## Data Sufficiency

#### Data Interpretation

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 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. 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 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. 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. 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. 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.

1. Train ‘A’ running at a certain speed crosses another train ‘B’ running at a certain speed in the opposite direction in 12 seconds. What is the length of train ‘B’?
I. The length of both the trains together is 450 m.
II. Train ‘A’ is slower than train ‘B’.

1. As per the given all details in above question ,
Given , time = 12 seconds
From statement I , The length of both the trains together = 450 m
From statement II , Train ‘A’ is slower than train ‘B’.
Here, neither the speed of the train nor the individual length of the train is given.

##### Correct Option: D

As per the given all details in above question ,
Given , time = 12 seconds
From statement I , The length of both the trains together = 450 m
From statement II , Train ‘A’ is slower than train ‘B’.
Here, neither the speed of the train nor the individual length of the train is given. Hence, (d) is the correct answer.

1. What is the speed of a running train?
I. The train crosses a signal post in 6 seconds.
II. The train crosses another train running in the opposite direction in 15 seconds.

1. On the basis of above given details in question , we have
From statement I , Time taken in crosses a signal post = 6 seconds
From statement II , Time taken in crosses a another train = 15 seconds

##### Correct Option: D

On the basis of above given details in question , we can say that
From statement I , Time taken in crosses a signal post = 6 seconds
From statement II , Time taken in crosses a another train = 15 seconds
Data even in both statements I and II together are not sufficient to answer the question.