Data Sufficiency

Data Sufficiency

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Data Sufficiency

Direction: In each of the following questions, a question is asked followed by three statements. You have to study the questions and all the three statements given and decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the questions.

  1. How much time will the train ‘X’ take to cross another train ‘Y’ running in opposite direction?
    A. Train ‘X’ crosses a signal pole in 6 seconds.
    B. Ratio of the speeds of trains ‘X’ and ‘Y’ is 3 : 2.
    C. Length of the two trains together is 500 m.










  1. View Hint View Answer Discuss in Forum

    As per the given all details in above question ,
    From statement A , Time taken by train‘X’ = 6 seconds
    From statement B , Ratio of the speeds of trains ‘X’ and ‘Y’ = 3 : 2
    Let speed of train X is 3k and speed of train Y is 2k.
    Relative speed = 3k + 2k = 5k
    From statement C , Length of the two trains = 500 m
    Time taken = Length of the two trains / Relative speed = 500 / 5k = 100 / k seconds
    Anyone of the three statements is not sufficient to answer the question. So, anyone is not suitable statements.

    Correct Option: E

    As per the given all details in above question ,
    From statement A , Time taken by train‘X’ = 6 seconds
    From statement B , Ratio of the speeds of trains ‘X’ and ‘Y’ = 3 : 2
    Let speed of train X is 3k and speed of train Y is 2k.
    Relative speed = 3k + 2k = 5k
    From statement C , Length of the two trains = 500 m
    Time taken = Length of the two trains / Relative speed = 500 / 5k = 100 / k seconds
    Anyone of the three statements is not sufficient to answer the question. So, anyone is not suitable statements.The question cannot be answered even with the information in all the three statements.

  1. What will be the cost of painting the four walls of a room with length, width and height 5 m, 3 m and 8 m respectively? The room has one door and one window.
    A. Cost of painting per m2 is $ 25.00
    B. Area of window of 2.25 m2 is half of the area of the door.
    C. Area of the room is 15 m2.










  1. View Hint View Answer Discuss in Forum

    As per the given above question ,
    Given , Length = 5 m , Width = 3 m and Height = 8 m
    From statement A , Cost of painting = $ 25 per m2
    From statement B , Area of window = ( 1 / 2) x area of the door
    ⇒ 2.25 m2 = ( 1 / 2) x area of the door ⇒ area of the door = 4.50 m2
    From statement C , Area of the room = 15 m2.
    The area of four walls = 2h( l + b ) = 2 x 8 ( 5 + 3 ) = 16 x 8 = 128 m2.
    ∴ Cost of painting the four walls = area x Cost of painting per m2 = 128 x 25 = $ 3200

    Correct Option: D

    As per the given above question ,
    Given , Length = 5 m , Width = 3 m and Height = 8 m
    From statement A , Cost of painting = $ 25 per m2
    From statement B , Area of window = ( 1 / 2) x area of the door
    ⇒ 2.25 m2 = ( 1 / 2) x area of the door ⇒ area of the door = 4.50 m2
    From statement C , Area of the room = 15 m2.
    The area of four walls = 2h( l + b ) = 2 x 8 ( 5 + 3 ) = 16 x 8 = 128 m2.
    ∴ Cost of painting the four walls = area x Cost of painting per m2 = 128 x 25 = $ 3200
    The area off our walls can be easily determined with the help of the data given in the question. Now,the area of the windows and door with the help of (B) can be subtracted in the calculated area and then multiplied with the cost given in (A).

  1. Which is the area of the given right-angled triangle?
    A. Length of the diagonal of rectangle is 5 cm.
    B. Perimeter of the triangle is four times its base.
    C. One of the angles of the triangle is of 60°.










  1. View Hint View Answer Discuss in Forum

    Let, the length and breadth of the rectangle be l and b, respectively.
    From statement A → Diagonal of rectangle ( h ) = 5 ⇒ l2 + b2 = 25
    From statement B → l + b + h = 4b ⇒ l = 3b − 5

    Correct Option: B

    Let, the length and breadth of the rectangle be l and b, respectively.
    From statement A → Diagonal of rectangle ( h ) = 5 ⇒ l2 + b2 = 25
    From statement B → l + b + h = 4b ⇒ l = 3b − 5
    From statement C → One of the angles of the triangle = 60°
    From statement A and B , ( 3b - 5 )2 + b2 = 25 ⇒ 9b2 + 25 - 30b + b2 = 25
    ⇒ 9b2 - 30b + b2 = 0 ⇒ 10b2 - 30b = 0 ⇒ 10b( b - 3 ) = 0 ⇒ b = 3 cm
    ∴ l = 3 x 3 - 5 = 9 - 5 = 4 cm
    ∴ Area of right angle triangle = ( 1 / 2 ) x base x height
    = ( 1 / 2 ) x 3 x 4 = 6 cm2
    After combining any of the above two statements, we get the values of l and b. Hence, any of them can be dispensed with.

  1. What is the area of a right-angled triangle?
    A. The perimeter of the triangle is 30 cm.
    B. The ratio between the base and the height of the triangle is 5 : 12.
    C. The area of the triangle is equal to the area of rectangle of length 10 cm.










  1. View Hint View Answer Discuss in Forum

    Let, the base, height and hypotenuse of a right-angled triangle be b, p and h, respectively.
    From Statement A, b + P + h = 30 …(1)
    From Statement B, b : p = 5 : 12 …(2)
    Let the base of triangle is 5k and height of triangle is 12k .
    We know that
    h2 = p2 + b2 = 25k2 + 144k2 = 169k2
    ∴ h = 13k …(3)
    Combining equations (1), (2) and (3), we get
    5k + 12k + 13k = 30 ⇒ k = 1

    Correct Option: B

    Let, the base, height and hypotenuse of a right-angled triangle be b, p and h, respectively.
    From Statement A, b + P + h = 30 …(1)
    From Statement B, b : p = 5 : 12 …(2)
    Let the base of triangle is 5k and height of triangle is 12k .
    We know that
    h2 = p2 + b2 = 25k2 + 144k2 = 169k2
    ∴ h = 13k …(3)
    Combining equations (1), (2) and (3), we get
    5k + 12k + 13k = 30 ⇒ k = 1

    ∴ Area of triangle =1 x 5 x 12 = 30 cm2
    2

    Hence, only A and B together are sufficient.

  1. What is the sum of two numbers?
    A. The bigger of these two numbers is 6 more than the smaller number.
    B. 40% of the smaller number is equal to 30% of the bigger number.
    C. The ratio between half of the bigger number and one-third of the smaller number is 2 : 1.










  1. View Hint View Answer Discuss in Forum

    Let, the bigger and smaller numbers be p and q, respectively.
    From statement A, p − q = 6 ....... ( 1 )
    From statement B, 40% of q = 30% of p ⇒ 4q = 3p …......(2)

    Correct Option: E

    Let, the bigger and smaller numbers be p and q, respectively.
    From A, p − q = 6 ....... ( 1 )
    From B, 40% of q = 30% of p ⇒ 4q = 3p …(2)

    From C,p : q = 2 : 1 ⇒ 3p = 4q ....(3)
    23

    On solving equations ( 1 ) and ( 2 ) or ( 3 ) , we get
    q = 18 and p = 24
    Hence , the bigger and smaller numbers be 24 and 18.
    We see that equations (2) and (3) are same. Hence, A and either B or C is required.