## Data Sufficiency

#### Data Interpretation

Direction: Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to study the questions and decide the data in which of the statements are sufficient to answer the questions.

1. What is the speed of the train ‘A’?
I. Train A crosses 200-metre-long train B running in opposite direction in 20 seconds.
II. Speed of the train B is 60 Km/h.
III. Length of train A is twice that of train B.

1.  speed of train A + speed of train B = Distance of train A + Length of train B Time

##### Correct Option: D

As per given above question , we have
I.Length of train B = 200 m , Time = 20 seconds

 ∴ speed of train A + speed of train B = Distance of train A + Length of train B Time

 ⇒ VA + VB = DA + 200 20

II. Speed of train B ( VB ) = 60 Km/h
III. Length of train A ( DA ) = 2 x Length of train B = 2 x 200 = 400 m.
Putting the values of II and III in I, we get the value of VA = 48 Km/h.
 speed of train A + 60 = ( 400 + 200 ) x 18 20 5

 ⇒ VA + 60 = 120 x 9 10

⇒ VA + 60 = 12 x 9 = 108 ⇒ VA = 108 - 60 = 48 km//h.

1. What is the cost of flooring a rectangular hall?
I. Perimeter of the hall is 76 m
II. Area of the hall is 336 m2.
III. Cost of flooring per square metre is \$550.

1. Combining (II) and (III),
Total cost = Area of the hall x Cost of flooring per square metre
= 336 × 550 = \$184800.

##### Correct Option: B

From above given statement , we can see that
I. Perimeter of the rectangular hall = 2 ( length + breadth ) = 76 m
⇒ 2 ( L + B ) = 76
∴ L+ B = 38
II. Area of the hall = 336 m2
⇒ length x breadth = 336 m2
III. Cost of flooring per square metre = \$550.
Combining (II) and (III),
Total cost = Area of the hall x Cost of flooring per square metre
= 336 × 550 = \$184800.

1. What is the rate of interest p.c.p.a.?
I. The amount doubles itself in 5 years on simple interest.
II. Difference between the compound interest and the simple interest earned on this amount in two years is \$400.
III. Simple interest earned per annum is \$2000.

1. Let amount = \$ A
According to ( I ) statement ,
I. A = 2A
From I alone,
Here , A2 = \$ 2A , A1 = \$ A , T = 5 years

 Rate of interest = ( A2 - A1 ) x 100 A1

 Rate of interese = (2 - 1) x 100 = 20 % 5

##### Correct Option: E

Let amount = \$ A
According to ( I ) statement ,
I. A = 2A
From I alone,
Here , A2 = \$ 2A , A1 = \$ A , T = 5 years

 Rate of interest = ( A2 - A1 ) x 100 A1

 Rate of interese = (2 - 1) x 100 = 20 % 5

II. CI - SI = \$400.
III. Simple interest earned per annum = \$2000
From II and III
 Rate of interese = 2 x difference in CI and SI [For 2 years only] SI

 Rate of interese = 2 x 400 x 100 % 2 x 2000

 Rate of interese = 800 x 100 = 20 % 4000

Hence, either I alone or II and III together are sufficient.

1. What is the present age of Subir?
I. The present age of Subir is half that of his father.
II. After 5 years the ratio of Subir’s age to his father’swill be 6 : 11.
III. Subir is 5 years younger than his brother.

1. Let, the present age of Subir and his father be S and F, respectively.

 I. S = F 2

##### Correct Option: A

Let, the present age of Subir and his father be S and F, respectively.

 I. S = F 2

 II. After 5 years , S + 5 = 6 ⇒ 6F - 11S = 25 F + 5 11

III. Age of Subir’s brother - Age of Subir = 5
⇒ B − S = 5 [ B = age of Subir’s brother]
Now, with the help of I and II together, the value of S and F can be determined.

1. What was the amount of profit earned?
I. 10% discount was offered on the labelled price.
II. Had there been not discount, profit would have been 30%
III. Selling price was more than the cost price by 20%

1. None of the statements give the amount of labelled price or SP. So, even by combining all the statements together, question cannot be answered.

##### Correct Option: E

None of the statements give the amount of labelled price or SP. So, even by combining all the statements together, question cannot be answered.
Hence ,we cannot find the amount of profit earned because all the above given information are not sufficient .