Question

	Favorable	Unfavorable	Not Sure
Candidate M	40	20	40
Candidate N	30	35	35

The table above shows the results of a survey of 100 voters who each responded "Favorable" or "Unfavorable" or "Not Sure" when asked about their impressions of Candidate M and of Candidate N. What was the number of voters who responded "Favorable" for both candidates?
(1) The number of voters who did not respond "Favorable" for either candidate was 40.
(2) The number of voters who responded "Unfavorable" for both candidates was 10.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is A Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

• If x is the number of voters who responded “Favorable” for both candidates, then it follows from the table that the number of voters who responded “Favorable” to at least one candidate is 40 + 30 - x = 70 - x. This is because 40 + 30 represents the number of voters who responded “Favorable” for Candidate M added to the number of voters who responded “Favorable” for Candidate N, a calculation that counts twice each of the x voters who responded “Favorable” for both candidates.
  

1. Given that there were 40 voters who did not respond “Favorable” for either candidate and there were 100 voters surveyed, the number of voters who responded “Favorable” to at least one candidate is 100 - 40 = 60. Therefore, from the comments above, it follows that 70 - x = 60, and hence x = 10. Thus, sufficient.
2. The information given affects only the numbers of voters in the categories “Unfavorable” for Candidate M only, “Unfavorable” for Candidate N only, and “Unfavorable” for both candidates. Thus, the numbers of voters in the categories “Favorable” for Candidate M only, “Favorable” for Candidate N only, and “Favorable” for both candidates are not affected. Since these latter categories are only constrained to have certain integer values that have a total sum of 70 - x, more than one possibility exists for the value of x. Thus, not sufficient.

• The correct answer is A; statement 1 alone is sufficient. 149. A school administrator will assign each student in a group of n stud