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IMO - Mock Test - 3

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IMO - Mock Test - 3
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  • Question 1
    1.2 / -0
    What will come in place of the question mark?

    4 : 60 : : 5 : ?
    Solution
    Here,
    4 × 15 = 60
    So, 5 × 15 = 75
  • Question 2
    1.2 / -0
    In a modern art painting, there are 4 green dots in the first row, 12 green dots in the second row, 36 green dots in the third row, and 108 green dots in the fourth row. If this pattern continues, how many green dots will there be in the fifth row?
    Solution
    In the pattern, each number is multiplied by 3 to find the next number:

    There will be 324 green dots in the fifth row.
  • Question 3
    1.2 / -0
    Given is the diagram showing the mobile phones the students of a college have.



    According to the diagram, how many students have more than two mobile phones?
    Solution


    There are two students who have more than 2 mobile phones.
  • Question 4
    1.2 / -0
    Which of the following is to the immediate left of the eighth character from the right of the given number-letter arrangement?

    FBR57SDGVRNE4N
    Solution
    FBR57SDGVRNE4N

    The eighth character from the right of FBR57SDGVRNE4N is D.

    To the immediate left of D is S.
  • Question 5
    1.2 / -0
    Pick the odd one out of the following:
    Solution
    34 = 17 × 2
    68 = 17 × 4
    153 = 17 × 9
    All other numbers except 123 are multiples of 17.
  • Question 6
    1.2 / -0
    According to reverse alphabetical order, which letter is fourth to the left of the seventh letter from the left?
    Solution
    Reverse alphabetical order = ZYXWVUTSRQPONMLKJIHGFEDCBA
    7th letter from the left = ZYXWVUTSRQPONMLKJIHGFEDCBA = T
    4th to the left of T = ZYXWVUTSRQPONMLKJIHGFEDCBA = X
  • Question 7
    1.2 / -0
    Find the value of



    If
    Solution

    So,
    Now,
    So,
    Also,
    Hence,
  • Question 8
    1.2 / -0
    Which of following will replace the question mark?

    Dog : Puppy : : Cow : ?
    Solution
    Puppy is the young one of dog and calf is the young one of cow.
  • Question 9
    1.2 / -0


    Using the paths shown, how long is the shortest route from city H to city C?
    Solution
    There are two ways to reach city C.
    One is from city H to city L and finally to city C.
    Its total distance = (15.1 + 11.5) km = 26.6 km
    Another way is from city H to city G to city L and finally to city C.
    Its total distance = (9.4 + 7.0 + 11.5) km = 27.9 km
    Therefore, the shortest distance is 26.6 km long.
  • Question 10
    1.2 / -0
    If "CODING" is coded as "DPEJOH", then how will "PAGE" be coded?
    Solution
    "CODING" is coded as "DPEJOH".
    It implies the following:
    C + 1 = D
    O + 1 = P
    D + 1 = E
    I + 1 = J
    N + 1 = O
    G + 1 = H
    Similarly,
    P + 1 = Q
    A + 1 = B
    G + 1 = H
    E + 1 = F
    So, "PAGE" will be coded as "QBHF".
  • Question 11
    1.2 / -0
    Count the number of cubes in the figure given below:


    Solution


    Number of cubes in row 1 = 1
    Number of cubes in row 2 = 1
    Number of cubes in row 3 = 2
    Number of cubes in row 4 = 3
    Number of cubes in row 5 = 1
    Total number of cubes = 1 + 1 + 2 + 3 + 1 = 8
  • Question 12
    1.2 / -0
    Charlie goes 5 km towards North-East from a fixed point and from there he goes 3 km towards West. In which direction is he from his starting point?
    Solution


    So, Charlie is pointing the North direction from the starting point.
  • Question 13
    1.2 / -0
    Find the missing time in the series:

    09:30, 09:20, _____, 09:00, 08:50
    Solution
    In the series, the sequence is that it is getting lowered by 10 min each time.
    9:30 - 10 min = 9:20
    9:20 - 10 min = 9:10
    9:10 - 10 min = 9:00
    9:00 - 10 min = 8:55
    So, it will be 9:10.
  • Question 14
    1.2 / -0
    If 5x means 1 × 2 × 5 × 6, thus 5x = 60, and if 6x means 1 × 2 × 6 × 7, thus 6x = 84, then 8x is equal to
    Solution
    5x means 1 × 2 × 5 × 6 = 60.
    6x means 1 × 2 × 6 × 7 = 84.
    The pattern followed is 1 × 2 × number × (number + 1)
    So, 8x means 1 × 2 × 8 × 9 = 144.
  • Question 15
    1.2 / -0
    What number should replace the question mark in the given series?

    1, 4, 2, 5, 3, 6, 4, ?
    Solution
    1, 4, 2, 5, 3, 6, 4, ?
    The series consists of 2 sub-series.
    1st series: 1, 2, 3, 4

    1
    1 + 1 = 2
    2 + 1 = 3
    3 + 1 = 4
    2nd series: 4, 5, 6, ?

    4
    4 + 1 = 5
    5 + 1 = 6
    6 + 1 = ? = 7
    So, the missing number is '7'.
  • Question 16
    1.2 / -0
    Find the area of the square if its perimeter is 26 cm.
    Solution
    Perimeter of the square = 26 cm
    Or 4 × side = 26 cm
    Side = 6.5 cm
    So, area of the square = 6.5 cm × 6.5 cm
    = 42.25 cm2
  • Question 17
    1.2 / -0
    Which among the following is not a factor 48?
    Solution
    The factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
    So, 32 is not a factor of 48.
  • Question 18
    1.2 / -0
    Find the total number of common multiples of 8 and 12 from the following list of multiples:

    24, 36, 56, 72, 48, 96, 88
    Solution
    Prime factorisation of 8: 2 × 2 × 2
    Prime factorisation of 12: 2 × 2 × 3
    LCM of 8 and 12 = 2 × 2 × 2 × 3 = 24
    So, all multiples of 24 are the common multiples of 8 and 12.
    So, 24, 48, 72 and 96 are the required common multiples of 8 and 12.
    Hence, there are 4 common multiples in the given list.
  • Question 19
    1.2 / -0
    Which number should be added to 8.96 to get the result as 14.01?
    Solution
    Let the number be X.
    So, 8.96 + X = 14.01
    Hence, X = 14.01 - 8.96 = 5.05
  • Question 20
    1.2 / -0
    Raman has 209 candies with him. How would you represent the number of candies he has in Roman numeral?
    Solution
    We know,
    C = 100 and IX = 9
    So, 209 = 100 + 100 + 9 = CCIX
  • Question 21
    1.2 / -0
    Vivek is studying decimals. He does not know about rounding. He wants to round 7.502 to the nearest hundredth. Can you help him to select the right answer?
    Solution
    Step 1: Find the digit at the hundredth place in 7.502.
    So, it is 0.
    Step 2: Check the digit at the thousandth place in it.
    It is 2.
    As 2 < 5, so the digit at the hundredth place will remain the same.
    Hence, the number after rounding to the nearest hundredth is '7.50'.
  • Question 22
    1.2 / -0
    A car leaves at 8:30 a.m. and arrives Chennai at 1:30 p.m. It covers the distance of 250 km. Find the average speed of the car.
    Solution
    Total distance = 250 km
    Total time from 8:30 a.m. to 1:30 p.m. = 5 hours
    Average speed = Total distance/Total time
    = 250 km ÷ 5 hours = 50 km/h
  • Question 23
    1.2 / -0
    Which of the following is the least common multiple of 3, 12 and 25?
    Solution
    Prime factorisation of 3: 3
    Prime factorisation of 12: 2 × 2 × 3
    Prime factorisation of 25: 5 × 5
    Least common multiple of 3, 12 and 25 = 2 × 2 × 3 × 5 × 5 = 300
  • Question 24
    1.2 / -0
    The following graph shows that how many persons like the different flavours of ice cream:



    Here,
    A = Apple
    V = Vanila
    S = Strawberry
    B = Butterscotch
    M = Mango
    P = Pineapple

    Which is the most popular flavour after Pineapple?
    Solution
    Since Mango flavour is liked by the maximum number of people after Pineapple, this is the correct answer.
  • Question 25
    1.2 / -0
    Given below is a right-angled triangle, right-angled at A. If C = 55°, find the measure of B.


    Solution
    A = 90°
    C= 55°
    Sum of the angles of a triangle = 180°
    So, A + B + C = 180°
    Or 90° + B + 55° = 180°
    So, 145° + B = 180°
    Or B = 180° - 145° = 35°
  • Question 26
    1.2 / -0
    Which of the following is not equivalent to ?
    Solution








    Hence, is not equivalent to .
  • Question 27
    1.2 / -0
    Find the value of 9 + 6 - 8 + 3 × 7 + 4.
    Solution
    Using BODMAS
    9 + 6 - 8 + 3 × 7 + 4
    = 9 + 6 - 8 + 21 + 4
    = 15 - 8 + 21 + 4
    = 32
  • Question 28
    1.2 / -0
    Which of the following is the heaviest?
    Solution
    Option 1: 1 kg and 100 g = 1000 g + 100 g = 1100 g
    Option 2: 1 kg and 180 g = 1000 g + 180 g = 1180 g
    Option 3: 1190 g
    Option 4: 1100 g
    Now, 1190 > 1180 > 1100
    So, 1190 g is the heaviest.
  • Question 29
    1.2 / -0
    How many faces does this shape have?

    Solution

    There are 5 faces: 4 triangular faces and 1 square face at the base.
  • Question 30
    1.2 / -0


    If the perimeter of the given shape is 41 cm, then find the length of the missing side.
    Solution
    The perimeter of the shape is 41 cm.
    So, sum of all sides = 41 cm
    Let the missing side be 'x'.
    Then, (8 + 8 + 10 + 5 + x) cm = 41 cm
    So, (x + 31) cm = 41 cm
    or, x = 41 cm - 31 cm
    or, x = 10 cm
  • Question 31
    1.2 / -0
    If 'White' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Yellow', 'Yellow' is called 'Green', 'Green' is called 'Black', 'Black' is called 'Violet' and 'Violet' is called 'Orange', then what will be the colour of tomatoes?
    Solution
    Tomatoes are red in colour. But in this coded language, red is called yellow. Hence, yellow is the correct answer.
  • Question 32
    1.2 / -0
    Given is the graph of temperatures on different days:



    What is the difference between the temperatures on Day 2 and Day 5?
    Solution
    Temperature on Day 2 = 25°C
    Temperature on Day 5 = 30°C
    Required difference = 30°C - 25°C = 5°C
  • Question 33
    1.2 / -0


    The length of one side of the star is 5 cm, and all the sides have the same length. What is the perimeter of the star?
    Solution
    There are 10 sides in the given star.
    Length of each side = 5 cm
    Perimeter of the figure = Sum of all sides
    Length of all the sides is the same.
    So, sum of all the sides = 10 × Side
    Hence, the required perimeter = 10 × Side = 50 cm
  • Question 34
    1.2 / -0


    If ABCD is a square of side 5 cm, then what is the area of the shaded portion?
    Solution
    Area of the shaded portion = × Area of the square
    So, required area = × (5 × 5) cm2
    = 12.5 cm2
  • Question 35
    1.2 / -0
    If Ronit saves Rs. 145.78 in a month and Pawan saves Rs. 118.45 in a month, then how much more money does Ronit save than Pavan does?
    Solution
    Money Ronit saves in a month = Rs. 145.78
    Money Pawan saves in a month = Rs. 118.45
    Difference = Rs. 145.78 - Rs. 118.45 = Rs. 27.33
  • Question 36
    1.2 / -0
    Anjana wants to buy a pack of candies, each of which costs Rs. 40. If she has Rs. 160 with her, then how many maximum number of packs of candies can she buy?
    Solution
    Cost of one pack of candies = Rs. 40
    Amount she has = Rs. 160
    Number of packs of candies she can buy = 160 ÷ 40 = 4
  • Question 37
    1.2 / -0
    Find the total money earned by Ellie in a week if she gets Rs. 250 for a day.
    Solution
    Money she earns in a day = Rs. 250
    Money earned by Ellie in a week = 7 × Rs. 250 = Rs. 1750
  • Question 38
    1.2 / -0
    Jasmine spends Rs. 240.39 on Soft Drinks. Which digit is at hundreds place?
    Solution
    Number is 240.39
    Digit at one's place = 0
    Digit at ten's place = 4
    Digit at hundred's place = 2
    Hence, the required answer is 2.
  • Question 39
    1.2 / -0
    Ginni had Rs. 11.50 until he spent three 50-paise coins. How much money was left with Ginni?
    Solution
    Amount Ginni had with him = Rs. 11.50
    As, three 50 paise coins add up to 0.50 + 0.50 + 0.50 = 1.50
    Amount spent by Ginni = Rs. 1.50
    Amount left with Ginni = Rs. (11.50 – 1.50) = Rs. 10
    Hence, he was left with Rs. 10.
  • Question 40
    1.2 / -0
    A person is thinking of a number. He multiplies it by 18, divides it by 12 and then adds on 17 to it and the answer is 593. What number is that person thinking of?
    Solution
    Let the number be x.
    According to the question, x × 18 ÷ 12 + 17 = 593

    or, + 17 = 593

    or, = 593 - 17 = 576

    or = 576

    3x = 576 × 2

    x =

    So, x = 384
  • Question 41
    1.2 / -0
    Andrew went to watch a match. The match started at 4:10 pm and ended at 7:15 pm.

    How long did the match last?
    Solution
    Starting time = 4:10 pm
    Ending time = 7:15 pm
    Time for which the match lasted = (4:10 pm to 7:10 pm = 3 hours) + (7:10 pm to 7:15 pm = 5 minutes) = 3 hours and 5 minutes.
  • Question 42
    1.2 / -0
    Harry opens a new school for class L.K.G to class 5. There are 1176 desks to be placed in 28 classrooms. If equal numbers of desks are placed in each classroom, then how many desks will there be in each room?
    Solution
    Number of desks in 28 classrooms = 1176
    Number of desks in 1 classroom = 1176 28 = 42
    Hence, 42 desks are there in each classroom.
  • Question 43
    1.2 / -0
    Mandy measured a house and made a scale drawing. He used the scale 1 centimetre = 5 metres. If the actual length of the front portion of the house is 20 metres, then choose from the given options, how long will be the front portion of the house in the drawing?
    Solution
    For a drawing, 5 metres = 1 centimetres
    So, 1 metre = centimetres
    Hence, 20 metres = × 20 centimetres = 4 centimetres
  • Question 44
    1.2 / -0
    Which of the following is/are true?
    Solution
    Square is a polygon with all its 4 sides equal and all angles equal each 90°.
    Rectangle is a polygon with opposite sides equal and all angles equal to 90°. Hence, sum of its opposite angles is equal to 180°.
  • Question 45
    1.2 / -0
    Preetika bought 8.6 kilograms of mangoes, 4.2 kilograms of apples, 9.8 kilograms of oranges and 7.4 kilograms of bananas. After some time, she returned 3.5 kilograms of bananas and 4.2 kilograms of mangoes. How much fruit was left with her?
    Solution
    Quantity of fruits she bought = (8.6 + 4.2 + 9.8 + 7.4) kg = 30 kg
    Quantity of fruits she returned = (3.5 + 4.2) kg = 7.7 kg
    Quantity of fruits left with her = (30 - 7.7) kg = 22.3 kg
  • Question 46
    1.2 / -0
    Shine has 15 pink roses and 20 white roses with her. If she wants to make a bouquet with same number of flowers in each bouquet such that no flower is left over, then what is the greatest number of bouquets Shine can make?
    Solution
    Factors of 15 are 15, 5, 3, 1.
    Factors of 20 are 20, 10, 5, 4, 2, 1.
    The highest common factor of 15 and 20 is 5.
    So, number of flowers in 1 bouquet = 5

    Number of bouquets with pink roses = = 3

    Number of bouquets with white roses = = 4

    Total number of bouquets = 3 + 4 = 7
  • Question 47
    1.2 / -0
    Abhishek and Abninder each purchased a packet containing 95 sweets from a shop. The shopkeeper gave 5 extra sweets on each purchase. What was the total number of sweets Abhishek and Abninder had?
    Solution
    Number of purchases = 2 (1 of Abhishek and 1 of Abninder)
    Number of extra sweets = 2 × 5 = 10
    Number of sweets in 1 packet = 95
    Number of sweets in both the packets = 2 × 95 = 190
    Total number of sweets = 190 + 10 = 200
  • Question 48
    1.2 / -0
    What is the area of the given shape?

    Solution

    Area of rectangle = Length × Breadth
    Area of the figure = Area of rectangle I + Area of rectangle II
    Now, Area of rectangle I = 9 cm × 3 cm = 27 cm2
    Area of rectangle II = 6 cm × 3 cm = 18 cm2
    Total area = (27 + 18) cm2 = 45 cm2
  • Question 49
    1.2 / -0
    In a cinema hall, there was advanced booking of the tickets of the movie and the numbers of bookings were as follows:

    Monday: 7,258
    Tuesday: 9,257
    Wednesday: 7,356
    Thursday: 9,254
    Friday: 9,893

    How many more tickets were booked on Monday, Wednesday and Friday altogether than those booked on Tuesday and Thursday?
    Solution
    Tickets booked on Monday, Wednesday and Friday = 7,258 + 7,356 + 9,893 = 24,507
    Tickets booked on Tuesday and Thursday = 9,257 + 9,254 = 18,511
    Therefore, the difference = 24,507 - 18,511 = 5,996
    Hence, 5,996 more tickets were booked on Monday, Wednesday and Friday altogether than those booked on Tuesday and Thursday.
  • Question 50
    1.2 / -0


    Find out the value of A + B + C.
    Solution
    7 + 8 + C = 18
    Or, 15 + C = 18
    C = 18 - 15 = 3
    Now, 8 + 4 + 8 + 1(carry) = 21
    So, B = 1
    Proceeding in the same way, we get
    5 + 3 + A = 9
    or, 8 + A = 9
    A = 1

    So, A = 1, B = 1 and C = 3
    Hence, A + B + C = 1 + 1 + 3 = 5
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