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# Data Sufficiency

1.

How is R related to M ?

Statements:

1. M's brother is husband of P.

2. P is mother of R's sister.

From 2, we conclude that P is R's mother.

From 1, we conclude that M is the brother or sister of P's husband, who is also R's father. Thus, R is either nephew or niece of M.

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2.

Among A, B, C, D and E, who is in the middle while standing in a row ?

Statements:

1. C, who is third to the left of D, is to the immediate right of A and second to the left of E.

2. C is second to the left of E, who is not at any of the ends and who is third to the right of A. D is at one of the ends.

From each one of 1 and 2, we get the order : A, C, B, E, D. Clearly, B is in the middle.

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3.

Among A, B, C, D, E and F, who is the heaviest ?

Statements:

1. A and D are heavier than B, E and F but none of them is the heaviest.

2. A is heavier than D but lighter than C.

From 1, we conclude that since none of A and D is the heaviest and each one of B, E and F is lighter than both A and D, so C is the heaviest.

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4.

How is M related to N?

Statements:

1. P, who has only two kids, M and N, is the mother-in-law of Q, who is sister-in-law of N.

2. R, the sister-in-law of M, is the daughter-in-law of S, who has only two kids, M and N.

From 1, we conclude that P is the mother of M and N, while Q is the daughter-in-law of P and sister-in-law of N. Thus, Q is M's wife and hence, M is N's brother.

From 2, we conclude that M and N are the children of S. Also, R is the daughter-in-law of S and sister-in-law of M. So, R is N's wife and thus, N is M's brother. Hence, M is either brother or sister of N.

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5.

Four subjects - Physics, Chemistry, Mathematics and Biology - were taught in four consecutive periods of one hour each starting from 8.00 a.m. At what time was the Chemistry period scheduled ?

Statements:

1. Mathematics period ended at 10.00 a.m., which was preceded by Biology.

2. Physics was scheduled in the last period.

3. Mathematics period was immediately followed by Chemistry.

From 1 and 2, we conclude that Mathematics period began at 9.00 a.m., Biology period began at 8.00 a.m. and Physics period began at 11 a.m. So, the Chemistry period began at 10.00 a.m.

From 1 and 3, we conclude that Mathematics period ended and Chemistry period began at 10.00 a.m.

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6.

Who is the tallest among six boys P, T, N, D, Q and R ?

Statements:

1. P is taller than D and N but not-as tall as T.

2. R is taller than Q but not as tall as T.

3. Q is not taller than T and R

From 1, we have: P > D, P > N, T > P i.e. T > P > D > N or T > P > N > D ...(i)

From 2, we have: R > Q, T > R i.e. T > R > Q ...(ii)

From 3, we have: T > Q, R > Q ...(iii)

Clearly, from (i) and (ii), we conclude that T is taller than each one of P, N, D, R and Q. So, T is the tallest.

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7.

How is Tanya related to the man in the photograph ?

Statements:

1. Man in the photograph is the only son of Tanya's grandfather.

2. The man in the photograph has no brothers or sisters and his father is Tanya's grandfather.

From 1, we conclude that the man is the only son of Tanya's grandfather i.e. he is Tanya's father or Tanya is the man's daughter.

From 2, we conclude that the man's father is Tanya's grandfather. Since the man has no brothers or sisters, so he is Tanya's father or Tanya is the man's daughter.

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8.

How many speeches were delivered in the two days' programme ?

Statements:

1. 18 speakers were invited to give at least one speech (maximum of two speech), out of which one-sixth of the speakers could not come.

2. One-third of the speakers gave two speeches each.

From 1, we find that number of speakers who attended programme =18-(1/6) of 18 = 15.

From 2, we find that one-third of 15 i.e. 5 speakers gave 2 speeches each, while each of the remaining 10 speakers delivered only one speech.

So, total number of speeches delivered = (5 x 2 + 10 x 1) = 20.

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9.

What is Gagan's age ?

Statements:

1. Gagan, Vimal and Kunal are all of the same age.

2. Total age of Vimal, Kunal and Anil is 32 years and Anil is as old as Vimal and Kunal together.

As given in 1 and 2, we have: G = V = K, V + K + A = 32 and A = V + K.

Putting V + K = A in V + K + A = 32, we have: 2A = 32 or A = 16.

Thus, V + K = 16 and V = K. So, V = K = 8. Thus, G = 8.

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10.

How is F related to P?

Statements:

1. P has two sisters M and N.

2. F's mother is sister of M's father.