CBSE Class 8 Mathematics IMO Olympiad MCQs with Answers Set F

LOGICAL REASONING

Question. In a certain code language the word PATIENCE is written as TPNIEECA. How will the word SPACIOUS be written in that language?
A. ASOCSUIP
B. USSPOICA
C. USPSOICA
D. ACOSSUIP
Answer : B

Question. Seven boys are standing in a circle facing to the centre.
B is standing to the right of A after two boys. C is standing left side of B after four boys. C is in between D and F. B is standing beside F. G is standing to the immediate right of E. E is standing to the immediate right of A.
Who is standing to the immediate left of B?
A. A
B. G
C. F
D. E
Answer : B

Question. How many semicircles are there in the given figure?

A. 8
B. 12
C. 16
D. 20
Answer : C

Question. Select a figure from the options which shows the correct water-image of Fig. (X).

Answer : C

Question. Ajay wants to go to the Management Institute. He starts from home, which is in the East of a crossing.
He walks towards the crossing. The road to the left ends in a school, straight ahead is a community hall.
The road to the right leads to the Management Institute.
In which direction is the Management Institute from the crossing?
A. East
B. West
C. South
D. North
Answer : D

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

Answer : D

Question. There is a certain relationship between figures (1) and (2). Establish the same relationship between figures (3) and (4) by selecting a suitable figure from the options which will replace the (?) in figure (4).

Answer : D

Question. Select a figure from the options which is exactly embedded in Fig. (X) as one of its part.

Answer : B

Question. Select a figure from the options which completes the figure matrix.

Answer : D

Question. If it is possible to make only one meaningful word with the second, the seventh, the tenth and the eleventh letters of the word TRADITIONAL, what will be the second letter of the word? If no such word can be formed, give 'X' as the answer. If only two such words can be formed give 'Y' as the answer and if more than two such words can be formed give 'Z' as the answer.
A. L
B. Y
C. X
D. Z
Answer : D

Question. Study the given arrangement carefully.
• @ B D S 3 W A * V 6 9 Q J % H 8 U N 1 2 T 4 # 7 5 $ K
What should come in the place of the question mark (?) in the following series based on the given arrangement?
* 6 Q 9 J H % 8 N U 1 T ?
A. N
B. 4
C. #
D. 2
Answer : D

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 operation on numbers progresses from left to right.
Rules:
(i) If an odd number is followed by another composite odd number, they are to be multiplied.
(ii) If an even number is followed by an odd number, they are to be added.
(iii) If an even number is followed by a number which is a perfect square, the even number is to be subtracted from the perfect square.
(iv) If an odd number is followed by an even number, the second one is to be subtracted from the first one.
(v) If an odd number is followed by a prime odd number, the first number is to be divided by the second number.
27     18     3
21      x      9
If x is the resultant of the first row, what will be the resultant of the second row?
A. 63
B. 36
C. 3
D. 16
Answer : A

Question. If the first and the third digits of each number are interchanged and one is added to the second digit of each number, then which of the following pair of numbers will have highest total number of their numerical value?
382 473 568 728 847 629
A. 847 and 629
B. 568 and 728
C. 728 and 847
D. 568 and 847
Answer : B

Question. Select a Venn diagram from the options which best illustrates the relationship amongst “Metal, Copper, Wood”.

Answer : B

Question. Among P, Q, R, S and T, each having a different weight, R is heavier than only P. S is lighter than Q and heavier than T. Who among them is the heaviest?
A. Q
B. P
C. S
D. Data inadequate
Answer : A

MATHEMATICAL REASONING

Question. Which of the following statements is CORRECT?
A. For every rational number x, y and z, x + (y × z) = (x + y) × (x + z)
B. 0 is a rational number.
C. The rational number 57/23 lies to the left of zero on the number line.
D. Subtraction of rational numbers is commutative.
Answer : B

Question. In the given figure, P is a point in the interior of ∠AOB.
PM ⊥ OB and PN ⊥ OA. If ∠NOM = 60°, what is the measure of ∠NPM?
A. 30°
B. 120°
C. 60°
D. 150°
Answer : B

Question. The given figure shows 3 different views of a three dimensional figure constructed from cubes. Which could be the correct option ?

Answer : A

Question. Which of the following is a linear equation in one variable?
A. (2x – 2)² = 4x² + 4x – 4
B. (3x – 4)² = 3x – 3x² + 3
C. x² = 2x – 2
D. All of these
Answer : A

Question. The figure shows a rectangular block of wood which is 2/5 m long. It has a square base of area 9 cm².
(a) What is the greatest number of 2 cm cubes that can be cut from it?
(b) What is the volume of the block of wood left?

    (a)            (b)
A. 20        200 cm³
B. 140      200 cm³
C. 154      100 cm³
D. 159      200 cm³
Answer : A

Question. An amount becomes 6 times in 7 years when invested under S.I. at a certain rate. In how many years will the amount become 16 times of the original amount at the same rate?
A. 28 years
B. 20 years
C. 21 years
D. 30 years
Answer : C

Question. Find the value of 

A. 0.0032
B. 0.00032
C. 0.32
D. None of these
Answer : B

Question. What is the value of x in the given equation?
(3x+1)/16 + (2x-3)/7 = (x+3)/8 + (3x-1)/14
A. 2
B. 4
C. 3
D. 5
Answer : D

Question. Which of the following is the greatest?
A. 7 + 3
B. 6 + 2
C. 5 + 5
D. 2 + 8
Answer : C

Question. To construct a unique rectangle, the minimum number of measurements required is
A. 4
B. 3
C. 2
D. 1
Answer : C

Direction (a - b) : Answer the questions on the basis of the information given below:

Question a. In which school is the number of players participating in Hockey and Basketball together second highest?
A. School-1
B. School-2
C. School-3
D. School-4
Answer : B

Question b. What is the total number of players participating in Tennis from all the five schools together?
A. 324
B 288
C. 342
D. 250
Answer : D

Question. Find x : 2^0.2 × 64 × 8^1.3 × 4^0.2 = (8)^x
A. 2.7
B. 2.5
C. 3.7
D. 3.5
Answer : D

Question. In the figure, ABCD is a square of sides 30 cm. 
Find the area of the shaded region if the radius of the circle is 18 cm. (Take p = 3.14)

A. 112.36 cm²
B. 117.36 cm²
C. 119.36 cm²
D. 121.26 cm²
Answer : B

Question. If 35% of a number is 12 less than 50% of that number, then the number is _____.
A. 40
B. 50
C. 60
D. 80
Answer : D

Question. The approximate value of 6.385 x 6.385 - 5.385 x 5.385 / 6.385 x 6.385 + 2 x 6.385 x 5.385 + 5 385 x 5.385 is
A. 3
B. 2
C. 0.085
D. 0
Answer : C

Question. Given below are the steps of construction to construct a quadrilateral ABCD where AB = 5.6 cm, BC = 4.1 cm, CD = 4.4 cm, AD = 3.3 cm and ∠A = 75°. Which of the following is INCORRECT step?
Step-I : Draw AB = 5.6 cm and construct ∠BAX = 75°.
Step-II : With A as centre and radius = 3.3 cm, cut off AD = 3.3 cm along AX.
Step-III : Join BD. With D as centre and radius = 4.1 cm, draw an arc.
Step-IV : With B as centre and radius = 4.1 cm, draw an arc to cut the arc drawn in above step at C. Join BC, CD to obtain the required quadrilateral ABCD.
A. Step-I
B. Step-II
C. Step-III
D. Step-IV
Answer : C

Question. Which of the following expressions shows that rational numbers are associative under multiplication?

Answer : A

Question. A hat contains 5 red balls and 7 green balls. If a ball is drawn at random, then what is the probability that it is a red ball?
A. 5/22
B. 5/12
C. 7/12
D. 3/12
Answer : B

Question. The two adjacent sides of a rectangle are 5x² – 3y² and x² + 2xy. Find the perimeter.
A. 12x² + 5xy + 9y²
B. 12x² – 6y² + 4xy
C. 7x² – 3y² + 4xy
D. 8x² – 8y² + 3xy
Answer : B

EVERYDAY MATHEMATICS

Question. A man had ₹ 4800 in his locker two years ago.
In the first year, he deposited 20% of the amount in his locker. In the second year, he deposited 25% of the new amount in his locker. Find the amount at present in his locker.
A. ₹ 5200
B. ₹ 6800
C. ₹ 7200
D. ₹ 8000
Answer : C

Question. In a garden there are as many trees in a row as there are number of rows in the garden. If there are 576 tress in the garden, find the number of trees in a row.
A. 22
B. 24
C. 34
D. 36
Answer : B

Question. Sam, Trishu and Sanchi begin to jog around a circular stadium. They complete their revolutions in 42 seconds, 56 seconds and 63 seconds respectively. After how many seconds will they be together at the starting point?
A. 366
B. 252
C. 504
D. Can’t be determined
Answer : C

Question. Raju purchased an item for ₹ 4,500 and sold it at a gain of 15%. From that amount he purchased another item and sold it at a loss of 10%. What is his overall gain/loss?
A. Gain of ₹ 152.50
B. Gain of ₹ 157.50
C. Loss of ₹ 165
D. Neither gain nor loss
Answer : B

Question. A rectangular garden 200 m long and 150 m wide has a path all around it, on the inner side, having a width of 3 m. In the centre of this plot, there is a circular pond of radius 7 m. What area of the land is left for the lawn and the flower beds?
A. 27,936 sq. m
B. 27,782 sq. m
C. 27,682 sq. m
D. 28,582 sq. m
Answer : B

Question. A house is purchased by Mohit, Arun and Armaan.
Arun contributes 23/60 of Mohit's contribution while,
Armaan contributes 1/3 of Mohit's contribution.
If Mohit's contribution is ₹ 1500000, then find the contribution of Armaan and Arun.
A. ₹ 5,00,000, ₹ 5,75,000
B. ₹ 5,00,000, ₹ 6,75,000
C. ₹ 6,00,000, ₹ 5,00,000
D. ₹ 6,25,000, ₹ 5,25,000
Answer : A

Question. Sudharshan invested ₹ 15,000 at the rate of 10% per annum compounded half yearly. What amount will Sudharshan get at the end of the year?
A. ₹ 16,537.50
B. ₹ 16,500
C. ₹ 16,525.50
D. ₹ 18,150
Answer : A

Question. The monthly income of Komal and Asha are in the ratio of 4 : 3. Their monthly expenses are in the ratio of 3 : 2. However both saves ₹ 600 per month. What is their total monthly income?
A. ₹ 8400
B. ₹ 5600
C. ₹ 4200
D. ₹ 2800
Answer : C

Question. P’s age is twice of Q, Q’s age is twice of R and R’s age is twice of S. If the average of the ages of P, Q, R and S is 15 years, then what is the sum of present ages of Q and S ?
A. 4 years
B. 20 years
C. 16 years
D. 32 years
Answer : B

Question. The outer dimensions of a closed box are 10 cm by 8 cm by 7 cm. Thickness of the wood is 1 cm. Find the total cost of wood required to make box, if 1 cm³ of wood costs ₹ 2.00.
A. ₹ 320
B. ₹ 1240
C. ₹ 640
D. ₹ 240
Answer : C

ACHIEVERS SECTION

Question. Match the following

A. (i) → Q; (ii) → P; (iii) → S; (iv) → R
B. (i) → R; (ii) → Q; (iii) → P; (iv) → S
C. (i) → S; (ii) → R; (iii) → P; (iv) → Q
D. (i) → R; (ii) → S; (iii) → P; (iv) → Q
Answer : C

Question. Which of the following statements is true?
Statement 1 : Gagan bought a plot of land for ₹ 2,35,000. If he built a boundary wall around the plot and levelled the land and sold it for ₹ 35,00,000 thus making a profit of 40% on his investment, then he spend ₹ 22,65,000 on the boundary wall and levelling the land.
Statement 2 : In a festive season, a retailer sells readymade clothes at a discount of 20% and still gains 20% of cost price. If the marked price for a pair of jeans is ₹ 4200, then the retailer's cost price is ₹ 4000.
A. Only Statement 1
B. Only Statement 2
C. Both Statement 1 and Statement 2
D. Neither Statement 1 nor Statement 2
Answer : A

Question. Sonia picks up a card from the given cards.

Find the probability of getting
(a) an odd number.
(b) a Y card.
      (a)          (b)
A. 1/2         3/10
B. 3/10       1/4
C. 3/10       1/2
D. 1/4         3/10
Answer : A

Question. Find P + Q – R.
(i) If a rectangle of length 44 cm is rolled along its length to form a cylinder, the radius of cylinder is P cm.
(ii) The cost of plastering the walls of a cuboidal room of dimensions 12 m × 10 m × 4 m at the rate of ₹ 25 per sq. m is ₹ Q .
(iii) The volume of a cuboid of dimensions 14 m × 7 m × 12 m is R m³.
A. 11776
B. 7362
C. 16162
D. 3231
Answer : D

Question. Look at the given data.
22, 10, 29, 22, 32, 5, 37, 14, 12, 23, 42, 15, 38,
26, 32, 18, 26, 28, 19, 27, 35, 31, 24, 37, 19, 20.
The frequency distribution is given below :

Which of the following tables is the frequency table of the given data?
A. Only P
B. Only Q
C. Neither P nor Q
D. None of these
Answer : C