CBSE Class 8 Mathematics IMO Olympiad MCQs with Answers Set 12

SECTION I : LOGICAL REASONING

Question. If FULFNHW is the code for CRICKET, then EULGH is the code for which word?
(A) PRIDE
(B) BRIDE
(C) BLADE
(D) BLIND
Answer : B

Question. Which letter represents the artists who are neither doctors nor scientists nor dancers?

(A) A
(B) D
(C) F
(D) G
Answer : A

Question. Choose one number which is similar to the numbers in the given set : 992, 733, 845, 632
(A) 114
(B) 326
(C) 425
(D) 947
Answer : C

Question. Choose the figure from the options which is different from the rest.

Answer : C

Question. Which letter is tenth to the right of the letter which is exactly the middle letter between F and D?
F J M P O W R N B E Y C K A V L D G X U H Q I S Z T
(A) D
(B) G
(C) H
(D) None of these
Answer : D

Question. Select a figure from amongst the given options which will continue the same series established by five problem figures.

Answer : C

Question. Which one of the following when placed at the sign of interrogation shall complete the matrix?

(A) E10
(B) E12
(C) S10
(D) S12
Answer : B

Question. A run said, "This girl is the wife of the grandson of my mother." Who is Arun to the girl?
(A) Father
(B) Grandfather
(C) Husband
(D) Father-in-law
Answer : D

Question. Deepa moved a distance of 75 metres towards the north. She then turned to the left and walked for about 25 metres, turned left again and walked 80 metres. Finally, she turned to the right at an angle of 45°. In which direction was she moving finally?
(A) North-east
(B) North-west
(C) South
(D) South-west
Answer : B

Question. Select a figure from amongst the options, which when placed in the blank space of fig. (X) would complete the pattern.

Answer : C

Question. Different alphabets stand for various symbols as indicated below.
Addition : O   Subtraction : M    Multiplication : A
Division : Q    Equal to : X          Greater than : Y
Less than : Z
Which one of the following is correct according to above definitions ?
(A) 2 Z 2 A 4 O 1 A 4 M 8
(B) 8 Y 2 A 3 A 4 Q 2 A 4
(C) 10 X 2 O 2 A 4 O 1 M 2
(D) 12 X 4 O 2 Q 1 A 4 A 2
Answer : A

Question. Group the given figures into three classes using each figure only once.

(A) 1, 4, 7 ; 3, 6, 9 ; 2, 5, 8
(B) 1, 6, 9 ; 2, 4, 7 ; 3, 5, 8
(C) 1, 4, 7 ; 2, 6, 9 ; 3, 5, 8
(D) 1, 5, 7 ; 2, 6, 9 ; 3, 4, 8
Answer : C

Question. If 'wall' is called 'window', 'window' is called 'door', 'door' is called 'floor', 'floor' is called 'roof' and 'roof' is called 'ventilator', what will a person stand on?
(A) Window
(B) Wall
(C) Floor
(D) Roof
Answer : D

Question. Find the number of triangles in the given figure.

(A) 34
(B) 35
(C) 36
(D) None of these
Answer : D

Question. The given question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Select a figure from the options which would most closely resemble the unfolded form of fig. (Z).

Answer : B

Question. Thirty six vehicles are parked in a parking lot in a single row. After the first car, there is one scooter. After the second car, there are two scooters. After the third car, there are three scooters and so on. Find the number of scooters in the second half of the row.
(A) 10
(B) 12
(C) 15
(D) 17
Answer : C

Question. The given question consists of figures 1, 2, 3 and 4. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the options that would replace the question mark (?) in fig. (4).

Answer : D

Question. Letters of the word given below have been jumbled up. Choose the option which gives the correct order of the letters as indicated by the numbers to form a meaningful word.
A C P E T S
1 2 3 4 5 6
(A) 1, 6, 3, 4, 2, 5
(B) 2, 3, 4, 1, 5, 6
(C) 5, 6, 3, 4, 1, 2
(D) 6, 5, 3, 4, 2, 1
Answer : A

Question. Which of the following collections of letters will look the same in the mirror?
(A) OSMIHOM
(B) VHRTRVH
(C) HIMOSTA
(D) AOVIVOA
Answer : D

Question. Which would be the proper order of the following (in ascending order)?
1. T rillion 2. T housand 3. Billion
4. Hundred 5. Million
(A) 1, 2, 4, 3, 5
(B) 1, 5, 3, 2, 4
(C) 4, 2, 3, 5, 1
(D) 4, 2, 5, 3, 1
Answer : D

SECTION II : MATHEMATICAL REASONING

Question. If x² + y² = 25 and xy = 12, then the value of x^–1 + y –1 is _____.
(A) 12/5
(B) 7/12
(C) −7/12
(D) Both (B) and (C)
Answer : D

Question. What is the least number which must be subtracted from 369 to make it a perfect cube?
(A) 8
(B) 26
(C) 2
(D) 25
Answer : B

Question. If ab + bc + ca = 0, then the value of 1/a²-bc + 1/b²-ca + 1/c²-ab will be _____.
(A) –1
(B) a + b + c
(C) abc
(D) 0
Answer : D

Question. Find the number of factors of 512.
(A) 8
(B) 10
(C) 4
(D) 14
Answer : B

DIRECTION (Q.No. a - b) : Study the following graph carefully and answer the following questions

Question. In the year 2006, the people who prefer playing Tennis is what percent of the people who prefer playing Cricket, Football and Tennis together in that year?
(A) 25(1/2)
(B) 24(3/4)
(C) 21(1/3)
(D) 23(1/3)
Answer : D

Question. The number of people who prefer playing Tennis in 2006, is how many millions less than the number of people who prefer playing Tennis in 2005?
(A) 110
(B) 105
(C) 100
(D) 95
Answer : C

Question. What is the ratio of the number of people who prefer playing Cricket in 2001 to the number of people who prefer playing Tennis in the year 2003?
(A) 14 : 17
(B) 16 : 13
(C) 15 : 11
(D) 13 : 15
Answer : B

Question. Solve for x : 4x+17/18 - 13x-2/32 + x/3 =  7x/12 - x+16/36
(A) 418/117
(B) 6
(C) 1
(D) − 8/3
Answer : A

Question. Two-fifth of one-third of three-seventh of a number is 15. What is 40 percent of that number ?
(A) 72
(B) 84
(C) 136
(D) 105
Answer : D

Question. The question given below is followed by two statements. You have to study the question and the two statements given to decide which of the statement(s) is/are required to answer the question.
What is the area of the right-angled triangle?
I. Length of the hypotenuse is 5 cm.
II . Perimeter of the triangle is four times its base.
(A) I only
(B) II only
(C) I and II both
(D) Data inadequate
Answer : C

Question. In a two-digit number, the digit in the unit's place is four times the digit in ten's place and sum of the digits is equal to 10. What is the number?
(A) 14
(B) 41
(C) Data inadequate
(D) None of these
Answer : D

Question. Find the sum of 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132 .
(A) 7/8
(B) 11/12
(C) 15/16
(D) 17/18
Answer : B

Question. In the given figure, AE = BC and AE || BC and the three sides AB, CD and ED are equal in length.
If ∠A = 102°, find the measure of ∠BCD.

(A) 138°
(B) 162°
(C) 88°
(D) None of these
Answer : B

Question. If x+y/x-y = 5/3 and x/(y+2) = 2, the value of (x, y) is _____.
(A) (4, 1)
(B) (2, 8)
(C) (1, 4)
(D) (8, 2)
Answer : D

Question. If m, n are the positive integers (n > 1) such that mn = 121, then value of (m – 1)n + 1 is ______.
(A) 12321
(B) 1
(C) 1000
(D) 11
Answer : C

Question. The greatest divisor of (a – b)(a + b)(a2 + b2)(a4 + b4)(a8 + b8)(a16 + b16) is ______.
(A) a¹⁶ – b¹⁶
(B) a¹⁶ + b¹⁶
(C) a³¹ – b³¹
(D) a³² – b³²
Answer : D

Question. In the given figure, RISK and CLUE are parallelograms and ∠R = 70° and ∠L is half of ∠ESI. Find the measure of x.

(A) 75°
(B) 55°
(C) 65°
(D) 30°
Answer : A

Question. Find the area of the following polygon, if AL = 10 cm, AM = 20 cm, AN = 50 cm, AO = 60 cm and AD = 90 cm.

(A) 337.5 cm²
(B) 384 cm²
(C) 5500 cm²
(D) 5050 cm²
Answer : D

Question. Two dice are thrown simultaneously. Find the probability of getting a multiple of 3 as the sum.
(A) 1/2
(B) 1/3
(C) 1/4
(D) 5/6
Answer : B

Question. The value of is equal to (x-y)³ + (y-z)³ + (z-x)³/9(x-y)(y-z)(z-x) _____.
(A) 0
(B) 1/2
(C) 1/3
(D) 1
Answer : C

SECTION III : EVERYDAY MATHEMATICS

Question. What annual payment will discharge a debt of ₹ 1025 due in 2 years at the rate of 5% compound interest?
(A) ₹ 550
(B) ₹ 551.25
(C) ₹ 560
(D) ₹ 560.75
Answer : B

Question. A man bought apples at the rate of 8 for ₹ 34 and sold them at the rate of 12 for ₹ 57. How many apples should be sold to earn a net profit of ₹ 45?
(A) 90
(B) 100
(C) 135
(D) 150
Answer : A

Question. The average age of three boys is 25 years and their ages are in the proportion 3 : 5 : 7. The age of the youngest boy is _____.
(A) 21 years
(B) 18 years
(C) 15 years
(D) 9 years
Answer : C

Question. A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work can they finish in a day ?
(A) 1/6
(B) 1/9
(C) 2/5
(D) 2/7
Answer : A

Question. A sum of money invested at compound interest amounts to ₹ 4624 in 2 years and to ₹ 4913 in 3 years. The sum of money is _____.
(A) ₹ 4360
(B) ₹ 4260
(C) ₹ 4335
(D) ₹ 4096
Answer : D

Question. Three equal cubes are placed in a row touching each other. Find the ratio of the total surface area of the resulting cuboid to that of the sum of surface areas of the three cubes.
(A) 5 : 7
(B) 7 : 9
(C) 9 : 7
(D) None of these
Answer : B

Question. A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is _____.
(A) 29(1/5)
(B) 37(1/4)
(C) 42
(D) 54
Answer : C

Question. If 1/8 of a pencil is black, 1/2 of the remaining is white and the remaining 3(1/2) cm is blue, find the total length of the pencil.
(A) 8 cm
(B) 10 cm
(C) 7 cm
(D) 6 cm
Answer : A

Question. A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is _____.
(A) 10
(B) 20
(C) 40
(D) 73
Answer : C

Question. A shopkeeper sold a T.V. set for ₹ 17,940 with a discount of 8% and earned a profit of 19.6%. What would have been the percentage of profit earned if no discount was offered?
(A) 24.8%
(B) 25%
(C) Cannot be determined
(D) None of these
Answer : D