## 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 height of a triangle?
I. The area of the triangle is 20 times its base.
II. The perimeter of the triangle is equal to the perimeter of a square of 10 cm side.

1. On the basis of above given details in question ,
Let b be the base of triangle and h be height of triangle .
From statement II , The perimeter of the triangle = The perimeter of a square of 10 cm side.
⇒ 2s = 4 x 10 = 40 ⇒ s = 40 / 2 = 20 cm
From statement I , The area of the triangle = 20 x base.
⇒ ( 1 / 2 ) x b x h = 20 x b
⇒ h = 20 x 2 = 40 cm
Hence , the height of a triangle = 40 cm

##### Correct Option: A

On the basis of above given details in question ,
Let b be the base of triangle and h be height of triangle .
From statement II , The perimeter of the triangle = The perimeter of a square of 10 cm side.
⇒ 2s = 4 x 10 = 40 ⇒ s = 40 / 2 = 20 cm
From statement I , The area of the triangle = 20 x base.
⇒ ( 1 / 2 ) x b x h = 20 x b
⇒ h = 20 x 2 = 40 cm
Hence , the height of a triangle = 40 cm
Thus , the height can be determined with the help of statement I alone. correct answer is A .

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. 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 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. 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 was the cost price of the suitcase purchased by Samir?
I. Samir got 20 percent concession on the labeled price.
II. Samir sold the suitcase \$ 2000 with 25 percent profit on the labeled price.

1. As per the given all details in above question , we have
Let the labelled price be \$100.
From statement I , Concession on the labeled price = 20%
From statement II , Samir sold the suitcase = \$ 2000 and profit = 25%
Combing both the statements together,
Now, SP of the suitcase = 125% of 100 = \$125

 ∴ Labelled price = 2000 x 100 = \$ 1600 125

##### Correct Option: E

As per the given all details in above question , we have
Let the labelled price be \$100.
From statement I , Concession on the labeled price = 20%
From statement II , Samir sold the suitcase = \$ 2000 and profit = 25%
Combing both the statements together,
Now, SP of the suitcase = 125% of 100 = \$125

 ∴ Labelled price = 2000 x 100 = \$ 1600 125

 ∴ CP of the suitcase = 1600 x 3 = \$ 1200 4

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. 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.