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IMO - Mock Test - 8

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IMO - Mock Test - 8
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  • Question 1
    1.2 / -0
    The letters S and T stand for numbers. If S - 100 = T - 100, than which statement is true?
    Solution
    We have,
    S - 100 = T - 100
    S = T - 100 + 100 S = T
  • Question 2
    1.2 / -0
    There is a certain rule being followed in figures (i), (ii) and (iii). Identify the rule and find the missing number.


    Solution
    The pattern is,
    6, 21, 81 and 93 all are divisible by 3.
    24, 18, 96 and 108 all are divisible by 6.
    So, from the options only 729 is divisible by 9.
  • Question 3
    1.2 / -0
    The given diagram shows four persons stationed at the four corners of a square piece of plot. B starts crossing the field diagonally. After walking half the distance, he turns right, walks some distance and turns left. Which direction is B facing now?

    Solution
  • Question 4
    1.2 / -0
    How many dots lie opposite to the face having four dots, when the given net of cube is folded?

    Solution
    The opposite faces are (4, 5), (6, 3) and (1, 2).
  • Question 5
    1.2 / -0
    Which of the following shapes do not have a line of symmetry?


    Solution


    Shape P and R do not have any line of symmetry.
  • Question 6
    1.2 / -0
    Select the correct mirror image of the Figure (X).


    Solution
  • Question 7
    1.2 / -0
    Identify the two figures which are out of position/place and require interchanging of position to put the entire series in order.

    Solution
    The correct series is:


  • Question 8
    1.2 / -0
    Which of the following diagrams satisfies the condition of placement of dot as in the given Figure (X)?

    Solution
    In Figure (X), the dot is placed in the common area of circle, triangle and rectangle only. The figure in option 2 satisfies the given condition.

  • Question 9
    1.2 / -0
    Given below is a set of three figures X, Y, Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the paper has been cut. Select the figure from the options which shows the unfolded form of the paper.

    Solution
    Unfolded form of the paper is:


  • Question 10
    1.2 / -0
    If is related to , then is related to _________.
    Solution
    Four sided figure is rotated 45° anticlockwise and a five sided figure is added as the outer shape. Similarly, three sided figure is rotated 45° anticlockwise and a four sided figure is added as the outer shape.
  • Question 11
    1.2 / -0
    If F = 6 and LAMB = 7, then HOTEL = ____.
    Solution
    We have, A = 1, B = 2, ........., Z = 26
    Now, F =
    Also LAMB =
    Similarly, HOTEL = = 12
  • Question 12
    1.2 / -0
    Find the figure from the given options which contains fig. (X) as its embedded part.


    Solution


    Hence, option 3 is the correct answer.
  • Question 13
    1.2 / -0
    There are four figures (1), (2), (3) and (4). Out of these four figures three are similar in a certain way. However, one figure is not like the other three. Choose the figure which is different from the rest.
    Solution
    If we rotate the shape in option 1 to the left by 90°, then we will get the shape same as option 3.
    If we rotate the shape in option 3 to the left by 90°, then we will get the shape same as option 2.
    But the shape in option 4 can not be obtained by any of the rotation.

    Hence, option 4 is the correct answer.


  • Question 14
    1.2 / -0
    Find the figure from the options which will continue the series established by the problem figures.

    Solution

    Letter 'T' and '=' signs are moving anticlockwise by 90° without any Rotation.
    * is moving anticlockwise by 90° in three steps only. Then it has been replaced by the new shape square. Similarly, square will also move by 90° angle in 3 steps.
    Letter F is moving anticlockwise by 90°. Each time it is getting rotated to the left.





  • Question 15
    1.2 / -0
    Arrange the words given below in a meaningful sequence.

    (i) Fibre
    (ii) Plant
    (iii) Saree
    (iv) Cotton
    (v) Cloth
    Solution
    The meaningful sequence is, Plant, Cotton, Fibre, Cloth, Saree. (Saree is the final outcome here and the given is the process).
  • Question 16
    1.2 / -0
    Estimate the sum (21,497 + 47,807) to the nearest thousand.
    Solution
    Sum = 21,497 + 47,807 = 69,304
    So, estimated sum nearest to thousand = 69,000
  • Question 17
    1.2 / -0
    The value of XVI + CCCVII =
    Solution
    XVI = 16, CCCVII = 307
    XVI + CCCVII = 16 + 307 = 323
    And 323 = CCCXXIII
  • Question 18
    1.2 / -0
    The largest number which divides 38, 46 and 62 leaving remainder 2 in each case is _______.
    Solution
    The largest number which divides 38, 46 and 62 leaving remainder 2 in each case is H.C.F of 36, 44 and 60.
    H.C.F. of 36, 44 & 60.
    36 = 2 × 2 × 3 × 3
    44 = 11 × 2 × 2
    60 = 2 × 2 × 3 × 5
    So, H.C.F. = 4
    Required number = 4
  • Question 19
    1.2 / -0
    Which symbol is located at -3 on the number line shown below?

    Solution


    So, = - 3
  • Question 20
    1.2 / -0
    The figure is made of three squares joined together. What is the area of the figure in square cm?

    Solution


    Area of the given figure = Area of square ABCD + Area of square BCEF + Area of square BFGH
    = 3 × 3 + 3 × 3 + 3 × 3 = 9 + 9 + 9 = 27 cm2
  • Question 21
    1.2 / -0
    Which of the following squares would you shade to make the figure symmetrical?

    Solution
  • Question 22
    1.2 / -0
    The given table shows the area, in square kilometres, of four lakes. Lake E has a greater area than Lake O, but a smaller area than Lake M. What could be the area of Lake E?

    Area of Four Lakes
    Lake Area (km2)
    H 59,600
    M 57,800
    S 82,100
    O 18,960
    E ?
    Solution
    According to the question,
    Only 25,700 from the given options lies between 18,960 and 57,800.
    57,800 > 25,700 > 18,960
    Hence, option 3 is the correct answer.
  • Question 23
    1.2 / -0
    The Hindu-Arabic numeral form for MLXXXIX is _______
    Solution
    M = 1000
    L = 50
    X = 10
    IX = 9

    So, MLXXXIX = 1000 + 50 + 10 + 10 + 10 + 9 = 1089
    Hence, option 3 is the correct answer.
  • Question 24
    1.2 / -0
    Estimate the sum of (21,397 + 42,505) to nearest thousand.
    Solution
    21,397 + 42,505 = 63,902, when rounded to nearest thousand it becomes 64,000.
  • Question 25
    1.2 / -0
    Which of the following numbers is divisible by 9?
    Solution
    Option 1 - 9,076,185 - Sum of digits - 9 + 7 + 6 + 1 + 8 + 5 = 36
    Option 2 - 9,21,06,345 - Sum of digits = 9 + 2 + 1 + 6 + 3 + 4 + 5 = 30
    Option 3 - 1,03,49,576 - Sum of digits = 1 + 3 + 4 + 9 + 5 + 7 + 6 = 35
    Option 4 - 9,51,03,476 - Sum of digits = 9 + 5 + 1 + 3 + 4 + 7 + 6 = 35

    Sum of digits in option 1 only is divisible by 9, so the given number is divisible by 9.
  • Question 26
    1.2 / -0
    Find the value of -12 - (-48) - [(-13) + (-8) - (-3) + 4].
    Solution
    We have,
    -12 - (-48) - [-13 + (-8) - (-3) + 4]
    = -12 - (-48) - [-13 - 8 + 3 + 4)
    = -12 + 48 + 13 + 8 - 3 - 4
    = 48 + 13 + 8 - 12 - 3 - 4 = 69 - 19 = 50
  • Question 27
    1.2 / -0
    Find the fraction of curved lines with respect to the total number of lines in the given figure.

    Solution
    Number of curved lines (circles) = 7
    Number of straight lines = 6 (as there are two triangles with 3 sides each)
    Total number of lines = 6 + 7 = 13
    So, fraction of curved lines =
  • Question 28
    1.2 / -0
    Find the missing number.


    Solution
    We have,
    L.H.S. =

    =

    =

    = = 115
    Now, 115 = - 4
    = 115 + 4 = 119
  • Question 29
    1.2 / -0
    Estimate the following by rounding off each number to nearest hundreds.

    78203 - 16407
    Solution
    We have, 78203 - 16407
    Rounding off each number to nearest hundreds, we get
    78203 rounded to nearest hundreds is 78200 because digit in 10s column is 0 so we round it down to nearest multiple of 100 which is 78200.
    16407 rounded to nearest hundreds is 16400 because digit in 10s column is 0 so we round it down to nearest multiple of 100 which is 16400.
    78200 - 16400 = 61800
  • Question 30
    1.2 / -0
    When we multiply a whole number and the multiplicative identity of that whole number, then we get
    Solution
    The multiplicative identity of whole numbers is 1. This means that any whole number multiplied by 1 will be equal to that same whole number. For example, 2 x 1 = 2, 12 x 1 = 12.
    Hence, option (1) is the correct answer.
  • Question 31
    1.2 / -0
    Which of the following statements is incorrect?
    Solution
    Two lines are parallel if and only if they lie in the same plane and do not intersect. Parallel lines never cross. Parallel lines are always the same distance apart. Therefore, statement in option (1) is incorrect.
    An equilateral triangle is one with three equal sides. An isosceles triangle is one with two equal sides. Therefore, every equilateral triangle is isosceles, but not every isosceles triangle is equilateral. Therefore, statement in option (2) is correct.
    Measure of straight angle 180 degrees measure of right angle is 90 degrees. Therefore, statement in option (3) is also correct.
    The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius. Therefore, statement in option (4) is also correct.
    Hence, statement in option (1) is incorrect.
  • Question 32
    1.2 / -0
    of the books in a box are English books, are Maths books and the rest are Science books. What fraction of the books are Science books?
    Solution
    According to the question, we have
    + Fraction of science books = 1
    Fraction of Science books
    =
  • Question 33
    1.2 / -0
    Priya drove from town P to town Q. She took 14 hours 35 minutes for the journey. The clock shows the time she arrived at Town Q in the afternoon. When did she set off from Town P?


    Solution
    Time on clock is 4 : 45 p.m. (p.m. as she arrived in the afternoon)
    12 hours before 4 : 45 p.m. = 4 : 45 a.m.
    2 hours 35 minutes before 4 : 45 a.m. = 2 : 10 a.m.
    Hence, 14 hours 35 minutes before 4 : 45 p.m. = 2 : 10 a.m.
  • Question 34
    1.2 / -0
    The ratio of the volume of water in bottle P to that in bottle Q is 3 : 4. Rajeev drank 40 ml of the water from bottle P and the ratio then became 13 : 20. How much water was there in bottle P at first?
    Solution
    Let the quantity of water in bottle P be 3x and that of in bottle Q be 4x.
    According to the question,

    20(3x - 40) = 4x × 13
    60x - 800 = 52x
    8x = 800
    x = 100
    So, quantity of water in bottle P = 3 × 100 = 300 ml.
  • Question 35
    1.2 / -0
    Machine P can shred 12 sheets of paper in 15 seconds. Machine Q can shred 18 sheets of paper in 20 seconds. Which machine can shred more sheets of paper in one minute and how many more?
    Solution
    Number of sheets shred by machine P in 15 seconds = 12
    So, number of sheets machine P shred in 1 minute = × 60 = 48
    Also number of sheets shred by machine Q in 20 seconds = 18
    Number of sheets machine Q shred in 1 minute = = 54
    So, difference in number of sheets = 54 - 48 = 6
    So, machine Q shred 6 more sheets than machine P.
  • Question 36
    1.2 / -0
    Count the number of line segments.


    Solution
    Line segments are AB, AC, AD, AE, BC, BD, BE, CD, CE and DE.



    Total number of line segments = 10.
  • Question 37
    1.2 / -0
    Four different electronic devices make a beep after every 30 minutes, 1 hour, hours and 1 hour 45 minutes, respectively. All the devices beeped together at 12 noon. They will again beep together at ______.
    Solution
    Time taken to beep by four devices, respectively is 30 minutes, 1 hour, hours and 1 hour 45 minutes.
    i.e. 30 minutes, 60 minutes, 90 minutes and 105 minutes.
    L.C.M. of 30, 60, 90, 105 is,



    L.C.M.= 2 × 2 × 3 × 3 × 5 × 7 = 1260
    So, they will beep together again after 1260 minutes, i.e. after = 21 hours.
    So, required time = 12:00 noon + 21 hours = 9:00 a.m. ( 12 .00 noon + 12 hours = 12 : 00 midnight, now 12 : 00 midnight + 11 hours = 9:00 a.m.)
  • Question 38
    1.2 / -0
    A vessel has 5 litres 120 milliliters of mango shake. How many glasses each of 40 ml capacity, can be filled with it?
    Solution
    Quantity of mango shake in the vessel = 5 litres 120 milliliters
    = (5 × 1000 + 120) ml = 5120 ml
    1 litre = 1000 ml
    Quantity of juice each glass holds = 40 ml
    Number of glasses = 5120 40 = 128
  • Question 39
    1.2 / -0
    Eight copies of a book cost Rs. 523.60. What is the cost of one copy of the book?
    Solution
    Cost of 8 copies of a book = Rs. 523.60
    Cost of 1 copy of book = Rs.
    = Rs. 65.45
  • Question 40
    1.2 / -0
    There are 45 cookies in a box. 27 of them have raisins while the rest are plain. What is the ratio of the number of plain cookies to that of raisin cookies in the box?
    Solution
    Total number of cookies = 45
    Number of raisin cookies = 27
    Number of plain cookies = 45 - 27 = 18
    So, required ratio = 18 : 27 = 2 : 3
  • Question 41
    1.2 / -0
    Sanchi distributed equal number of sweets and equal number of biscuits to each of her classmates at her birthday party. She gave out 220 sweets and 300 biscuits in total. Find the largest possible number of classmates at the party.
    Solution
    Largest possible number of classmates is the H.C.F. of 300 and 220.



    H.C.F. = 20
    So, maximum number of classmates = 20
  • Question 42
    1.2 / -0
    Mayank is times as tall as Vansh. If Mayank is 38 cm taller than Vansh, then what is Mayank's height?
    Solution
    Let the height of Vansh be x cm.
    Then, the height of Mayank = cm
    According to the question,




    So, the height of Mayank = = 133 cm
  • Question 43
    1.2 / -0
    Three boys and four girls shared 198 sweets. Each girl received twice as many sweets as each boy. How many sweets did each girl receive?
    Solution
    Let the number of sweets each boy received be x.
    So, the number of sweets each girl received = 2x.
    Thus, three boys received 3x sweets and four girls received 8x sweets.
    According to the question,
    3x + 8x = 198
    11x = 198
    x = 18
    So, number of sweets each girl received = 2 × 18 = 36
  • Question 44
    1.2 / -0
    Vikas Electronics Store is having a sale. To advertise the sale, the store manager wants to outline the store window with a colourful ribbon.

    How many metres of ribbon will be needed to outline the 4 sides of the window?


    Solution
    Length of window = 7 m
    Breadth of window = 5 m
    Perimeter of window = 2 (Length + Breadth) = 2(7 + 5)
    = 2 × 12 = 24 m
    So, length of ribbon needed = 24 m
  • Question 45
    1.2 / -0
    It takes 90 minutes to wash 20 vehicles at a car wash. At this rate, how many minutes does it take to wash 5 vehicles?
    Solution
    Time taken to wash 20 vehicles = 90 minutes
    Time taken to wash 1 vehicle = minutes
    Time taken to wash 5 vehicles = = minutes
    = minutes
  • Question 46
    1.2 / -0
    Which of the following statements is INCORRECT?
    Solution


    -3 > -5, since -5 lies on the left side of -3 in the number line.
    Hence, statement in option (4) is incorrect.
  • Question 47
    1.2 / -0
    Avni completed of her holiday homework on Monday and of it on Tuesday. How much of her holiday homework did Avni complete in the two days?
    Solution
    Holiday homework completed on Monday =
    Holiday homework completed on Tuesday =
    Total holiday homework completed in two days =
  • Question 48
    1.2 / -0
    Find the correct match.

    Length of
    rectangle
    (cm)    		 Breadth of
    rectangle
    (cm)    		 Area
    (cm2)    		 Perimeter
    (cm)
    25 P 300 Q
    18 R S 66
    Solution
    Area = 300 cm2
    25 × P = 300
    P = 12 cm
    Perimeter = 2(12 + 25) = 74 cm
    So, P = 12, Q = 74
    Also,
    Perimeter = 66
    2(18 + R) = 66 18 + R = 33
    R = 15 cm
    and area = S = 15 × 18 = 270 cm2
    R = 15 and S = 270
  • Question 49
    1.2 / -0
    In a farm there were 3c cows, 5p pigs and 11d ducks.Find the total number of legs of the remaining animals, if 3 cows, 2 pigs and 4 ducks were sold.
    Solution
    Number of cows in the farm = 3c
    Number of cows sold = 3
    Remaining number of cows = 3c - 3
    Similarly, remaining number of pigs = 5p - 2
    And remaining number of ducks = 11d - 4
    Number of legs each animal has = 4
    So, number of legs pigs and cows have
    = 4(3c - 3 + 5p - 2)
    = 4 × (3c + 5p - 5)
    = 12c + 20p - 20
    Number of legs ducks have = 2 × (11d - 4)
    = 22d - 8
    Total number of legs = 12c + 20p + 22d - 28
  • Question 50
    1.2 / -0
    Pia, Ridhi and Muskaan divided 11.775 kg of wheat flour equally among themselves. Pia used all her wheat flour equally to bake 5 chocolate cakes. How much wheat flour did each cake need?
    Solution
    Total quantity of wheat flour = 11.775 kg
    Share of Pia = 11.775 3 = 3.925 kg
    Now, total chocolates cakes baked = 5
    Wheat flour needed in each cake = 3.925 5 = 0.785 kg.
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