analytical Reasoning - 2

Olympiad Test: Mathematical And Analytical Reasoning - 2 for Class 4 2024 is part of Class 4 preparation. The Olympiad Test: Mathematical And Analytical Reasoning - 2 questions and answers have been prepared according to the Class 4 exam syllabus.The Olympiad Test: Mathematical And Analytical Reasoning - 2 MCQs are made for Class 4 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Mathematical And Analytical Reasoning - 2 below.
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Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 1

In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 1

Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x(4/3) = 24.
If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.
Therefore Number of girls in the class = (36 – 24) = 12.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 2

A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 2

Let son’s age be x years. Then, father’s age = (3x) years.
Five years ago, father’s age = (3x – 5) years and son’s age = (x – 5) years.
So, 3x – 5 = 4 (x – 5)
⇒ 3x – 5 = 4x – 20 ⇒ x = 15.

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Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 3

A waiter’s salary consists of his salary and tips. During one week his tips were 5/4 of his salary. What fraction of his income came from tips?

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 4

If you write down all the numbers from 1 to 100, then how many times do you write 3?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 4

Clearly, from 1 to 100, there are ten numbers with 3 as the unit’s digit- 3, 13, 23, 33, 43, 53, 63, 73, 83, 93; and ten numbers with 3 as the ten’s digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
So, required number = 10 + 10 = 20.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 5

If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 6

Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 6

L.C.M. of 6, 5, 7, 10 and 12 is 420.
So, the bells will toll together after every 420 seconds = 420/60 = 7 minutes.
Now, 7 x 8 = 56 and 7 x 9 = 63.
Thus, in 1-hour (or 60 minutes), the bells will toll together 8 times, excluding the one at the start.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 7

A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 10 men leave the bus and five women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 7

Originally, let number of women = x. Then, number of men = 2x.
So, in city Y, we have :
(2x – 10) = (x + 5) or x = 15.
Therefore Total number of passengers in the beginning
= (x + 2x) = 3x = 3 × 15
 = 45.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 8

A, B, C, D and E play a game of cards. A says to B, “If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has.” A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 8

Clearly, we have :
A = B – 3 ...(i)
D + 5 = E ...(ii)
A + C = 2E ...(iii)
B + D = A+C = 2E ...(iv)
A+B + C + D + E=150 ...(v)
From (iii), (iv) and (v),
we get : 5E = 150 or E = 30.
Putting E = 30 in (ii), we get :
D = 25.
Putting E = 30 and D = 25 in (iv), we get:
B = 35.
Putting B = 35 in (i), we get :
A = 32.
Putting A = 32 and E = 30 in (iii), we get:
C = 28.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 9

A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether?​

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 9

Since each pole at the corner of the plot is common to its two sides, so we have:
Total number of poles needed = 27 x 4 – 4 = 108 – 4 = 104.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 10

In a city, 40% of the adults are illiterate while 85% of the children are literate. If the ratio of the adults to that of the children is 2 : 3, then what percent of the population is literate?

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 11

A is three times as old as B. C was twice-as old as A four years ago. In four years’ time, A will be 31. What are the present ages of B and C?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 11

We have : A = 3B ...(i) and
C – 4 = 2 (A - 4) ...(ii)
Also, A + 4 = 31 or A= 31 – 4 = 27.
Putting A = 27 in (i), we get: B = 9.
Putting A = 27 in (ii), we get C = 50.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 12

Today is Varun’s birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 12

Let Varun’s age today = x years.
Then, Varun’s age after 1 year = (x + 1) years.
Therefore x + 1 = 2 (x – 12) ⇒ x + 1 = 2x – 24 ⇒ x = 25.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 13

A bird shooter was asked how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 13

There were all sparrows but six’ means that six birds were not sparrows but only pigeons and ducks. Similarly, number of sparrows + number of ducks = 6
and number of sparrows + number of pigeons = 6. This is possible when there are 3 sparrows, 3 pigeons and 3 ducks i.e. 9 birds in all.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 14

Mr. Johnson was to earn £ 300 and a free holiday for seven weeks’ work. He worked for only 4 weeks and earned £ 30 and a free holiday. What was the value of the holiday?

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 15

What is the smallest number of ducks that could swim in this formation - two ducks in front of a duck, two ducks behind a duck and a duck between two ducks?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 15

Clearly, the smallest such number is 3. Three ducks can be arranged as shown above to satisfy all the three given conditions.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 16

Three friends had dinner at a restaurant. When the bill was received, Amita paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Tanya paid. What fraction of the bill did Veena pay?

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 17

In a class, 20% of the members own only two cars each, 40% of the remaining own three cars each and the remaining members own only one car each. Which of the following statements is definitely true from the given statements?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 17

Let total number of members be 100, Then, number of members owning only 2 cars = 20.
Number of members owning 3 cars
= 40% of 80 = 32.
Number of members owning only 1 car = 100 – (20 + 32) = 48.
Thus, 48% of the total members own one car each.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 18

When Rahul was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rahul’s brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul’s sister when he was born?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 18

When Rahul was born, his brother’s age = 6 years; his father’s age = (6 + 32) years = 38 years, his mother’s age = (38 – 3) years = 35 years; his sister’s age = (35 – 25) years = 10 years.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 19

A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses’ back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 19

Let number of horses = number of men = x. Then, number of legs = 4x + 2 x (x/2) = 5x. So, 5x = 70 or x = 14.

Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 20

Ravi’s brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi’s father and mother respectively when his brother was born?

Detailed Solution for Olympiad Test: Mathematical And Analytical Reasoning - 2 - Question 20

When Ravi’s brother was born, let Ravi’s father’s age = x years and mother’s age = y years. Then, sister’s age = (x – 28) years. So, x – 28 = 4 or x = 32.
Ravi’s age = (y – 26) years. Age of Ravi’s brother = (y – 26 + 3) years = (y – 23) years.
Now, when Ravi’s brother was born, his age = 0 ⇒ y – 23 = 0 or y = 23.

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