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IMO - Mock Test - 2

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IMO - Mock Test - 2
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  • Question 1
    1.2 / -0
    3 A # 7 & 8 9 J @ 6 K L ! T ? P 4 2 W %

    If all the letters are dropped, then which among the following would be fifth from the right?
    Solution
    If all the letters are dropped, then the sequence would be as follows:
    3 # 7 & 8 9 @ 6 ! ? 4 2 %
    Hence, '!' would be fifth from the right.
  • Question 2
    1.2 / -0
    Which of the following will replace the question mark in the given series?

    7, 2, 11, 4, 15, 6, 19, ?
    Solution
    7, 2, 11, 4, 15, 6, 19, ?
    The given series consists of 2 series.
    1st series: 7, 11, 15, 19
    7 + 4 = 11
    11 + 4 = 15
    15 + 4 = 19
    2nd series: 2, 4, 6, ?
    2 + 2 = 4
    4 + 2 = 6
    6 + 2 = ?
    The next term comes from the 2nd series.
    So, next term = 6 + 2 = 8
  • Question 3
    1.2 / -0
    Out of the given options, choose the correct one to replace the question mark.

    ADEF : BEFG : : CFGH : ?
    Solution
    In the first part:
    ADEF : BEFG
    A + 1 = B
    D + 1 = E
    E + 1 = F
    F + 1 = G
    Similarly,
    C + 1 = D
    F + 1 = G
    G + 1 = H
    H + 1 = I
    Hence, CFGH : DGHI
  • Question 4
    1.2 / -0
    Shilpa wants to dress up for a party. She has two pairs of jeans and four tops. In how many ways can she choose her dress?
    Solution
    Number of pairs of jeans with Shilpa = 2
    Number of tops with her = 4
    With 1 pair of jeans, she can opt for any of the 4 tops.
    Total combinations with 1 pair of jeans are 4.
    Similarly, total combinations with the other pair of jeans are 4.
    Hence, total combinations are 8.
  • Question 5
    1.2 / -0
    How many straight lines are there in the given figure?

    Solution


    There are total 9 lines in this figure namely a, b, c, d, e, f, g, h and i.
  • Question 6
    1.2 / -0
    How many dots will there be in figure E?

    Solution
    Number of dots in figure A = 1
    Number of dots in figure B = 1 + 1 = 2
    Number of dots in figure C = 2 + 2 = 4
    Number of dots in figure D = 4 + 3 = 7
    Number of dots in figure E = 7 + 4 = ?
    The pattern used is: +1, +2, +3, +4.
    Therefore, number of dots in figure E = 7 + 4 = 11
  • Question 7
    1.2 / -0
    Find the number that will come in place of the question mark.

    Solution


    Hence, ? = 11 + 10 = 21
  • Question 8
    1.2 / -0
    What should come in the place of the question mark in the following series?

    3, 8, 6, 16, 12, 27, ?
    Solution
    3, 8, 6, 16, 12, 27, ?
    The pattern used is: +5, -2, +10, -4, +15, -6, and so on.
    3 + 5 = 8
    8 – 2 = 6
    6 + 10 = 16
    16 – 4 = 12
    12 + 15 = 27
    27 – 6 = 21
    Hence, 21 is the required answer.
  • Question 9
    1.2 / -0
    If in a certain code language, REDDISH is coded as TGFFKUJ, then how will you code CARROT in that language?
    Solution
    Here, REDDISH is coded as TGFFKUJ.
    R + 2 = T
    E + 2 = G
    D + 2 = F
    D + 2 = F
    I + 2 = K
    S + 2 = U
    H + 2 = J
    Similarly,
    For CARROT:
    C + 2 = E
    A + 2 = C
    R + 2 = T
    R + 2 = T
    O + 2 = Q
    T + 2 = V
    Hence, CARROT will be coded as ECTTQV.
  • Question 10
    1.2 / -0
    If Rita goes for swimming on every 5th day in the month of April, starting from April 3, then which date would be her last day of practice for the month?

    Solution


    As per the given data, the dates in the month of April on which she goes for swimming are: 3, 8, 13, 18, 23, 28.
    Hence, the last day of her practice will be April 28.
  • Question 11
    1.2 / -0
    Which of the following figures will have the given figure embedded in it?

    Solution


    Hence, option (2) is correct.
  • Question 12
    1.2 / -0
    Find the wrong term in given series.

    1, 6, 13, 28, 33, 46.
    Solution
    1, 6, 13, 28, 33, 46
    The pattern followed is as given below:
    2 × 2 - 3 = 1
    3 × 3 - 3 = 6
    4 × 4 - 3 = 13
    5 × 5 - 3 = 22
    6 × 6 - 3 = 33
    7 × 7 - 3 = 46
    Hence, 28 is the wrong term.
  • Question 13
    1.2 / -0
    One out of the following is different from the rest in some way. Pick the odd one out.
    Solution
    134 = 2 × 67
    153 = 3 × 51
    167 = 1 × 167
    183 = 3 × 61
    All the numbers, except 167, are composite numbers. Only 167 is a prime number.
  • Question 14
    1.2 / -0
    If '-' means '÷', '÷' means '+', '×' means '-', and '+' means '×', then find the value of 4 + 16 × 32 - 8 ÷ 4.
    Solution
    The required expression is as follows:
    4 × 16 - 32 ÷ 8 + 4
    Now, using BODMAS, we get
    4 × 16 - 32 ÷ 8 + 4 = 4 × 16 - 4 + 4
    = 64 - 4 + 4 = 64
  • Question 15
    1.2 / -0
    Count the cubes in the figure given below:
    Solution


    Number of cubes in column 1 = 3
    Number of cubes in column 2 = 2
    Number of cubes in column 3 = 2
    So, total number of cubes in the figure = 3 + 2 + 2 = 7
  • Question 16
    1.2 / -0
    Rahul went to play cricket in the evening. The time at which the game started and ended is shown in the clocks below.

    For how long did the game last?

    Solution
    Starting time is 4:50 pm.
    Ending time is 6:20 pm.
    Total time taken = (4:50 to 5:50 = 1 hour) + (5:50 to 6:20 = 30 minutes) = 1 hour and 30 minutes
  • Question 17
    1.2 / -0
    What would be the perimeter of the rectangle if its length is 7 cm and the area is 35 cm2?
    Solution
    Area of the rectangle = l × b
    35 cm2 = 7 cm × b

    b = cm

    b = 5 cm
    Now, perimeter of the rectangle = 2(l + b)
    = 2(7 + 5) cm = 2(12) cm = 24 cm
  • Question 18
    1.2 / -0
    How many lines of symmetry are there in a scalene triangle?
    Solution
    There is no line that will divide scalene triangle in equal parts.
    Hence, a scalene triangle will have 0 or no line of symmetry.
  • Question 19
    1.2 / -0
    Johny built a hall, which was in a cuboid shape. What would be the volume of the hall if the length, breadth and height of the hall were 15 m, 13 m, and 10 m, respectively?
    Solution
    Volume of the cuboid = l × b × h
    = 15 m × 13 m × 10 m
    = 1950 m3
  • Question 20
    1.2 / -0
    The marks obtained by 40 students of a class in an examination are given below:

    8, 47, 22, 31, 17, 13, 38, 26, 3, 34, 29, 11, 22, 7, 1, 24, 38, 31, 21, 35, 42, 24, 45, 23, 21, 27, 29, 49, 25, 48, 21, 15, 18, 27, 19, 45, 14, 34, 37, 34

    How many students got the marks that are prime numbers?
    Solution
    Prime numbers have only 2 factors: 1 and the number itself.
    The prime numbers from the above data are as given below:
    47, 31, 17, 13, 3, 29, 11, 7, 23, 19, 37
    But 31 and 29 are repeated.
    Hence, there are 13 students who got marks that are prime numbers.
  • Question 21
    1.2 / -0
    If the radius of a circle is 17.89 m, then what would be its diameter in cm?
    Solution
    Radius of the circle = 17.89 m
    Diameter of the circle = 2 × radius
    = 2 × 17.89 m = 35.78 m
    As 1 m = 100 cm,
    So, 35.78 m = 35.78 × 100 cm = 3578 cm
  • Question 22
    1.2 / -0
    Find out the HCF of 32 and 48.
    Solution
    Factors of 32 = 2 × 2 × 2 × 2 × 2
    Factors of 48 = 2 × 2 × 2 × 2 × 3
    Product of all common prime factors is the HCF.
    So, HCF = 2 × 2 × 2 × 2 = 16
  • Question 23
    1.2 / -0
    What will be the area of the triangle having base 12 cm and height 10 cm?
    Solution
    Base of the triangle = 12 cm
    Height of the triangle = 10 cm

    Area of the triangle = × base × height
    = × 12 cm x 10 cm = 60 cm2
  • Question 24
    1.2 / -0
    Four players are playing a card game and all the cards have been equally divided among the four players.

    If one player out of them has four cards of hearts, then what fraction of cards with him are cards of hearts?
    Solution
    Number of cards with each player = 52 ÷ 4 = 13
    Number of cards of hearts = 4

    Required fraction =
  • Question 25
    1.2 / -0
    Express the answer of as decimal.
    Solution



    =

    =

    =

    = 0.75
  • Question 26
    1.2 / -0
    What will be the simplest form of the fraction of red cards in a deck of 52 playing cards, if there are 26 red cards?
    Solution
    Number of red cards in the deck of cards = 26
    Total number of cards = 52

    Required fraction =
  • Question 27
    1.2 / -0
    In a certain way, if 100 divided by 50 is 1, 270 divided by 90 is 2, then in the same way, what will 500 ÷ 100 be equal to?
    Solution
    100 ÷ 50 = 2, but 2 has been changed to (2 - 1) = 1
    270 ÷ 90 = 3, but 3 has been changed to (3 - 1) = 2
    So, 500 ÷ 100 = 5, but 5 should be changed to (5 - 1) = 4
  • Question 28
    1.2 / -0
    What is the number of digits that can come in place of the question mark to make it divisible by 9?

    817?218
    Solution
    To make it divisible by 9, sum of the digits should be divisible by 9.
    Sum of digits = 8 + 1 + 7 + ? + 2 + 1 + 8 = 27 + ?
    So, 27 + ? should be divisible by 9. So, ? can be 0 and 9
    Hence, 2 digits either 0 or 9 can come in the place of '?'.
  • Question 29
    1.2 / -0
    Amit can cover 100 km in 10 hours. How much distance can he cover in 15 hours?
    Solution
    Distance covered in 10 hours = 100 km

    Distance covered in 1 hour = km = 10 km

    Distance covered in 15 hours = 15 × 10 km = 150 km
  • Question 30
    1.2 / -0
    The ratio of number of elephants to that of crocodiles in a zoo is 3 : 5. If there are a total of 160 elephants and crocodiles in the zoo, then find the number of elephants.
    Solution
    Let the number of elephants be 3x.
    Number of crocodiles = 5x
    According to the question,
    Number of elephants + Number of crocodiles = Total number of animals
    3x + 5x = 160
    8x = 160
    x = 20
    So, number of elephants = 3x = 3 × 20 = 60
  • Question 31
    1.2 / -0
    What will be the time taken by Karan to solve a Rubik's Cube if he takes 12 seconds for each turn and can solve it in 29 turns?

    Solution
    Time taken for each turn = 12 seconds
    Number of turns = 29
    Total time taken = 29 × 12 seconds = 348 seconds
    So, 348 seconds = 300 seconds + 48 seconds
    As, 1 minute = 60 seconds

    So, 348 seconds = minutes + 48 seconds

    = 5 minutes 48 seconds
  • Question 32
    1.2 / -0
    If the perimeter of a square is equal to the perimeter of a rectangle with length 10 units and breadth 8 units, then what will be the area of the square in sq. units?
    Solution
    Length of the rectangle = 10 units
    Breadth of the rectangle = 8 units
    Perimeter of the rectangle = 2 (length + breadth) = 2 (10 + 8) units = 36 units
    According to the question,
    Perimeter of the square = Perimeter of the rectangle
    So, 4 × Side = 36 units
    or, Side = (36 ÷ 4) units = 9 units
    So, area of the square = 9 units × 9 units = 81 sq. units.
  • Question 33
    1.2 / -0
    What will be the area (in sq. units) of the largest square formed whose side is a single digit and a multiple of 3?
    Solution
    Multiples of 3 which are single digits: 3,6,9
    So, largest side = 9 units.
    Hence, largest area = 9 × 9 sq. units = 81 sq. units
  • Question 34
    1.2 / -0
    of the students in an Art class are currently painting with water colours. Another of them are painting with oil colours. What fraction of the students in the Art class are painting?
    Solution
    Fraction of students painting with water colours =

    Fraction of students painting with oil colours =

    Total fraction of students painting =
  • Question 35
    1.2 / -0
    In a party, there are 12 tables and 4 persons can sit at each table. How many plates are required in total if a person needs one plate for starter and one for main course?
    Solution
    Number of persons who can sit on a table = 4
    Number of tables = 12
    Total number of persons = 12 × 4 = 48
    Now, number of plates required by 1 person = 2
    So, number of plates required for 48 persons = 48 × 2 = 96
  • Question 36
    1.2 / -0
    A pattern is given below:



    Find the value of one triangle, if the value of a star is 2.
    Solution
    Given:



    Value of star = 2
    By putting the value of star in the question, we get



    Or 3 × Triangle = 30
    So, value of triangle = 10
  • Question 37
    1.2 / -0
    Sanchit is reading a book in which there are 1129 pages. How is 1129 written in Roman Numerals?
    Solution
    As, M = 1000
    C = 100
    X = 10
    V = 5
    I = 1
    So, 1129 = 1000 + 100 + 10 + 10 + 10 − 1 = 1000 + 100 + 20 + 9 = MCXXIX
  • Question 38
    1.2 / -0
    Sonam goes to school by bus and it takes 35 minutes to reach the school. If she leaves home at 7:25 am and the bus is 5 minutes late, then at what time does she reach school?
    Solution
    Time of leaving = 7:25 am
    Time taken to reach school = 35 minutes.
    Time by which bus is late = 5 minutes
    Total time to reach school = 40 minutes
    Time at which Sonam reaches school is 7:25 am + 40 minutes = 8:05 am.
  • Question 39
    1.2 / -0
    It is Aman's birthday and he gets 190 toffees to distribute among his 21 friends. What will be the number of toffees left over, if he tries to distribute them completely?
    Solution
    Number of toffees = 190
    Number of friends = 21
    Number of toffees given to each friend = 190 ÷ 21



    So, 1 toffee will be left with him.
  • Question 40
    1.2 / -0
    In total, an orchard has 145 trees and 5 rows. What is the number of columns in the orchard?
    Solution
    Total number of trees = 145
    Number of rows = 5
    Number of columns = 145 ÷ 5 = 29
  • Question 41
    1.2 / -0
    Given are the temperatures in 4 cities.

    A: 0 degrees
    B: – 1 degrees
    C: – 2 degrees
    D: 3 degrees

    In which city, was the temperature lowest?
    Solution
    The increasing order is:
    - 2 < - 1 < 0 < 3
    So, C < B < A < D
    Hence, the city with lowest temperature is C.
  • Question 42
    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 sunflower ?
    Solution
    Sunflower is actually yellow in colour. According to the question, 'yellow' is called 'green'.
  • Question 43
    1.2 / -0
    Given is a division problem:



    Find the value of:

    X - Y + W × Z
    Solution


    The value of X = 8, Y = 3, Z = 1 and W = 7.
    So, X - Y + W × Z = 8 – 3 + 7 × 1
    Using BODMAS, we get
    8 – 3 + 7 × 1 = 8 - 3 + 7 = 5 + 7 = 12
  • Question 44
    1.2 / -0
    Ashley has Rs. 495 in his pocket. She wants to buy crayons, and a pack of crayons costs Rs. 5.50. How many crayons can Ashley buy if there are 9 crayons in each pack?
    Solution
    Cost of 1 pack of crayons = Rs. 5.50
    Amount she has in her pocket = Rs. 495

    Number of packs that she can buy = = 90

    Number of crayons in 90 packs = 9 × 90 = 810
  • Question 45
    1.2 / -0
    Raghav wants to fence his plot from all four sides. The cost of fencing is Rs. 30 per/metre and he pays Rs. 15,000 in all. What is the measure of the length (in metres), if it is 40 metres more than the breadth?
    Solution
    Let, breadth = x metres
    Length = (x + 40) metres
    Perimeter = 2(length + breadth) = 2(x + 40 + x) metres = 2(2x + 40) metres
    According to the question:
    2(2x + 40) × 30 = 15,000
    or, 2x + 40 = 250
    or, 2x = 210
    or, x = 105
    Hence, length = 105 + 40 metres = 145 metres
  • Question 46
    1.2 / -0
    The pictograph below shows the number of cupcakes sold by a shopkeeper on different days in a week.



    How many more cupcakes were sold on Saturday and Monday combined than on Sunday and Thursday combined?
    Solution
    One cupcake in the figure represents 5 cupcakes.
    So, number of cupcakes sold on Saturday and Monday = (10 + 4) × 5 = 14 × 5 = 70
    Number of cupcakes sold on Sunday and Thursday = (9 + 3) × 5 = 12 × 5 = 60
    Difference between the number of cupcakes sold on Saturday and Monday and that on Sunday and Thursday = 70 - 60 = 10
  • Question 47
    1.2 / -0
    Part of a scale is shown below. What is the value of reading 'X'?

    Solution
    From 10.90 to 11.00, it is divided into 5 parts.
    So, measure of each part = (11.00 - 10.90)/5 = 0.02
    So, the scale reading is as follows:


    Going by this pattern: X = 11.24 cm
  • Question 48
    1.2 / -0
    Andrew and his brother buy 4 burgers and 2 pizzas. How much do they need to pay?

    Solution
    Cost of 8 burgers = Rs. 400
    Cost of 1 burger = Rs. 400 ÷ 8 = Rs. 50
    Cost of 4 burgers = Rs. 50 × 4 = Rs. 200
    Cost of 5 pizzas = Rs. 500
    Cost of 1 pizza = Rs. 500 ÷ 5 = Rs. 100
    Cost of 2 pizza = Rs. 100 × 2 = Rs. 200
    Total amount to be paid = Rs. (200 + 200) = Rs. 400
  • Question 49
    1.2 / -0
    A city recorded the number of people who went to the cafeteria each day.



    What is the ratio of number of riders who went to cafeteria on Tuesday and Saturday to the number of riders who went on Wednesday and Thursday?
    Solution
    Number of riders who went on Tuesday and Saturday = 6,598 + 6,596 = 13,194
    Number of riders who went on Wednesday and Thursday = 6,691 + 6,698 = 13,389
    Required Ratio = 13,194 : 13,389 = 4,398 : 4,463
  • Question 50
    1.2 / -0
    A taxi service charges Rs. 15 for the first km, Rs. 10 per kilometre for the next 5 km and Rs. 5 per kilometre for the remaining distance. Then, what will be the amount paid by Aman if he travels 13 km in the taxi?
    Solution
    Total distance that he travels is 13 km.
    Distance covered = (1 + 5 + 7) km
    Charges to be paid = Rs. 15 + 5 × Rs. 10 + 7 × Rs. 5
    = Rs. 15 + Rs. 50 + Rs. 35
    = Rs. 100
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