CBSE Class 8 Mathematics IMO Olympiad MCQs with Answers Set N

LOGICAL REASONING

Question. Two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered. The operations of numbers progress from left to right.
Rules
I. If an odd number is followed by a two-digit even number then they are to be added.
II. If an odd number is followed by a two-digit odd number then the second number is to be subtracted from the first number.
III. If an even number is followed by a number which is a perfect square of a number then the second number is to be divided by the first number.
IV. If an even number is followed by a two-digit even number then the first number is to be multiplied by the second number.
8 16 16 14
13 11 12 144
What is the difference between the resultant of the first set of numbers and the second set of numbers?
A. 106
B. 118
C. 210
D. 222
Answer : A

Question. A set of figures carrying certain characters, is given.
Assuming that the characters in each set follow a similar pattern, find the character which would replace the question mark (?).

A. 262
B. 226
C. 136
D. 206
Answer : D

Question. A square transparent sheet with a pattern is given.
Select an option as to how the pattern would appear when the transparent sheet is folded along the dotted line.

Answer : B

Question. Study the following information carefully and answer the question given below:
Four players P, Q, R and S are holding 4 cards each.
Each of them has an Ace, a King, a Queen and a Jack. All of them have all the suits (spade, heart, club and diamond).
I. P has Ace of spade and Queen of diamond.
II. Q has Ace of club and King of diamond.
III. R has Queen of club and King of spade.
IV. S has jack of club.
Ace of diamond is with
A. P
B. R
C. Q
D. S
Answer : D

Question. Count the minimum number of straight lines required to make the given figure.

A. 8
B. 10
C. 12
D. 14
Answer : C

Question. Select the option which will exactly make up the key figure (X).

Answer : C

Question. The post office is to the east of the school while my house is to the south of the school. The market is to the north of the post office. If the distance of the market from the post office is equal to the distance of my house from the school, in which direction is the market with respect to my school?
A. North
B. East
C. North-east
D. South-west
Answer : C

Question. A watch reads 4.30. If the minute hand points East, in what direction will the hour hand point?
A. North
B. North-west
C. South-east
D. North-east
Answer : D

Question. Select a figure which will continue the same series as established by the five Problem Figures.

Answer : A

Question. Find the missing figure in the given figure matrix.

Answer : B

Question. Rewrite the word vocalist in the numeric form by writing its first four letters in the reverse order and then the next four letters in the reverse order by substituting I by 7, O by 1, L by 3, T by 6, V by 5, S by 8, A by 9 and C by 2.
A. 92156873
B. 92157683
C. 92516783
D. 92156837
Answer : A

Question. There is a certain relationship between the figures (i) and (ii) & (iii) and (iv). Identify the relationship and find the missing figure.

Answer : B

Question. Three different positions X, Y and Z of a dice are shown in the figures given below. Answer the following question which is based upon these figures.

Sum of top and bottom faces in position Y.
A. More than 5
B. 5
C. L ess than 5
D. Cannot be determined
Answer : A

Question. If > denotes +; < denotes –; + denotes ÷; – denotes =; = denotes 'less than'; and × denotes 'greater than'; then which of the following is incorrect statement ?
A. 3 + 2 > 4 × 9 + 3 < 2
B. 3 > 2 > 4 × 18 + 3 < 1
C. 3 > 2 < 4 × 8 + 4 < 2
D. 3 + 2 < 4 × 9 + 3 < 3
Answer : D

Question. Deepanshu said to Naman, "That boy playing football is the younger of the two brothers of the daughter of my father's wife." How is the boy playing football related to Deepanshu?
A. Son
B. Brother
C. Cousin
D. Nephew
Answer : B

Question. There is a series of seven figures. First and last unnumbered figures are the beginning and end of series. 
One of the five numbered figures does not fit into the series. Identify the figure need to be replaced.

A. 1
B. 2
C. 3
D. 4
Answer : D

Question. Read the following information carefully to answer the question given below:
A person is asked to put in a basket one apple when ordered 'One', one guava when ordered 'Two', one orange when ordered 'Three' and is asked to take out from the basket one apple and one guava when ordered 'Four' and 'Five' respectively.
4 4 5 4 5 3 4 5 3 1 4 5 3 1 2 4 5 4 5 3 4 5 3
If 8 of each type of fruits are already in the basket then, how many apples will be there in the basket at the end of the above order sequence?
A. 1
B. 2
C. 3
D. 4
Answer : B

Question. Read the following information carefully to answer the question given below:
The sum of the incomes of A and B is more than that of C and D taken together. The sum of the incomes of A and C is the same as that of B and D taken together. Moreover, A earns half as much as the sum of the incomes of B and D. If A's income be ₹ 80,000 per annum and the difference between the incomes of B and D be the same as A's income, B's income is _____.
A. ₹ 40,000
B. ₹ 60,000
C. ₹ 80, 000
D. ₹ 1,20,000
Answer : D

Question. In a class of 46 students, 18 played football, 17 played cricket including 6 who played football. 16 students played hockey including 4 who played cricket, but not
football. Five students played carrom but no outdoor games. Which of the following figures represents these facts?

Answer : C

Question. Count the number of faces in the given solid.

A. 17
B. 18
C. 19
D. None of these
Answer : D

MATHEMATICAL REASONING

Question. Simplify

A. –1
B. 1
C. –2
D. 2
Answer : A

Question. Find the area of the shaded region in the following figure.

A. 28. 45 sq. cm
B. 113.6 sq. cm
C. 59.8 sq. cm
D. 103.5 sq. cm
Answer : D

Question. Which of the following is a possible net for the solid?

Answer : C

Question. Find a + b + c + d + e + f in the given figure if, AOD, BOE and FOC are straight lines.

A. 360°
B. 540°
C. 420°
D. 120°
Answer : A

Question. If x = 4√2/√2+1, then find the value of 1/√2(x+2/x-2 + x+2√2/x-2√2)
A. √2
B. 12 + 8√2/5
C. 12 − 8√2/5
D. 16√2+24/5
Answer : A

Question. Three friends distributed their total property. The ratio of total property, share of first friend and share of second friend is 24 : 7 : 8. Find the central angle of sector, which represents the share of the third friend.
A. 72(1°/2)
B. 135º
C. 105º
D. 67(1°/2)
Answer : B

Question. In the figure below, PQRS is a square, LSR is an equilateral triangle. Find the value of x + y + z.

A. 240°
B. 90º
C. 105º
D. 60º
Answer : A

Question. An unbiased dice is thrown two times having first six consecutive odd numbers on each six faces. Find the probability of getting even sum.
A. 1
B. 0
C. 1/36
D. 4/36
Answer : A

Question. In an Atlas, a map occupies 2/5 ^th of a page with dimensions 25 cm and 30 cm respectively. If the real area of the map is 10800 sq. m, the scale to which the map is drawn, is
A. 1 cm = 36 m
B. 1 cm = 26 m
C. 1 cm = 33 m
D. 1 cm = 6 m
Answer : D

Question. Q and R borrowed ₹26000 and ₹25000 respectively, for a period of 2 years. Q paid simple interest at the rate of 2% p.a., while R paid compound interest at the same rate, compounded annually. Who paid more interest and by how much?
A. R paid more than Q by ₹40
B. R paid more than Q by ₹30
C. Q paid more than R by ₹40
D. Q paid more than R by ₹30
Answer : D

Question. If P : Q : R = 6 : 5 : 4 and P² + Q² + R² = 192500, then find (P +Q − R)/2.
A. 175
B. 165
C. 185
D. 200
Answer : A

Question. If a = (2^–2 – 2^–3), b = (2^–3 – 2^–4) and c = (2^–4 – 2^–2) then find the value of 3abc.
A. −63/1024
B. −63/2048
C. −9/2048
D. 9/1024
Answer : C

Question. If

A. ±(10/3)
B. 0
C. 1
D. –1
Answer : A

Question. The volume of a hemispherical ball is given by the V = (2/3)πr³, where V is the volume and r is the radius.
Find the diameter of the hemisphere whose volume is (468512/21)m³.
A. 22 m
B. 11 m
C. 33 m
D. 44 m
Answer : D

Question. Factorise :
(x – y)² a² + 2(x – y) (x + y) ab + b² (x + y)²
A. (ax – by) (ax + by)
B. (ax + by) (bx + ay)
C. (ax – ay + bx + by) (ax – ay + bx + by)
D. (ax + ay + bx + by) (ax – ay + bx + by)
Answer : C

EVERYDAY MATHEMATICS

Question. Ravi borrowed ₹45000 from Sahil. A part of the sum is borrowed at 10% p.a. under simple interest for 4 years and the remaining part at 11% p.a. under simple interest for 4(1/2) years. If the total interest earned by Sahil is ₹ 19900, then find the sum borrowed at each rate.
A. 10000, 35000
B. 25000, 20000
C. 15000, 30000
D. 5000, 40000
Answer : B

Question. In an office, the ratio of the salary of an officer to that of a clerk is 30 : 7. If the salary of the clerk is ₹14375 less than that of the officer, then what is the salary of the officer?
A. ₹15600
B. ₹18625
C. ₹17650
D. ₹18750
Answer : D

Question. In a Winter sale offer, a shopkeeper allows a discount of 15%. Even after giving the discount, he makes a profit of 6.25%. Raghav bought a sweater which was marked at ₹5000. Find the cost price of this sweater for the shopkeeper.
A. ₹ 5000
B. ₹ 4000
C. ₹ 4250
D. ₹ 5250
Answer : B

Question. The age of Sarthak is one-fifth of the age of his mother and the sum of the ages of the son and the mother is equal to the age of the father. After 15 years, the sum of the ages of the son and his mother will be four-third of his father's age. Find the ratio of the present ages of Sarthak, mother and father respectively.
A. 1 : 5 : 7
B. 2 : 10 : 10
C. 1 : 5 : 6
D. 2 : 8 : 9
Answer : C

Question. Twenty two men can complete a piece of work in 17 days. They work for 2 days. How many more men should now be employed so as to complete the work in another 10 days.
A. 11
B. 22
C. 33
D. None of these
Answer : A

Question. In a company, the average salary of male employees is ₹ 9200 and that of female employees is ₹ 8200. 
If the average salary per employees is ₹ 8900, the percentage of female employees of the total employees is_______.
A. 30
B. 40
C. 50
D. 25
Answer : A

Question. A test consists of questions each carrying 3 mark, 4 mark and 6 marks in the ratio 2 : 2 : 1. If the maximum marks in the exam is 100, then find the number of questions of each type.
A. 20, 20, 10
B. 10, 10, 5
C. 15, 15, 30
D. 15, 15, 10
Answer : B

Question. A fountain pen with a cylindrical barrel of diameter 3 cm and height 14 cm, filled with ink, can write 3600 words. How many words can be written with that pen using 220 ml of ink? (Take 1cc = 1 ml)
A. 6000
B. 5000
C. 7000
D. 8000
Answer : D

Question. One day, the ratio of the number of first class and second class passengers who travelled were in the ratio 1 : 30. The ratio of the first and second class fares is 3 : 1. The total amount collected from the passengers that day was ₹66000. Find the amount collected from the first class passengers (in ₹).
A. ₹ 3000
B. ₹ 6000
C. ₹ 9000
D. ₹ 12000
Answer : B

Question. A man purchased a plot which is in the shape of a square. The area of the plot is 12 hectares 3201m².
Find the length of each side of the plot (in cm).
A. 34900
B. 35100
C. 35900
D. 36100
Answer : B

ACHIEVERS SECTION

Question. Lets, m and f denote the respective time taken by son, mother and father to complete the work.
If 1/z + 1/m = 1/24, 1/z + 1/f = 1/18 and 1/m + 1/f = 1/36 then find 1/z + 1/m + 1/f and 1/z, 1/m, 1/f respectively
A. 1/16, 1/144, 5/144, 3/144
B. 1/16, 5/144, 1/144, 3/144
C. 1/16, 3/144, 1/144, 5/144
D. None of these
Answer : B

Question. Study the statements and select the correct option

A. Statement 1 is true and statement 2 is false
B. Statement 1 and 2 are true
C. Statement 1 and 2 are false
D. Statement 1 is false and statement 2 is true
Answer : A

Question. Fill in the blanks :
Cubes of the numbers for which the digits in the units place are 2, 8 and 3, 7 end in _____ and _____ respectively.
A. 4, 6 and 2, 7
B. 2, 3 and 7, 3
C. 8, 2 and 7, 3
D. 5, 4 and 3, 7
Answer : C

Question. In the given figure, m || l || n and PT || QR If ∠TUV = x, ∠QRS = y and ∠QVW = z, then which of the following is necessarily true?

A. x > y = z
B. x < y = z
C. x = y = z
D. Cannot be determined
Answer : C

Question. In the figure given below, O is the centre of the circle and OPQR is a rectangle. A is a point on PO such that AO = 1/3 PO and B is the mid point of OR.
Find the area of the shaded region if PA = 8 cm and BR = 4 cm (Use π = 3.14)

A. 132.68 cm²
B. 121.12 cm²
C. 108.56 cm²
D. None of these
Answer : B