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 was the ratio between the ages of P and Q four years ago?
    I. The ratio between the present ages of P and Q is 3 : 4.
    II. The ratio between the present ages of Q and R is 4 : 5.








  1. View Hint View Answer Discuss in Forum

    As per the given above question ,
    From statement I , The ratio present ages of P and Q = 3 : 4 .
    From statement II , The ratio present ages of Q and R = 4 : 5 .
    Combining the both statements , we get
    Ratio of present ages of P , Q and R = 12 : 16 : 20 = 3 : 4 : 5
    Let ages of P , Q and R be 3k , 4k and 5k .
    4 years ago , Age of P = ( 3k - 4 )
    and Age of Q = ( 4k - 4 )

    Correct Option: D

    As per the given above question ,
    From statement I , The ratio present ages of P and Q = 3 : 4 .
    From statement II , The ratio present ages of Q and R = 4 : 5 .
    Combining the both statements , we get
    Ratio of present ages of P , Q and R = 12 : 16 : 20 = 3 : 4 : 5
    Let ages of P , Q and R be 3k , 4k and 5k .
    4 years ago , Age of P = ( 3k - 4 )
    and Age of Q = ( 4k - 4 )
    4 years ago , Ratio of P and Q = ( 3k - 4 ) : ( 4k - 4 )
    For solving this question, we want two equations in terms of P and Q .

  1. What is the speed of a running train which takes 9 seconds to cross a signal post?
    I. The length of the train is 90 m.
    II. The train takes 27 seconds to cross a platform of 180 m.








  1. View Hint View Answer Discuss in Forum

    On the basis of above given details in question , we can say
    Time taken in crosses a signal post = 9 seconds
    From statement I , The length of the train = Distance = 90 m
    Speed of running train = distance / time taken = 90 / 9 = 10 m / sec
    From statement II , The length of platform = 180 m and time taken = 27 seconds
    Speed of running train = distance / time taken = ( 90 + 180 ) / 27 = 270 / 27 = 10 m / sec

    Correct Option: C

    On the basis of above given details in question , we can say
    Time taken in crosses a signal post = 9 seconds
    From statement I , The length of the train = Distance = 90 m
    Speed of running train = distance / time taken = 90 / 9 = 10 m / sec
    From statement II , The length of platform = 180 m and time taken = 27 seconds
    Speed of running train = distance / time taken = ( 90 + 180 ) / 27 = 270 / 27 = 10 m / sec
    Data either in statement I alone or in statement II alone are sufficient to answer the question.Hence , option C is correct answer .

  1. What selling price should be marked on the article?
    I. Discount of 5% is to be given and profit percentage should be double the discount. Purchase cost is in the range of $ 300 to $ 400.
    II. 10% discount is to be allowed and 15% profit is to be obtained on the purchase cost of $ 200 of the article.








  1. View Hint View Answer Discuss in Forum

    According to question ,
    From statement I , → The fixed value of CP is not given, so SP of the article cannot be determined.
    From statement II , → Let, K be SP of an article

    Correct Option: B

    According to question ,
    From statement I , → The fixed value of CP is not given, so SP of the article cannot be determined.
    From statement II , → Let, K be SP of an article

    K x 100 - 10= 200 x ( 100 + 15 )
    100100

    K x 90= 200 x 115
    100100

    ∴ K= 200 x 115= $ 255.55
    90

    Therefore , 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. 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.

  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.