## The table above shows the results of a survey of 100…

## Solution:

We are given that 100 voters were surveyed about their impressions of candidate M and of candidate N, and they responded in the following ways:

favorable

unfavorable

not sure

We need to determine the number of voters who responded favorable for both candidates.

**Statement One Alone: **

The number of voters who did not respond “favorable” for either candidate was 40.

We also can create the following equation:

Total surveyed = number who responded favorable for at least one candidate + number who did not respond favorable for either candidate.

100 = responded favorable + 40

60 = responded favorable

Since we need to determine how many voters responded favorable to both candidates we can create one more equation.

Total favorable votes = favorable for candidate M + favorable for candidate N – favorable for both

60 = 40 + 30 – both

60 = 70 – both

both = 10

Thus, 10 voters responded favorable to both candidates. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

**Statement Two Alone: **

The number of voters who responded “unfavorable” for both candidates was 10.

Since statement two only provides information about the number of voters who responded in the unfavorable category, we do not have enough information to determine how many responded favorable to both candidates. Statement two alone is not sufficient to answer the question.

**Answer: A**