Nayyar29
-----------Approve----Disapprove----- No Opinion
Policy A-----30----------- 40------------- 30
Policy B-----25----------- 55------------- 20
The table above shows the results of a survey of 100 voters who each responded “Approve,” “Disapprove,” or “No Opinion” when asked about their opinions on two government policies, Policy A and Policy B. What was the number of voters who responded “Disapprove” for both policies?
(1) 10 voters responded “No Opinion” for both policies and the number of voters who did not respond “No Opinion” for either policy is 400% of the number of voters who responded “Disapprove” for both policies.
(2) The number of voters who did not respond “Disapprove” for either policy was 20.
Here's how I took on the question.
Voters who had "No Opinion" for Policy A = 30, Voters who had "No Opinion" for Policy B = 20
Starting with Statement (1), it is given that 10 voters responded “No Opinion” for both policies
With this, we can find out the voters who had "No Opinion"
ONLY for Policy A = 30 - 10 = 20; similarly, voters who had "No Opinion"
ONLY for Policy B = 20 - 10 = 10
Now, the total number of voters who responded "No Opinion" = 40 (20 (ONLY A) + 10 (ONLY B) + 10 (BOTH)), and hence, the total number of voters who did not respond "No Opinion" = 100 - 40 =
60, and this is 400% of the number of voters who responded “Disapprove” for both policies (as given in Statement 1), and hence, the number of voters who responded “Disapprove” for both policies = 15
Statement (1) is SUFFICIENT;
Now looking at Statement (2), number of voters who did not respond “Disapprove” for either policy was 20
Voters who responded "Disapprove" for A = 40; Voters who responded "Disapprove"
ONLY for A = 40 - (Both) [Both refers to the voters who responded "Disapprove" for both the policies]
Voters who responded "Disapprove" for B = 55; Voters who responded "Disapprove"
ONLY for B = 55 - (Both)
Now, simply writing this as 40 - Both + 55 - Both + Both + 20 = 100
115 - 100 = Both
And hence, the number of voters who responded “Disapprove” for both policies = 15
Statement (2) is SUFFICIENT;
Since both statements are individually sufficient to arrive at the answer, the correct answer choice here is (D)