## 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 will be the area of a plot in sq. metres?
I. The length of that plot is 113 times the breadth of that plot.
II. The diagonal of that plot is 30 metres.

1. From statement I , The length of that plot = 113 x the breadth of that plot
⇒ L = 113B
Where , L = length of plot and B = breadth of plot
From statement II , The diagonal of that plot = 30 metres
Combining statements (I) and (II),
l2 + b2 = 9000

##### Correct Option: E

From statement I , The length of that plot = 113 x the breadth of that plot
⇒ L = 113B
Where , L = length of plot and B = breadth of plot
From statement II , The diagonal of that plot = 30 metres
Combining statements (I) and (II),
l2 + b2 = 9000

 25 b2 + b2 = 900 9

∴ b = 15 m and l = 25 m
∴ Area = 375 m2

1. How long will it take to fill a tank?
I. One pipe can fill the tank completely in 3 hrs.
II. Second pipe can empty that tank in 2 hrs.

1. On the basis of above given details in question , we have
From statement I , One pipe can fill the tank completely = 3 hrs.
From statement II , Second pipe can empty that tank = 2 hrs
The question cannot be answered even with the information in both statements.

##### Correct Option: D

On the basis of above given details in question , we have
From statement I , One pipe can fill the tank completely = 3 hrs.
From statement II , Second pipe can empty that tank = 2 hrs
The question cannot be answered even with the information in both statements.
The data even in both statements I and II together are not sufficient to answer the question.

1. How many items did the distributor purchase?
I. The distributor purchased all the items for \$ 4500.
II. If the distributor had given \$ 5 more for each item he would have purchased 10 items less.

1. From statement I,

 Rate of an item = 4500 = ....(1) n

Here, n = total number of items
Combining statement II and (i), we have 4500 + 5 ( n - 10 ) = 4500 n

##### Correct Option: E

From statement I,

 Rate of an item = 4500 = ....(1) n

Here, n = total number of items
Combining statement II and (i), we have 4500 + 5 ( n - 10 ) = 4500 n

⇒ n2 - 10n - 9000 = 0 ∴ n= 100
Hence, both statements together are sufficient.

1. What will be the cost of the second necklace?
I. The cost of the first necklace is 1 / 5 more than the second and the cost of the third necklace is 2 / 5 more than the second. The total cost of all the three necklaces is \$ 120000.
II. The cost of the first necklace is 2 / 5 more than the second. The cost of the third necklace is the least and total cost of all the three necklaces is \$ 120000.

1. As per the given above question ,
From statement I,
Ratio of the costs of first, second and third necklace is 6 : 5 : 7.

##### Correct Option: A

As per the given above question ,
From statement I,
Ratio of the costs of first, second and third necklace is 6 : 5 : 7. Hence, the price of second necklace can be calculated.

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. What was the profit earned on the cost price by Mahesh by selling an article?
A. He got 15% concession on labelled price in buying that article.
B. He sold it for \$ 3060
C. He earned a profit of 2% on the labelled price.

1. From statement A , concession on labelled price = 15%
From statement B , Sold article = \$ 3060
From statement C , Profit on article = 2%
From A and B,

 Labelled price = 3,060 x 100 = \$ 3600 ....(1) 85

##### Correct Option: E

From statement A , concession on labelled price = 15%
From statement B , Sold article = \$ 3060
From statement C , Profit on article = 2%
From A and B,

 Labelled price = 3,060 x 100 = \$ 3600 ....(1) 85

Combining (1) and statement C,
 Profit = 3600 x 2 = \$ 72 ....(2) 100

Combining (2) and statement B,
CP = 3,060 − 72 = \$ 2988
 ∴ % profit = 72 x 100 = 2.40 % 2988

Hence, all statements are required.