Data Sufficiency
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
 What is the height of a rightangled triangle?
I. The area of the rightangled triangle is equal to the area of a rectangle whose breadth is 12 cm.
II. The length of the rectangle is 18 cm.

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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 rightangled 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 cm^{2}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 rightangled 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 cm^{2}
∴ 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.
 Which is the smaller of the two numbers?
I. The difference between these two numbers is onethird of the largest number.
II. The sum of these two numbers is 30.

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Let p and q be the two numbers .
According to question ,From statement I. p  q = 1 p
, ⇒ 2p  3q = 03 Correct Option: E
Let p and q be the two numbers .
According to question ,From statement I. p  q = 1 p
, ⇒ 2p  3q = 0 ..........( 1 )3
From statement II. p + q = 30 ...........( 2 )
On solving equations ( 1 ) and ( 2 ) , we get p = 18 and q = 12.
Hence , the smaller number is 12 .So , correct answer is option E .
 What is the rate of compound interest on a sum of money?
I. The total compound interest at the end of two years is $ 820.
II. The total simple interest at the same rate on $ 5000 at the end of three years is $ 750.

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As per the given all details in above question , we can say
From statement I , CI in two years = $ 820
From statement II , Principal = $ 5000 , S.I. = $ 750 , Time = 3 yearsCorrect Option: B
As per the given all details in above question , we can say
From statement I , CI in two years = $ 820
From statement II , Principal = $ 5000 , S.I. = $ 750 , Time = 3 yearsRate = S.I. x 100 % Principal Rate = 250 x 100 = 5 % 5000
Hence, the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
 How many marks did Prakash obtain in Mathematics?
I. Prakash secured on an average 55 percent marks in Mathematics, Physics and Chemistry together.
II. Prakash secured 10 percent more than the average in Mathematics.

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As per the given above question ,
From statement I , Average of mathematics , physics and chemistry = 55%
⇒ M + Ph + Ch = 165%
From statement II , Prakash → M + 10% (average)
Where , M → Mathematics , Ph → Ph and Ch → ChemistryCorrect Option: D
As per the given above question ,
From statement I , Average of mathematics , physics and chemistry = 55%
⇒ M + Ph + Ch = 165%
From statement II , Prakash → M + 10% (average)
Where , M → Mathematics , Ph → Ph and Ch → Chemistry
Hence , both statements I and II together are not sufficient to answer the question.
 What is the cost of polishing the rectangular floor?
I. Room is 9 m long and 7 m wide.
II. Cost of polishing the floor of 10 m by 5 m is $ 112.50.

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On the basis of above given details in question ,
From statement I → Area of the room = L x B = 9 × 7 = 63 m^{2}From statement II → Rate = Cost of polishing the floor Area of floor Correct Option: E
On the basis of above given details in question ,
From statement I → Area of the room = L x B = 9 × 7 = 63 m^{2}From statement II → Rate = Cost of polishing the floor Area of floor Rate = 112.50 = 2.25 per m^{2} 10 x 5
∴ Combining both the statements, cost of polishing the rectangular floor = 63 × 2.25 = $ 141.75.