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Quantitative Aptitude Test - 1

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Quantitative Aptitude Test - 1
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Weekly Quiz Competition
  • Question 1
    1 / -0.25

    A number X when divided by Y gives 25 as the remainder. When 3 times X is divided by Y, the remainder is 4. What is the value of Y?

    Solution

    According to the statement
    => X = Q + 25 Y=> X = YQ + 25
    So 3 times of X = 3YQ + 75
    If 3 times of X is divided by Y gives a remainder 4
    Then (3YQ+75)Y gives a remainder 43YQ is divisible by Y and only when 75 is divided by 71 gives a remainder 4.
    Therefore the value of Y is 71.

    Hence, the correct option is (d).
  • Question 2
    1 / -0.25

    What is the 4th digit from the right of the ternary sum of the decimal numbers 598 and 222?

    Solution

    Ternary value of 598 = 211011
    Ternary value of 222 = 22020
    Ternary sum = 1010101

    So, 4th digit from the right is 0.

    Hence, the correct option is (d).
  • Question 3
    1 / -0.25

    A rectangular playground has a length that is twice as great as its width. If its length is halved while its width is quadrupled, what is the ratio of its original area to its new area?

    Solution
    Initially, if width is x then length is 2x,
    i.e. A1 = 2x.
    x=2x2 then length is halved and width is quadrupled
    So, A2=12(2x).
    4x=4x2
    The ratio of or original area to final area is A1A2 = 2x24x2=12
    i.e., 1 : 2.
    Hence, the correct option is (a).
  • Question 4
    1 / -0.25

    Directions: A question is followed by two statements, numbered (1) and (2). Using the information provided and general knowledge, decide whether the information given is sufficient to solve the problem.

    In a regular pentagon PQRST and a regular hexagon STUVWX, side ST is common to both. What is the area of ΔRSX?

    (1) ST = 4 cm

    (2) RX = 6 cm

    Solution

    This is an isosceles triangle with angle at S as (360° − 120° − 108°) degrees.
    So any of the statements is sufficient to answer the question.

    Hence, the correct option is (d).
  • Question 5
    1 / -0.25

    Find the sum of the first 20 terms of the sequence S1 where

    S1: 3, 15, 35, 63, …

    Solution
    The general term is (4n2-1)
    So sum is 4n(n+1)(2n+1)6- n
    Put n=20 Sum = 11460
    Hence, the correct option is (b).
  • Question 6
    1 / -0.25

    If 12x2ax+7=ax2+9x+3 has only one (repeated) solution, then the positive integral solution of a is:

    Solution

    Given, 12x2ax+7=ax2+9x+3

    (a12)x2+(a+9)x4=0

    If ax2+bx+c=0 has equal roots, then b2=4ac

    (a+9)2=4(a12)(4)

    a2+81+18a=19216a

    a2+34a111=0

    On solving above equation, we get a=3 and a=37

    So, the positive integral solution will be 3.

  • Question 7
    1 / -0.25

    A 100-metre long train crossed a milestone in 10 seconds. It crossed another train of the same length as its own in 8 seconds. If both the trains travelled in opposite directions, what is the distance travelled by the second train in 3 hours?

    Solution
    The speed of the first train = 10010 = 10 m/s
    Relative speed when the trains travelled in opposite directions = (100 + 100)8 = 25 m/s
    Therefore, the speed of the second train = 25 – 10 = 15 m/s
    15 × 185 = 54 km/h
    Distance travelled by the second train in 3 hours = 54 × 3 = 162 km.  
    Hence, the correct option is (b).
  • Question 8
    1 / -0.25

    Directions For Questions

    Directions: Use the following chart, which represents the value of exports and imports (in Rs hundred crore) of a country for a certain period, to answer the given question.

    ...view full instructions

    During which year is the percentage increase/decrease in imports from the previous year the lowest?

    Solution
    Yearwise % change in imports from the previous year:
    In 2004% Change in import = (150 – 75)×10075 = 100%
     
    In 2005% Change in import = (250 – 150)×100150 = 66.67%
    In 2006% Change in import = (225 – 250)×100250 = -10%
    In 2007% Change in import = (350 – 225)×100225 = 55.5%
    Hence, the correct option is (d).
  • Question 9
    1 / -0.25

    Directions For Questions

    Directions: Use the following chart, which represents the value of exports and imports (in Rs hundred crore) of a country for a certain period, to answer the given question.

    ...view full instructions

    What is the ratio of total imports to total exports for all the given years together?

    Solution
    Total imports = 75 + 150 + 250 + 225 + 350 + 275 =1325
    Total exports = 150 + 225 + 375 + 300 + 450 + 175 = 1675
    Ratio of imports and exports = 1325 : 1675 = 53 : 67.
    Hence, the correct option is (d).
  • Question 10
    1 / -0.25

    Directions For Questions

    Directions: Use the following chart, which represents the value of exports and imports (in Rs hundred crore) of a country for a certain period, to answer the given question.

    ...view full instructions

    During which period is the total value of import equal to the total value of export (in Rs hundred crore)?

    Solution
    Options wise, Total values of import and export:
    Option A, 2003-04 import=225 export=375
    Option B, 2004-07 import=975 export=1375
    Option C, 2005-07 import=825 export=1125
    Option D, 2007-08 import=625 export=625
    Hence, the correct option is (d).
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