CBSE Class 8 Mathematics IMO Olympiad MCQs with Answers Set E

LOGICAL REASONING

Question. Following question is based on five words given below:
          RAG FIN PUT LOW SUE
(The new words formed after performing the mentioned operations may or may not necessarily be meaningful English words.)
If in each of the given words, consonants are changed to previous letter and vowels are changed to next letter in the English alphabetical series, then in how many words thus formed will no vowels appear?
A. None
B. One
C. Two
D. Three
Answer : D

Question. In a row of children, Trishika is fifteenth from the left end of the row. If she is shifted towards the right end of the row by four places, she becomes eighth from the right end. How many children are there in the row?
A. 27
B. 26
C. 28
D. 24
Answer : B

Question. Two rows of number 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 a two-digit even number is followed by another even number, the first one is to be divided by the second one.
(ii) If an even number is followed by a prime number, the two are to be multiplied.
(iii) If an odd number is followed by another odd number, the two are to be added.
(iv) If a three-digit number is followed by a two-digit number which is a perfect square, the second number is to be subtracted from the first number.
(v) If a three-digit number is followed by a two-digit number which is not a perfect square, the first number is to be divided by the second number.
84      14      13
360    24      17
What is the difference between the resultants of the first row and the second row?
A. 100
B. 46
C. 56
D. 90
Answer : B

Question. Study the following information carefully and answer the questions given below.
(i) A, B, C, D, E, F and G are playing cards sitting around a circular table.
(ii) D is not the neighbour of C and E.
(iii) A is the neighbour of B and C.
(iv) G, who is second to the left of D, is the neighbour of E and F.
What is the position of ‘C’?
A. To the immediate left of A.
B. To the immediate right of E.
C. Third to the right of F.
D. Second to the right of B.
Answer : D

Question. Pointing to a photograph Monika said, “He is the brother of the son of my grandfather’s only child.”
How is the man related to Monika?
A. Brother
B. Cousin
C. Nephew
D. Can’t be determined
Answer : A

Question. Which of the following Venn diagrams best illustrates the relationship amongst, “Sun, Moon and Stars”?

Answer : C

Question. Find out the missing number, if same rule is followed in all the three figures.

A. 117
B. 100
C. 78
D. 63
Answer : C

Question. Two positions of a dice are shown here. When 4 is at the bottom, which number will be on the top?

A. 1
B. 2
C. 5
D. 6
Answer : A

Question. Three figures (X), (Y) and (Z) shows a sequence of folding of a sheet of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Select a figure from the options which represents the unfolded form of Fig. (Z).

Answer : A

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

Answer : D

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

Answer : A

Question. Select a figure from the options which satisfies the same conditions of placement of the dots as in

Answer : C

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 (?) in Fig. 4.

Answer : D

Question. Select a figure from the options which will complete the given figure matrix.

Answer : A

Question. If a ⊗ b = a + b / 2 and a Θ b = 2a + b / 3, then what is the value of (4 ⊗ 6) Θ (12 ⊗ 4)?
A. 4
B. 6
C. 8
D. 10
Answer : B

MATHEMATICAL REASONING

Question. Which of the following statements is always true?
A. x − y/2 is a rational number between x and y.
B. x + y/2 is a rational number between x and y.
C. x × y/2 is a rational number between x and y.
D. x ÷ y/2 is a rational number between x and y.
Answer : B

Question. Which of the following equations having x = 12, as its solution?

Answer : C

Direction (a - b) : In the given pie-chart, the percentage of students studying in 6 different schools A, B, C, D, E and F has been shown.

Question a. What is the average number of students studying in schools B, D and E?
A. 11200
B. 10600
C. 10000
D. 10500
Answer : D

Question b. Ratio between the number of students studying in schools C and E is .
A. 7 : 3
B. 5 : 3
C. 3 : 5
D. 2 : 1
Answer : D

Question. Using Euler’s formula, find the value of P, Q and R.

    P      Q     R
A. 6     19     9
B. 6     18     10
C. 7     20     9
D. 9     6       20
Answer : A

Question. In the given figure, DO and CO are the bisectors of ∠ADC and ∠BCD respectively. If ∠ADC = ∠BCD = 60°, and ∠DAB = 100°, find the measures of ∠DOC and ∠ABC respectively.

A. 160°, 40°
B. 110°, 140°
C. 120°, 140°
D. 140°, 120°
Answer : C

Question. The volume of two cubes is in the ratio 1 : 64. If the volume of the larger cube is 504 cm3 more than that of the smaller cube, then
(a) What is the volume of the smaller cube?
(b) What is the length of each side of the larger cube?
       (a)             (b)
A. 8 cm³        8 cm
B. 8 cm³        7 cm
C. 7 cm³        8 cm
D. 7 cm         8 cm³
Answer : A

Question. What must be subtracted from x⁴ + 2x² – 3x + 7 to get x³ + x² + x – 1?
A. x⁴ – x³ + x² – 4x + 8
B. x³ + x² – 4x + 8
C. x⁴ – x³ + x² + 4x – 8
D. x⁴ – x³ – x² + 4x – 8
Answer : A

Question. Six more than four times a number is four less than five times the same number. Find the number.
A. 7
B. 8
C. 10
D. 9
Answer : C

Question. Match the following

A. (1) → (t), (2) → (s), (3) → (r), (4) → (p), (5) → (q)
B. (1) → (p), (2) → (q), (3) → (r), (4) → (s), (5) → (t)
C. (1) → (r), (2) → (q), (3) → (t), (4) → (p), (5) → (s)
D. (1) → (q), (2) → (r), (3) → (p), (4) → (t), (5) → (s)
Answer : D

Question. If 

A. 728/9
B. 520/27
C. 728/27
D. 328/15
Answer : C

Question. If 5^{x –1} + 5^x + 5^{x + 1} = 775, then the value of x, where x is a positive integer is .
A. 1
B. 3
C. 2
D. 4
Answer : B

Question. What is the approximate value of (15.01)² × √730 ?
A. 6125
B. 6225
C. 6200
D. 6100
Answer : D

Question. How many non-overlapping triangles can we make in a n-gon (polygon having n sides), by joining the vertices?
A. n – 1
B. n – 2
C. n – 3
D. n – 4
Answer : B

Question. To construct a unique parallelogram, the minimum number of measurements required is .
A. 2
B. 3
C. 4
D. 5
Answer : B

Question. Mohit invests a sum of ₹ 41,250 at the rate of 6% per annum. What approximate compound interest will he obtain at the end of 3 years?
A. ₹ 8,100
B. ₹ 7,425
C. ₹ 8,210
D. ₹ 7,879
Answer : D

Question. If x² + y² = 47 and xy = 19/2, then the value of 2(x + y)² + (x – y)² is .
A. 160
B. 270
C. 226
D. 86
Answer : A

Question. The numerical expression 3/8 + (-5)/7 = -19/56 shows that
A. Rational numbers are closed under addition.
B. Rational numbers are not closed under addition.
C. Rational numbers are closed under multiplication.
D. Addition of rational numbers is not commutative.
Answer : A

Question. If one member of a pythagorean triplet is 2m, then the other two members are .
A. m, m² + 1
B. m² + 1, m² – 1
C. m², m² – 1
D. m², m + 1
Answer : B

Question. Sam cut out 6 identical circles from a rectangular piece of paper. Find the shaded area. (Take π = 22/7)

A. 62 cm²
B. 294 cm²
C. 63 cm²
D. 98 cm²
Answer : C

EVERYDAY MATHEMATICS

Question. Mini buys 39/20 kg ghee at the rate ₹ 166 per kg, 3/5 kg butter at the rate of ₹ 90 per kg and 9/5 kg peas at the rate of ₹ 75 per kg. If she gives a ₹ 1000 note to the shopkeeper, how much change should she get back?
A. ₹ 487.30
B. ₹ 512.70
C. ₹ 524.70
D. ₹ 647.40
Answer : A

Question. 4096 soldiers are arranged in an auditorium in such a manner that there are as many soldiers in a row as there are rows in the auditorium. How many rows are there in the auditorium?
A. 94
B. 58
C. 44
D. 64
Answer : D

Question. A person has to completely put each of the three liquids i.e. 403 litres of petrol, 465 litres of diesel and 496 litres of mobil oil in bottles of equal size without mixing any of the three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required ?
A. 44
B. 34
C. 31
D. 43
Answer : A

Question. Sonika spent ₹ 45760 on the interior decoration for her home, ₹ 27896 on buying air conditioner and the remaining 28% of the total amount she had as cash with her. What was the total amount?
A. ₹ 98540
B. ₹ 102300
C. ₹ 134560
D. Cannot be determined
Answer : B

Question. The compound interest earned by Suresh on a certain amount at the end of two years at the rate of 8% per annum was ₹ 1414.40. What was the total amount that Suresh got back at the end of two years in the form of principal plus interest earned?
A. ₹ 9414.40
B. ₹ 9914.40
C. ₹ 9014.40
D. ₹ 8914.40
Answer : B

Question. A man sells a book at a profit of 20%. If he had bought it at 20% less and sold it for ₹ 18 less, he would have gained 25%. The cost price of the book is .
A. ₹ 80
B ₹ 70
C. ₹ 60
D. ₹ 90
Answer : D

Question. Amar wrote exams in four subjects - Physics, Chemistry, Biology and Social Studies. The ratio of marks he got in these exams was 2 : 3 : 4 : 5. He got an aggregate of 70% in these exams. Each exam had the same maximum marks. In how many of these exams did he get more than 50%?
A. 1
B. 2
C. 3
D. 4
Answer : C

Question. A swimming pool is 24 m long and 15 m broad, when a number of men dive into the pool, the height of the water rises by 1 cm. If the average amount of water displaced by one of the men be 0.1 cu. m, how many men are there in the pool?
A. 42
B. 46
C 32
D. 36
Answer : D

Question. Present ages of Trishika and Sanchi are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Sanchi’s present age?
A. 24 years
B. 27 years
C. 40 years
D. 30 years
Answer : A

Question. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
A. 20 hours
B. 18 hours
C. 25 hours
D. 19 hours
Answer : A

ACHIEVERS SECTION

Question. State 'T' for true and 'F' for false.
(i) y² + 9 is a linear equation in one variable.
(ii) The terms linear equation and linear expression are same.
(iii) If x is an even number, then the next odd number is (2x + 1).
(iv) If both sides of an equation is to be divided by the same (non-zero) number, then there is a change in equality.
(v) 1 is the solution of 2x + 1 / 3x + 5 = 3/8
    (i)   (ii)   (iii)  (iv)  (v)
A. T     F     T     F     T
B. T     T     T     T     T
C. F     F     F     F    T
D. F     T     F     F    F
Answer : C

Question. Which of the following statements is/are true?
Statement 1 : The value of a car depreciates at the rate of 10% per year. A car which was bought three years back is now worth ₹ 473850. Its original price was ₹ 650000.
Statement 2 : In fixed deposit, a bank gives 10% interest compounded annually for senior citizens.
In 6 years it will take for a sum of money to be double.
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. If seven slips of paper are labelled as 1, 2, 3, 4, 6, 7, 8 and one is drawn out of it, then
(i) What is the probability that it is a 3?
(ii) What is the probability that it is greater than 5?
(iii) What is the probability that it is an even number?
      (i)      (ii)     (iii)
A. 1/7     3/7     4/7
B. 1/7     4/7     3/7
C. 1/7     2/7     5/7
D. 1/7     5/7     2/7
Answer : A

Question. Match the following:

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

Question. Which of the following is correct with respect to the given solids?

Answer : B