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- Question
Question: How many speeches were delivered in the two days' programme?
Statements:
- 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.
- One-third of the speakers gave two speeches each.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient
- Correct Answer
- Both I and II are sufficient
ExplanationFrom 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.
Data Sufficiency problems
Search Results
- 1. Question: In a row of five buildings - P, Q, R, S and T, which building is in the middle?
Statements:
- Buildings S and Q are at the two extreme ends of the row.
- Building ,T is to the right of building R.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Neither I nor II is sufficient
Explanation:
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.- 2. Question: What is the rank of P from the bottom in a class of 30 students?
Statements:
- M is third from the top and there are five students between M and P.
- The rank of K is fourth from the bottom and there are 17 students between K and P.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Either I or II is sufficient
Explanation:
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.
- 3. Question: Gaurav ranks eighteenth from the top in a class. What is his rank from the last?
Statements:
- There are 47 students in the class.
- Jatin who ranks 10th in the same class, ranks 38th from the last.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Either I or II is sufficient
Explanation:
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.
- 4. Question: How many visitors saw the exhibition yesterday?
Statements:
- Each entry pass holder can take up to three persons with him/her.
- In all, 243 passes were sold yesterday.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Neither I nor II is sufficient
Explanation:
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.
- 5. Question: What is the numerical code for 'water' in a certain code?
Statements:
- The code for 'give me water' is '719'.
- The code for 'you can bring water for me' is written as '574186'.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Neither I nor II is sufficient
Explanation:
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'.- 6. Question: Among five friends, who is the tallest?
Statements:
- D is taller than A and C.
- B is shorter than E but taller than D.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Both I and II are sufficient
Explanation:
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.
- 7. Question: What time did the train leave today?
Statements:
- The train normally leaves on time.
- The scheduled departure is at 14 : 30.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Neither I nor II is sufficient
Explanation:
Clearly, even both I and II together do not reveal the exact time of departure of the train today.- 8. Question: What does '$' mean in a code language?
Statements:
- '5$#3' means 'flowers are really good'.
- '7#35' means 'good flowers are available'.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Both I and II are sufficient
Explanation:
In I and II, the common codes are '5', '#' and '3' and the common words are 'flowers', 'are' and 'good'. Thus, in I, the remaining code '$' stands for 'really'.- 9. Question: How many sons does D have?
Statements:
- A's father has three children.
- B is A's brother and son of D.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: Neither I nor II is sufficient
Explanation:
From both I and II together, we can conclude that A and B are the children of D, but the sex of A and the third child of D is not known. So, both I and II together are also not sufficient to answer the question.- 10. Question: How is M related to N?
Statements:
- P, who has only two kids, M and N, is the mother-in-law of Q, who is sister-in-law of N.
- R, the sister-in-law of M, is the daughter-in-law of S, who has only two kids, M and N.
Options- A. I alone is sufficient while II alone is not sufficient
- B. II alone is sufficient while I alone is not sufficient
- C. Either I or II is sufficient
- D. Neither I nor II is sufficient
- E. Both I and II are sufficient Discuss
Correct Answer: I alone is sufficient while II alone is not sufficient
Explanation:
From I, 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 II, 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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- 1. Question: In a row of five buildings - P, Q, R, S and T, which building is in the middle?