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Data Sufficiency - Verbal and Reasoning

Directions to SolveIn 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 andGive 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.
Q1:

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.

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

ANS:E - Both I and II are sufficient

Explanation: 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.