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. A, B and C are integers. Is B an even number?
    I. (A + B) is an odd number.
    II. (C + B) is an odd number.








  1. View Hint View Answer Discuss in Forum

    According to question ,
    I. A + B is odd ⇒ If A is an even number then B will be an odd number and vice versa.
    II. C + B is odd ⇒ if B is an even number then C will be an odd number and vice versa.

    Correct Option: D

    According to question ,
    I. A + B is odd ⇒ If A is an even number then B will be an odd number and vice versa.
    II. C + B is odd ⇒ if B is an even number then C will be an odd number and vice versa.
    So, even by combining the two statements together, we are not able to say that B is an even integer.

  1. What is the two-digit number where the digit at the unit’s place is smaller?
    I. The difference between the digits is 5.
    II. The sum of the two digits is 7.










  1. View Hint View Answer Discuss in Forum

    Let, the two-digit number be 10p + q (q < p)
    From statement I. p − q = 5 ........ ( 1 )
    From statement II. p + q = 7 ....... ( 2 )
    On solving equations ( 1 ) and ( 2 ) , we get
    p = 6 and q = 1

    Correct Option: E

    Let, the two-digit number be 10p + q (q < p)
    From statement I. p − q = 5
    From statement II. p + q = 7
    On solving equations ( 1 ) and ( 2 ) , we get
    p = 6 and q = 1
    Now ,the two-digit number = 10p + q = 10 x 6 + 1 = 61
    Hence, both statements together are sufficient to answer the question.

  1. What is the speed of the boat in still water?
    I. It takes 2 hours to cover the distance between A and B downstream.
    II. It takes 4 hours to cover the distance between A and B upstream.








  1. View Hint View Answer Discuss in Forum

    Let, the distance between A and B be D Km .
    From statement I , Speed downstream = D / 2 km / hr
    From statement II , Speed upstream = D / 4 km / hr.
    Speed of boat in still water = 1 / 2 [ ( D / 2 ) + ( D / 4 ) ] km / hr.

    Correct Option: D

    Let, the distance between A and B be D Km .
    From statement I , Speed downstream = D / 2 km / hr
    From statement II , Speed upstream = D / 4 km / hr.
    Speed of boat in still water = 1/ 2 [ ( D / 2 ) + ( D / 4 ) ] km / hr.
    Even if we combine both statements I and II , we cannot find out the answer .

  1. What is the rate of simple interest per annum?
    I. The sum triples in 20 years at simple interest.
    II. The difference between the sum and the simple interest earned after 10 years is $ 1000.








  1. View Hint View Answer Discuss in Forum

    As per the given question , we can say

    From statement I. R = (3 - 1) x
    100
    		 = 10%
    20

    From statement II. Here, the sum is not given.

    Correct Option: A

    As per the given question , we can say

    From statement I. R = (3 - 1) x
    100
    		 = 10%
    20

    From statement II. Here, the sum is not given. Therefore, statement I alone is sufficient.

  1. The area of a rectangle is equal to the area of a right- angled triangle. What is the length of the rectangle?
    I. The base of the triangle is 40 cm.
    II. The height of the triangle is 50 cm.








  1. View Hint View Answer Discuss in Forum

    On the basis of above given details in question , we can say that
    From statement I , The base of the triangle ( b ) = 40 cm.
    From statement II , The height of the triangle ( h ) = 50 cm
    According to question ,
    area of a rectangle = area of a right- angled triangle
    L x B = ( 1 / 2 ) x b x h
    Combining both statements , we get
    L x B = ( 1 / 2 ) x 40 x 50 ⇒ L x B = 20 x 50 = 1000 cm2

    Correct Option: D

    On the basis of above given details in question , we can say that
    From statement I , The base of the triangle ( b ) = 40 cm.
    From statement II , The height of the triangle ( h ) = 50 cm
    According to question ,
    area of a rectangle = area of a right- angled triangle
    L x B = ( 1 / 2 ) x b x h
    Combining both statements , we get
    L x B = ( 1 / 2 ) x 40 x 50 ⇒ L x B = 20 x 50 = 1000 cm2
    Since without knowing the breadth of the rectangle, length of the rectangles cannot be determined.