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. 12 men and 8 women can complete a piece of work in 10 days. How many days will it take for 15 men and 4 women to complete the same work?
    A. 15 men can complete the work in 12 days.
    B. 15 women can complete the work in 16 days.
    C. The amount of work done by a woman is three - fourth of the work done by a man in one day.










  1. View Hint View Answer Discuss in Forum

    As per the given all details in above question , we can say
    Given , 12 men and 8 women can complete a piece of work = 10 days
    Let 15 men and 4 women to complete the same work in D days .
    From statement A , 15 men can complete the work = 12 days.
    From statement B , 15 women can complete the work = 16 days.
    From statement C , Women = ( 3 / 4 ) x men ⇒ 4W = 3M
    According to question ,
    ( 12M + 8W ) x 10 = ( 15M + 4W ) x D
    ⇒ ( 4 x 4W + 8W ) x 10 = ( 5 x 4W + 4W ) x D ⇒ 24W x 10 = 24W x D ⇒ D = 10 days

    Correct Option: D

    As per the given all details in above question , we can say
    Given , 12 men and 8 women can complete a piece of work = 10 days
    Let 15 men and 4 women to complete the same work in D days .
    From statement A , 15 men can complete the work = 12 days.
    From statement B , 15 women can complete the work = 16 days.
    From statement C , Women = ( 3 / 4 ) x men ⇒ 4W = 3M
    According to question ,
    ( 12M + 8W ) x 10 = ( 15M + 4W ) x D
    ⇒ ( 4 x 4W + 8W ) x 10 = ( 5 x 4W + 4W ) x D ⇒ 24W x 10 = 24W x D ⇒ D = 10 days
    Any two of the three statements are sufficient to answer the question. Hence, anyone of the statements can be dispensed with.

  1. The difference between the compound interest and the simple interest at the same rate on a certain amount at the end of two years is $ 12.50. What is the rate of interest?
    A. Simple interest for two years is $ 500.
    B. Compound interest for two years is $ 512.50.
    C. Amount on simple interest after two years becomes $ 5500.










  1. View Hint View Answer Discuss in Forum

    As per the given all details in above question , we can say that
    Anyone of the three statements is alone sufficient to answer the question. So, any two can be dispensed with.
    From (A) alone :

    Rate =(CI - SI) x 2x 100 = 25 x 100 = 5%
    SI500

    Correct Option: E

    As per the given all details in above question , we can say that
    Anyone of the three statements is alone sufficient to answer the question. So, any two can be dispensed with.
    From (A) alone:

    Rate =(CI - SI) x 2x 100 = 25 x 100 = 5%
    SI

    From (B) alone :
    CI = $512.5
    ∴ SI = $512.5 − $12.5 = $ 500
    Again,
    Rate = (CI - SI) x 2x 100
    SI

    Rate = 25x 100 = 5%
    500

    From (C) alone :
    Suppose Principal = P and Rate of Interest = r%
    Then, P 1 + r2= 5500 + 12.5 = 5512.5 ...(1)
    100

    and, P + 2rP = 5500
    100

    or, P 1 + 2r= 5500 ...(2)
    100

    Dividing (1) by (2) we have
    [1 + ( r / 100 )]2 /[1 + ( 2r / 100 )] = 5512.5 / 5500 ....(3)
    This is a quadratic equation which has only one variable, r. It can be solved. Hence, value of r can be obtained.
    Note : is satisfied with the value r = 5.
    So, it confirms that equation is solvable.

  1. What will be the sum of the ages of father and the son after five years?
    A. Father’s present age is twice son’s present age.
    B. After ten years the ratio of father’s age to the son’s age will become 12 : 7.
    C. Five years ago the difference between the father’s age and son’s age was equal to the son’s present age.










  1. View Hint View Answer Discuss in Forum

    On the basis of above given details in question ,
    Let father’s present age is F and son’s present age is S .
    From statement A , Father’s present age = 2 x son’s present age
    ⇒ F = 2S
    From statement B , After 10 years , ratio of father’s age to the son’s age = 12 : 7
    ⇒ ( F + 10 ) : ( S + 10 ) = 12 : 7
    From statement C , 5 years ago , father’s age - son’s age = son’s present age
    ⇒ ( F - 5 ) - ( S - 5 ) = S
    From statement B and A , we have
    ⇒ ( 2S + 10 ) / ( S + 10 ) = 12 / 7 { ∴ putting F = 2S }
    ⇒ 14S + 70 = 12S + 120 ⇒ 14S - 12S = 120 - 70 ⇒ 2S = 50 ⇒ S = 50 / 2 = 25 years and F = 2 x 25 = 50 years
    After 5 years , Father’s age = Father’s present age + 5 = 50 + 5 = 55 years
    and Son’s age = Son’s present age + 5 = 25 + 5 = 30 years
    Sum of the ages of father and the son after five years = 55 + 30 = 85 years

    Correct Option: E

    On the basis of above given details in question ,
    Let father’s present age is F and son’s present age is S .
    From statement A , Father’s present age = 2 x son’s present age
    ⇒ F = 2S
    From statement B , After 10 years , ratio of father’s age to the son’s age = 12 : 7
    ⇒ ( F + 10 ) : ( S + 10 ) = 12 : 7
    From statement C , 5 years ago , father’s age - son’s age = son’s present age
    ⇒ ( F - 5 ) - ( S - 5 ) = S
    From statement B and A , we have
    ⇒ ( 2S + 10 ) / ( S + 10 ) = 12 / 7 { ∴ putting F = 2S }
    ⇒ 14S + 70 = 12S + 120 ⇒ 14S - 12S = 120 - 70 ⇒ 2S = 50 ⇒ S = 50 / 2 = 25 years and F = 2 x 25 = 50 years
    After 5 years , Father’s age = Father’s present age + 5 = 50 + 5 = 55 years
    and Son’s age = Son’s present age + 5 = 25 + 5 = 30 years
    Sum of the ages of father and the son after five years = 55 + 30 = 85 years
    Any two of the three statements are sufficient to answer the question (As to find the two unknowns we need two equations). Hence, anyone of the statements can be dispensed with.

  1. What will be the cost of fencing a circular plot?
    ∏ = 22....
    7

    A. Area of the plot is 616 m2.
    B. Cost of fencing a rectangular plot whose perimeter is 120 m is $780.
    C. Area of a square plot with side equal to the radius of the circular plot is 196 m2.










  1. View Hint View Answer Discuss in Forum

    As per the given question , we can say From statement A , Area of the plot = πr2 = 616 m2 .
    ⇒ ( 22 / 7 ) x r2 = 616 ⇒ r2 = 616 x ( 7 / 22 ) = 28 x 7 = 196
    ⇒ r = 14 cm
    From statement B , Cost of fencing a rectangular plot = $ 780 and perimeter =120 m
    From statement C , Area of a square plot = a2 = 196 m2
    ⇒ a = √196 = 14
    ∴ a = 14 = radius of the circular plot
    From statement A , we have
    Area of the plot = 616 m2
    ∴ Cost of fencing a circular plot = Area x Cost of fencing a rectangular plot = 616 x 780 = $ 480480

    Correct Option: C

    As per the given question , we can say
    From statement A , Area of the plot = πr2 = 616 m2 .
    ⇒ ( 22 / 7 ) x r2 = 616 ⇒ r2 = 616 x ( 7 / 22 ) = 28 x 7 = 196
    ⇒ r = 14 cm
    From statement B , Cost of fencing a rectangular plot = $ 780 and perimeter =120 m
    From statement C , Area of a square plot = a2 = 196 m2
    ⇒ a = √196 = 14
    ∴ a = 14 = radius of the circular plot
    From statement A , we have
    Area of the plot = 616 m2
    ∴ Cost of fencing a circular plot = Area x Cost of fencing a rectangular plot = 616 x 780 = $ 480480
    (B) is necessary because only this statement gives the rate of fencing. Anyone of (A) or (C) gives the value of radius, which enables us to find the circumference.
    Hence, either (A) or (C) can be dispensed with.