Data Sufficiency
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.
 How many marks did Arun get in English?
A. Arun secured an average of 60 marks in four subjects including English.
B. He secured a total of 170 in English and Mathematics together.
C. He secured a total of 180 in Mathematics and Science together.

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As per the given all details in above question , we have'
From statement A , average of four subjects marks including English = 60 marks
Total Sum of four subjects marks = 60 x 4 = 240 marks
From statement B , Total marks in English and Mathematics together = 170 marks
From statement C , Total marks in Mathematics and Science together = 180 marks
Anyone of the three statements is not sufficient to answer the question.Correct Option: E
As per the given all details in above question , we have
From statement A , average of four subjects marks including English = 60 marks
Total Sum of four subjects marks = 60 x 4 = 240 marks
From statement B , Total marks in English and Mathematics together = 170 marks
From statement C , Total marks in Mathematics and Science together = 180 marks
Anyone of the three statements is not sufficient to answer the question. The question cannot be answered even with the information in all the three statements.
 What is the sum of two numbers?
A. The bigger of these two numbers is 6 more than the smaller number.
B. 40% of the smaller number is equal to 30% of the bigger number.
C. The ratio between half of the bigger number and onethird of the smaller number is 2 : 1.

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Let, the bigger and smaller numbers be p and q, respectively.
From statement A, p − q = 6 ....... ( 1 )
From statement B, 40% of q = 30% of p ⇒ 4q = 3p …......(2)Correct Option: E
Let, the bigger and smaller numbers be p and q, respectively.
From A, p − q = 6 ....... ( 1 )
From B, 40% of q = 30% of p ⇒ 4q = 3p …(2)From C, p : q = 2 : 1 ⇒ 3p = 4q ....(3) 2 3
On solving equations ( 1 ) and ( 2 ) or ( 3 ) , we get
q = 18 and p = 24
Hence , the bigger and smaller numbers be 24 and 18.
We see that equations (2) and (3) are same. Hence, A and either B or C is required.
 What is the area of a rightangled triangle?
A. The perimeter of the triangle is 30 cm.
B. The ratio between the base and the height of the triangle is 5 : 12.
C. The area of the triangle is equal to the area of rectangle of length 10 cm.

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Let, the base, height and hypotenuse of a rightangled triangle be b, p and h, respectively.
From Statement A, b + P + h = 30 …(1)
From Statement B, b : p = 5 : 12 …(2)
Let the base of triangle is 5k and height of triangle is 12k .
We know that
h^{2} = p^{2} + b^{2} = 25k^{2} + 144k^{2} = 169k^{2}
∴ h = 13k …(3)
Combining equations (1), (2) and (3), we get
5k + 12k + 13k = 30 ⇒ k = 1Correct Option: B
Let, the base, height and hypotenuse of a rightangled triangle be b, p and h, respectively.
From Statement A, b + P + h = 30 …(1)
From Statement B, b : p = 5 : 12 …(2)
Let the base of triangle is 5k and height of triangle is 12k .
We know that
h^{2} = p^{2} + b^{2} = 25k^{2} + 144k^{2} = 169k^{2}
∴ h = 13k …(3)
Combining equations (1), (2) and (3), we get
5k + 12k + 13k = 30 ⇒ k = 1
∴ Area of triangle = 1 x 5 x 12 = 30 cm^{2} 2
Hence, only A and B together are sufficient.
 What is R’s share of profit in a joint venture?
A. Q started a business investing $ 80000.
B. R joined him after 3 months.
C. P joined after 4 months with a capital of $ 120000 and got $ 6000 as his share of profit.

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On the basis of above given details in question , we can say that
From statement A , Invested amount by Q = $ 80000.
From statement B , R joined him after 3 months.
From statement C , After 4 months , Invested amount by P = $ 120000
and profit = $ 6000
Investment ratio or amount is not given.Correct Option: D
On the basis of above given details in question , we can say that
From statement A , Invested amount by Q = $ 80000.
From statement B , R joined him after 3 months.
From statement C , After 4 months , Invested amount by P = $ 120000
and profit = $ 6000
Investment ratio or amount is not given, hence even all statements together are not sufficient.
 What will be the cost of painting the four walls of a room with length, width and height 5 m, 3 m and 8 m respectively? The room has one door and one window.
A. Cost of painting per m^{2} is $ 25.00
B. Area of window of 2.25 m^{2} is half of the area of the door.
C. Area of the room is 15 m^{2}.

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As per the given above question ,
Given , Length = 5 m , Width = 3 m and Height = 8 m
From statement A , Cost of painting = $ 25 per m^{2}
From statement B , Area of window = ( 1 / 2) x area of the door
⇒ 2.25 m^{2} = ( 1 / 2) x area of the door ⇒ area of the door = 4.50 m^{2}
From statement C , Area of the room = 15 m^{2}.
The area of four walls = 2h( l + b ) = 2 x 8 ( 5 + 3 ) = 16 x 8 = 128 m^{2}.
∴ Cost of painting the four walls = area x Cost of painting per m^{2} = 128 x 25 = $ 3200Correct Option: D
As per the given above question ,
Given , Length = 5 m , Width = 3 m and Height = 8 m
From statement A , Cost of painting = $ 25 per m^{2}
From statement B , Area of window = ( 1 / 2) x area of the door
⇒ 2.25 m^{2} = ( 1 / 2) x area of the door ⇒ area of the door = 4.50 m^{2}
From statement C , Area of the room = 15 m^{2}.
The area of four walls = 2h( l + b ) = 2 x 8 ( 5 + 3 ) = 16 x 8 = 128 m^{2}.
∴ Cost of painting the four walls = area x Cost of painting per m^{2} = 128 x 25 = $ 3200
The area off our walls can be easily determined with the help of the data given in the question. Now,the area of the windows and door with the help of (B) can be subtracted in the calculated area and then multiplied with the cost given in (A).