# Data Sufficiency

In 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 Give answer.

(A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question

(B) If 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

(C) If the data either in statement I alone or in statement II alone are sufficient to answer the question

(D) If the data given in both statements I and II together are not sufficient to answer the question and

(E) If the data in both statements I and II together are necessary to answer the question.

Question:
Among five friends, who is the tallest ?
Statements:

1. D is taller than A and C.
2. B is shorter than E but taller than D.

From I, we have: D > A, D > C.

From II, we have: E > B > D.

Combining the above two, we get :E > B > D > A > C or E > B > D >C > A.

Thus, E is the tallest.

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

From II, 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.

Question:
In a row of five buildings – P, Q, R, S and T, which building is in the middle ?
Statements:

1.  Buildings S and Q are at the two extreme ends of the row.
2.  Building ,T is to the right of building R.

From I, we have the order : S, -, -, -, Q. From II, we have the order : R, T. Combining the above two, we get two possible orders : S, R, T, P, Q or S, P, R, T, Q. Thus, either T or R is in the middle.

Question:
What is the rank of P from the bottom in a class of 30 students ?
Statements:

1. M is third from the top and there are five students between M and P.
2. The rank of K is fourth from the bottom and there are 17 students between K and P.

From I, we conclude that P is 9th from the top. Thus, in a class of 30 students, P ranks 22nd from the bottom.

From II, we conclude that P is 22nd from the bottom.

Question:
Gaurav ranks eighteenth from the top in a class. What is his rank from the last?
Statements:

1. There are 47 students in the class.
2. Jatin who ranks 10th in the same class, ranks 38th from the last.

From I, we conclude that in a class of 47 students, Gaurav ranks 18th from the top and hence 30th from the last.

From II, we conclude that there are 9 students above and 37 students below Jatin in rank. Thus, there are (9 + 1 + 37) = 47 students in the class.

So, Gaurav who ranks 18th from the top, is 30th from the last.

Question:
How many visitors saw the exhibition yesterday ?
Statements:

1. Each entry pass holder can take up to three persons with him/her.
2. In all, 243 passes were sold yesterday.

From I and II, we find that maximum (243 x 3) i.e. 729 visitors saw the exhibition.

But the exact number cannot be determined.

Question:
What is the numerical code for ‘water’ in a certain code ?
Statements:

1. The code for ‘give me water’ is ‘719’.
2. The code for ‘you can bring water for me’ is written as ‘574186’.

In I and II, the common words are 'me' and 'water' and the common code numbers are '7' and '1'. So, the code for 'water' is either '7' or '1'.

Question:
Which code word stands for ‘good’ in the coded sentence ‘sin co bye’ which means ‘He is good’ ?
Statements:

1. In the same code language, ‘co mot det’ means ‘They are good’.
2. In the same code language, ‘sin mic bye’ means ‘He is honest’.

In the given statement and I, the common word is 'good' and the common code word is 'co'. So, 'co' is the code for 'good'.

In the given statement and II, the common words are 'He' and 'is' and the common code words are 'sin' and 'bye'. So 'sin' and 'bye' are the codes for 'He' and 'is'. Thus, in the given statement, 'co' is the code for 'good'.

Question:
Who among P, Q, T, V and M is exactly in the middle when they are arranged in ascending order of their heights ?
Statements:

1. V is taller than Q but shorter than M.
2. T is taller than Q and M but shorter than P.

From I, we have: M > V > Q.

From II, we have: T > Q, T > M, P > T.

Combining the above two, we have: P>T>M>V>Q i.e. Q

Clearly, M is in the middle.

Question:
How is ‘No’ coded in the code language ?
Statements:
‘Ne Pa Sic Lo’ means ‘But No None And’ and ‘Pa Lo Le Ne’ means ‘If None And But’.
‘Le Se Ne Sic’ means ‘If No None Will’ and ‘Le Pi Se Be’ means ‘Not None If All’.