Numerical Ability


  1. S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked, S and M have 6 hour shifts in a day, whereas E and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the project?
    1. 1 : 1
    2. 1 : 2
    3. 1 : 4
    4. 2 : 1

  1. View Hint View Answer Discuss in Forum

    M efficiency = 2 [efficiency of S, E and F]
    Contribution of M in the project = x days × 6 hrs × 2
    Contribution of E in the project = 2x days × 12 hrs × 1
    Contribution of M: Contribution of E x × 6 × 2 : 2x × 12 × 1
    1: 2

    Correct Option: B

    M efficiency = 2 [efficiency of S, E and F]
    Contribution of M in the project = x days × 6 hrs × 2
    Contribution of E in the project = 2x days × 12 hrs × 1
    Contribution of M: Contribution of E x × 6 × 2 : 2x × 12 × 1
    1: 2


  1. The binary operation – is defined as a– b = ab + (a + b), where a and b are any two real numbers. The value of the identity element of this operation, defined as the numberx such that a– x = a, for any a, is ______.
    1. 0
    2. 1
    3. 2
    4. 10

  1. View Hint View Answer Discuss in Forum

    The binary operation – is defined
    ⇒ a – b = ab + (a + b)
    a – x = a
    ∴ From the equation ‘b’ is the variable
    Option A: x = 0
    a – o = a × 0 + (a + 0) = 0 + a = a
    Option B: x = 1
    a – 1 = a × 1 + (a + 1) = a + a + 1 = 2a + 1
    Option C: x = 2
    a – 2 ⇒ a × 2 + (a + 2) = 2a + a + 2 = 3a+ 2
    Option D: x = 10
    a – 10 ⇒ a × 10 + (a + 10) = 10a + a + 10 = 11a + 10
    ∴ Option ‘A’ only True.

    Correct Option: A

    The binary operation – is defined
    ⇒ a – b = ab + (a + b)
    a – x = a
    ∴ From the equation ‘b’ is the variable
    Option A: x = 0
    a – o = a × 0 + (a + 0) = 0 + a = a
    Option B: x = 1
    a – 1 = a × 1 + (a + 1) = a + a + 1 = 2a + 1
    Option C: x = 2
    a – 2 ⇒ a × 2 + (a + 2) = 2a + a + 2 = 3a+ 2
    Option D: x = 10
    a – 10 ⇒ a × 10 + (a + 10) = 10a + a + 10 = 11a + 10
    ∴ Option ‘A’ only True.



  1. Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun's place?
    1. 3.00
    2. 4.99
    3. 6.02
    4. 7.01

  1. View Hint View Answer Discuss in Forum


    I = I live
    AH = Ahmed lives
    M = Michel lives
    S = Susan lives
    A = Arun lives

    Correct Option: C


    I = I live
    AH = Ahmed lives
    M = Michel lives
    S = Susan lives
    A = Arun lives


  1. Right triangle PQR is to be constructed in the xy– plane so that the right angle is at P and line PR is parallel to the-axis. The x and y coordinates of P, Q, and R are to be integers that satisfy the inequalities: -4 <, x < 5 and 6 < y < 16. How many different triangles could be constructed with these properties?
    1. 110
    2. 1,100
    3. 9,900
    4. 10,000

  1. View Hint View Answer Discuss in Forum

    We have the rectangle with dimensions 10 ×11 (10 horizontal dots and 11 vertical). PQ is parallel to y-axis and PR is parallel to x-axis.
    Choose the (x, y) coordinates for vertex P (right angle): 10C1 × 11C1
    Choose the x coordinate for vertex R (as y coordinate is fixed by A): 9C1, (10 – 1 = 9 as 1 horizontal dot is already occupied by A)
    Choose the y coordinate for vertex Q (as x coordinate is fixed by A): 10C1, (11 – 1 = 10 as 1 vertical dot is already occupied by A).
    Hence, required number of triangles will be 10C1 × 11C1 × 9C1 × 10C1 = 9900.

    Correct Option: C

    We have the rectangle with dimensions 10 ×11 (10 horizontal dots and 11 vertical). PQ is parallel to y-axis and PR is parallel to x-axis.
    Choose the (x, y) coordinates for vertex P (right angle): 10C1 × 11C1
    Choose the x coordinate for vertex R (as y coordinate is fixed by A): 9C1, (10 – 1 = 9 as 1 horizontal dot is already occupied by A)
    Choose the y coordinate for vertex Q (as x coordinate is fixed by A): 10C1, (11 – 1 = 10 as 1 vertical dot is already occupied by A).
    Hence, required number of triangles will be 10C1 × 11C1 × 9C1 × 10C1 = 9900.



  1. A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occurs in three tosses. Based on the above information, which one of the following statements is TRUE?
    1. X and Y are not independent
    2. Y and Z are dependent
    3. Y and Z are independent
    4. X and Z independent

  1. View Hint View Answer Discuss in Forum

    x = {HHT, HHH}
    y depends on x
    z = {TTH, TTT}
    ∴ ‘d’ is the correct choice.

    Correct Option: B

    x = {HHT, HHH}
    y depends on x
    z = {TTH, TTT}
    ∴ ‘d’ is the correct choice.