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.
 How many children are there in the class?
I. Numbers of boys and girls are in the respective ratio of 3 : 4.
II. Number of girls is more than the number of boys by 18.

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On the given all information in above question , we can say that
From I : Ratio of boys and girls = 3k : 4k
From II : Number of girls − Number of boys = 18
From I and II : 4k − 3k = 18Correct Option: E
On the given all information in above question , we can say that
From I : Ratio of boys and girls = 3k : 4k
From II : Number of girls − Number of boys = 18
From I and II : 4k − 3k = 18
∴ k = 18
Now , total number of children in the class = Number of boys + Number of girls
∴ 4k + 3k = 7 × 18 = 126.
Hence , Combining statement I and statement II .
 What was the population of State ‘A’ in 1999?
I. Population of the State increases every year by 20% and its population in 1997 was 120000.
II. Population of State A in 1997 was twice that of State B in the same year.

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According to above given statements , we have
From statement I ,
Population in 1997 = 120000.
Population increases in 1997 = 120000 of 20% = 120000 x ( 20 / 100 ) = 24000
Population in 1998 = Population in 1997 + Population increase = 120000 + 24000 = 144000
Population increases in 1998 = 144000 of 20% = 144000 x ( 20/ 100 ) = 28800
Now , Population in 1999 = Population in 1998 + Population increase = 144000 + 28800 = 172800
From statement II ,
Population of State A in 1997 = 2 x Population of State B in 1997Correct Option: A
According to above given statements , we have
From statement I ,
Population in 1997 = 120000.
Population increases in 1997 = 120000 of 20% = 120000 x ( 20 / 100 ) = 24000
Population in 1998 = Population in 1997 + Population increase = 120000 + 24000 = 144000
Population increases in 1998 = 144000 of 20% = 144000 x ( 20/ 100 ) = 28800
Now , Population in 1999 = Population in 1998 + Population increase = 144000 + 28800 = 172800
From statement II ,
Population of State A in 1997 = 2 x Population of State B in 1997
From above both statements , it is clear that Only statement I alone is sufficient.
 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.
 What is the rate of interest p.c.p.a.?
I. Difference between compound interest and simple interest on an amount or $ 10,000 for two years is $ 225.
II. The amount doubles itself on simple interest in 6^{2}/_{3} years.

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We know, if we have been given difference of CI and SI during two years, then this difference (D) is equal to
P x r ^{2} 100 ^{2}
where, P = Principal, r = rate of interest
From I : We get the value of P and D. Hence, statement I alone is sufficient.Again, we known SI = P x R x T 100 Correct Option: C
We know, if we have been given difference of CI and SI during two years, then this difference (D) is equal to
P x r ^{2} 100 ^{2}
where, P = Principal, r = rate of interest
From I : We get the value of P and D. Hence, statement I alone is sufficient.
where, P = principalAgain, we known SI = P x R x T 100
r = rate of interest
T = time period
From II : We get value of P = K(say).Then, SI = K and T = 6 2 years 3
Hence, using the above formula we can get rate of interest from II alone also.