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
 A, B and C are integers. Is B an even number?
I. (A + B) is an odd number.
II. (C + B) is an odd number.

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According to question ,
I. A + B is odd ⇒ If A is an even number then B will be an odd number and vice versa.
II. C + B is odd ⇒ if B is an even number then C will be an odd number and vice versa.Correct Option: D
According to question ,
I. A + B is odd ⇒ If A is an even number then B will be an odd number and vice versa.
II. C + B is odd ⇒ if B is an even number then C will be an odd number and vice versa.
So, even by combining the two statements together, we are not able to say that B is an even integer.
 What is the area of a circle?
I. The circumference of the circle is 308 m,
II. The radius of the circle is 28 m.

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As per the given question ,
From statement I ,
The circumference of the circle = 2πr = 308 mRadius of circle ( r ) = 308 x 7 = 49 m 2 x 22 Area of circle = πr^{2} = 22 x 49 x 49 = 7564 m^{2} 7 Correct Option: C
As per the given question ,
From statement I ,
The circumference of the circle = 2πr = 308 mRadius of circle ( r ) = 308 x 7 = 49 m 2 x 22 Area of circle = πr^{2} = 22 x 49 x 49 = 7564 m^{2} 7
From statement II ,Area of circle = 22 x 28 x 28 = 2464 m^{2} 7
Hence, either I alone or II alone is sufficient for answering the question.
 A train crosses a signal post in X sec. What is the length of the train?
I. The train crosses a platform of 100 m in Y sec.
II. The train is running at the speed of 80 Km/h.

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Let, the length of the train be ‘d’ m.
Speed of train = d X
I. We know that when a train crosses a platform, it crosses not only its length but also the length of the platform.i.e., d = d + 100 ⇒ d = 100X X Y Y  X Correct Option: C
Let, the length of the train be ‘d’ m.
Speed of train = d X
I. We know that when a train crosses a platform, it crosses not only its length but also the length of the platform.i.e., d = d + 100 ⇒ d = 100X X Y Y  X II. Length of the train (d) = 80 × 5 X = 200X 18 9
Therefore, either I alone or II alone is sufficient to answer the question.
 What is the sum which earned interest?
I. The total simple interest was $ 7000 after 7 years.
II. The total of sum and simple interest was double of the sum after 5 years.

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On the basis of above given details in question , we get
Let the sum be Rs. P.
From statement I , Simple Interest (S.I.) = Rs. 7000 and T = 7 years.
From statement II , Sum + Simple Interest (S.I.) for 5 years = 2 x Sum ⇒ P + Simple Interest (S.I.) for 5 years = 2P
⇒ Sum ( P ) = Simple Interest (S.I.) for 5 years.
Now, Simple Interest (S.I.) for 7 years = Rs. 7000.Correct Option: E
On the basis of above given details in question , we get
Let the sum be Rs. P.
From statement I , Simple Interest (S.I.) = Rs. 7000 and T = 7 years.
From statement II , Sum + Simple Interest (S.I.) for 5 years = 2 x Sum ⇒ P + Simple Interest (S.I.) for 5 years = 2P
⇒ Sum ( P ) = Simple Interest (S.I.) for 5 years.
Now, Simple Interest (S.I.) for 7 years = Rs. 7000.
Simple Interest (S.I.) for 1 year = Rs. 7000 / 7 = Rs. 1000.
Hence , statement I and statement II are needed to obtain the answer .
 What is the rate of simple interest per annum?
I. The sum triples in 20 years at simple interest.
II. The difference between the sum and the simple interest earned after 10 years is $ 1000.

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As per the given question , we can say
From statement I. R = (3  1) x 100 = 10% 20
From statement II. Here, the sum is not given.Correct Option: A
As per the given question , we can say
From statement I. R = (3  1) x 100 = 10% 20
From statement II. Here, the sum is not given. Therefore, statement I alone is sufficient.