Data Sufficiency
Direction: Each of the following questions is followed by information in three statements. You are to find out which statement(s) is /are sufficient to answer the question and mark your answer accordingly.
 In how many days will B alone complete the work ?
I. A and B together can complete the work in 8 days.
II. B and C together can complete the work in 10 days.
III. A and C together can complete the work in 12 days.

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(A + B)'s 1 day's work = 1/8 .........(i)
(B + C)'s 1 day's work = 1/10 ...........(ii)
(C + A)'s 1 day's work = 1/12 ..............(iii)
Add the equation 1 , 2 and 3 and Solve the equation.Correct Option: C
(A + B)'s 1 day's work = 1/8 ..........(i)
(B + C)'s 1 day's work = 1/10 ..........(ii)
(C + A)'s 1 day's work = 1/12 ............(iii)
Add the equation (i), (ii), (iii)
2(A + B + c)'s 1 day's work = 1/8 + 1/10 + 1/12
(A + B + C)'s 1 day's work = 1/2[1/8 + 1/10 + 1/12] ..........(iv)
Subtracting Eq. (iii) from Eq. (iv), we get B's 1 day's work.
then, required number of days = 1/(B's 1 day's work) .
So we need all above 3 statements to solve the given question.
Direction: These question consists of a question and two statement numbered I and II given below it . You have to decide whether the data provided in the statement are sufficient the data provided in the statements are sufficient to answer the question . read both the statements and select the appropriate answer.
 How many student are there in the class ?
I. there are more than 20 but less that 27 student in the class .
II. there are more than 24 but less then 31 student in the class the number of student in the class can be divided into group such that each group contains 5 students.

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From Statement I,
Number of student in the class
= 21 or 22 or 23 or 24 or 25 or 26
From Statement II,
Number of student in the class
= 25 or 26 or 27 or 28 or 29 or 30
Sine , number of student can be divided into group of 5 students, therefore number of student must be multiple of 5.
∴ NUmber of student in the class = 25 or 30
Combining Statement I and II .
Number of Student in the class = 25
Hence , the data in both the Statement I and II together are necessary to answer the question .
Correct Option: A
From Statement I,
Number of student in the class
= 21 or 22 or 23 or 24 or 25 or 26
From Statement II,
Number of student in the class
= 25 or 26 or 27 or 28 or 29 or 30
Sine , number of student can be divided into group of 5 students, therefore number of student must be multiple of 5.
∴ NUmber of student in the class = 25 or 30
Combining Statement I and II .
Number of Student in the class = 25
Hence , the data in both the Statement I and II together are necessary to answer the question .
 Among five friend − J, K, L, M, and N each of a different height , who is the second tallest ?
I. N is taller than M and K,K is shorted than M.
II. L is taller than M and N. J is not the tallest.

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From Statement I,
N > M > K
From Statement II ,
L > N
From both the Statement
L > N > M > K
but height of J is not clear .
Thus second tallest friend cannot be determined.
Hence, data neither in Statement I nor in Statement II are sufficient to answer the question .Correct Option: B
From Statement I,
N > M > K
From Statement II ,
L > N
From both the Statement
L > N > M > K
but height of J is not clear .
Thus second tallest friend cannot be determined.
Hence, data neither in Statement I nor in Statement II are sufficient to answer the question .
Direction: Each of the question below consists of a question and two statements numbered I and II given below it . you have to decide whether the data given in the statements are sufficient to answer the questions, read both the statements .
 Five letter A, E, G, N and R are arranged left to right according to certain conditions. Which letter is placed third ?
I. G is placed second to the right of A. E is to the immediate right of G . There are only two letter between Rand G.
II. N is exactly between A and G, neither A nor G is at the extreme end of the arrangement.

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Form Statement I,
R A G E
Clearly , the left place or empty place is filled by N .
From Statement II ,
A N G
G N A
Clearly N is at third place ,
Hence, the data in Statement I alone or in Statement II alone are sufficient to answer the question .Correct Option: C
Form Statement I,
R A G E
Clearly , the left place or empty place is filled by N .
From Statement II ,
A N G
G N A
Clearly N is at third place ,
Hence, the data in Statement I alone or in Statement II alone are sufficient to answer the question .
Direction: These question consists of a question and two statement numbered I and II given below it . You have to decide whether the data provided in the statement are sufficient the data provided in the statements are sufficient to answer the question . read both the statements and select the appropriate answer.
 Is D the mother of s ?
I. L is the husband of D . L has only three children.
II. N is the brother of S and P. P is the daughter of L .

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From Statement I L is the husband of D . as L has three children , D also has three children .
From Statement II, N, S and P are siblings and are the children of L and of D also . Thus , D is the mother of S .
Hence , data in both the Statement I and II together are necessary to answer the question .Correct Option: D
From Statement I L is the husband of D . as L has three children , D also has three children .
From Statement II, N, S and P are siblings and are the children of L and of D also . Thus , D is the mother of S .
Hence , data in both the Statement I and II together are necessary to answer the question .