Data Sufficiency

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Data Sufficiency

Direction: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and Read both the statements and give answer

  1. What is the height of a right-angled triangle?
    I. The area of the right-angled triangle is equal to the area of a rectangle whose breadth is 12 cm.
    II. The length of the rectangle is 18 cm.








  1. View Hint View Answer Discuss in Forum

    As per the given above question ,
    From statement II , The length of the rectangle = 18 cm
    From statement I , breadth = 12 cm
    The area of the right-angled triangle = the area of a rectangle
    ⇒ ( 1 / 2 ) x b x h = L x B ⇒ ( 1 / 2 ) x b x h = 18 x 12
    ⇒ b x h = 216 x 2 = 432 cm2

    Correct Option: D

    As per the given above question ,
    From statement II , The length of the rectangle = 18 cm
    From statement I , breadth = 12 cm
    The area of the right-angled triangle = the area of a rectangle
    ⇒ ( 1 / 2 ) x b x h = L x B ⇒ ( 1 / 2 ) x b x h = 18 x 12
    ⇒ b x h = 216 x 2 = 432 cm2
    ∴ By combing I and II we can find the area of right angled triangle, but the height cannot be determined in absence of the base of the triangle.

  1. Which is the smaller of the two numbers?
    I. The difference between these two numbers is one-third of the largest number.
    II. The sum of these two numbers is 30.










  1. View Hint View Answer Discuss in Forum

    Let p and q be the two numbers .
    According to question ,

    From statement I. p - q = 1 p
    , ⇒ 2p - 3q = 0
    3

    Correct Option: E

    Let p and q be the two numbers .
    According to question ,

    From statement I. p - q = 1 p
    , ⇒ 2p - 3q = 0 ..........( 1 )
    3

    From statement II. p + q = 30 ...........( 2 )
    On solving equations ( 1 ) and ( 2 ) , we get p = 18 and q = 12.
    Hence , the smaller number is 12 .So , correct answer is option E .

  1. What is the rate of compound interest on a sum of money?
    I. The total compound interest at the end of two years is $ 820.
    II. The total simple interest at the same rate on $ 5000 at the end of three years is $ 750.








  1. View Hint View Answer Discuss in Forum

    As per the given all details in above question , we can say
    From statement I , CI in two years = $ 820
    From statement II , Principal = $ 5000 , S.I. = $ 750 , Time = 3 years

    Correct Option: B

    As per the given all details in above question , we can say
    From statement I , CI in two years = $ 820
    From statement II , Principal = $ 5000 , S.I. = $ 750 , Time = 3 years

    Rate = S.I. x 100 %
    Principal

    Rate = 250 x 100 = 5 %
    5000

    Hence, the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

  1. How many marks did Prakash obtain in Mathematics?
    I. Prakash secured on an average 55 percent marks in Mathematics, Physics and Chemistry together.
    II. Prakash secured 10 percent more than the average in Mathematics.








  1. View Hint View Answer Discuss in Forum

    As per the given above question ,
    From statement I , Average of mathematics , physics and chemistry = 55%
    ⇒ M + Ph + Ch = 165%
    From statement II , Prakash → M + 10% (average)
    Where , M → Mathematics , Ph → Ph and Ch → Chemistry

    Correct Option: D

    As per the given above question ,
    From statement I , Average of mathematics , physics and chemistry = 55%
    ⇒ M + Ph + Ch = 165%
    From statement II , Prakash → M + 10% (average)
    Where , M → Mathematics , Ph → Ph and Ch → Chemistry
    Hence , both statements I and II together are not sufficient to answer the question.

  1. What is the cost of polishing the rectangular floor?
    I. Room is 9 m long and 7 m wide.
    II. Cost of polishing the floor of 10 m by 5 m is $ 112.50.










  1. View Hint View Answer Discuss in Forum

    On the basis of above given details in question ,
    From statement I → Area of the room = L x B = 9 × 7 = 63 m2

    From statement II → Rate = Cost of polishing the floor
    Area of floor

    Correct Option: E

    On the basis of above given details in question ,
    From statement I → Area of the room = L x B = 9 × 7 = 63 m2

    From statement II → Rate = Cost of polishing the floor
    Area of floor

    Rate = 112.50 = 2.25 per m2
    10 x 5

    ∴ Combining both the statements, cost of polishing the rectangular floor = 63 × 2.25 = $ 141.75.