Two Statements S1 and S2 are given below followed by a Question: S1: There are not more than two figures on…
Two Statements S1 and S2 are given below followed by a Question:
S1: There are not more than two figures on any page of a 51-page book.
S2: There is at least one figure on every page.
Question: Are there more than 100 figures in that book?
Which one of the following is correct in respect of the above Statements and the Question?
Both S1 and S2 are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
S1 alone is sufficient to answer the Question.
S1 and S2 together are not sufficient to answer the Question.
S2 alone is sufficient to answer the Question.
Solution
S1 gives at most $2 \times 51 = 102$ figures. S2 gives at least $1 \times 51 = 51$ figures. Together the total figures lie between 51 and 102. This range includes values both more than 100 (101, 102) and not more than 100. So even both statements together cannot definitively answer whether there are more than 100 figures. Hence S1 and S2 together are not sufficient.