Data Sufficiency

The table above shows the result of survey of 100 students who responded with "For" or "Against" or "Not sure" when asked about the Debate choice of the Topic A and Topic B.


What was the number of students who responded "For" for both Topics?

(1) The number of students who did not respond "For" for either Topic was 40.

(2) The number of students who responded "Against" for both Topics was 20.

rijul007 wrote:

The table above shows the result of survey of 100 students who responded with "For" or "Against" or "Not sure" when asked about the Debate choice of the Topic A and Topic B.


What was the number of students who responded "For" for both Topics?


(1) The number of students who did not respond "For" for either Topic was 40.

(2) The number of students who responded "Against" for both Topics was 20.

Total "For" voters = total for A + total for B - total for both.

The big idea with overlapping groups is to SUBTRACT THE OVERLAP. In the problem above, there is an overlap between those who voted for A and those who voted for B. When we count the total voters for A and the total voters for B, the OVERLAP -- the students who voted "for" in regards to both topics -- gets counted twice. So we need to SUBTRACT these students so that they are not double-counted.

Since total for A = 30 and total for B = 40:
Total "For" = 30+40 - both
Both = 70 - total "For".

Question rephrased: What was the total number of "For" voters?

Statement 1: The number of students who did not respond "For" for either topic was 40.
Since there were 100 voters, and 40 did NOT respond "For", the total number who DID respond "For" -- in other words, the total number of "For" voters -- was 60.
SUFFICIENT.

Statement 2: The number of students who responded "Against" for both Topics was 20.
No way to determine the total number of "For" voters.
INSUFFICIENT.

The correct answer is A.

The table above shows the result of survey of 100 students who responded with "For" or "Against" or "Not sure" when asked about the Debate choice of the Topic A and Topic B.


What was the number of students who responded "For" for both Topics?

(1) The number of students who did not respond "For" for either Topic was 40.

(2) The number of students who responded "Against" for both Topics was 20.



Overall 1min and 46 secs taken to answer this question, and also got it right...

COrrect explanation given by Mitch!!!

Good Question. This is same as an OG Question in OG 12.

[quote="GMATGuruNY"][quote="rijul007"][img]https://s3.amazonaws.com/production.gro ... 5696/4.jpg[/img]

The table above shows the result of survey of 100 students who responded with "For" or "Against" or "Not sure" when asked about the Debate choice of the Topic A and Topic B.


What was the number of students who responded "For" for both Topics?


(1) The number of students who did not respond "For" for either Topic was 40.

(2) The number of students who responded "Against" for both Topics was 20.[/quote]


[b]Total "For" voters = total for A + total for B - total for both.[/b]

The big idea with overlapping groups is to SUBTRACT THE OVERLAP. In the problem above, there is an overlap between those who voted for A and those who voted for B. When we count the total voters for A and the total voters for B, the OVERLAP -- the students who voted "for" in regards to both topics -- gets counted twice. So we need to SUBTRACT these students so that they are not double-counted.

Since total for A = 30 and total for B = 40:
Total "For" = 30+40 - both
Both = 70 - total "For".

Question rephrased: What was the total number of "For" voters?

[b]Statement 1: The number of students who did not respond "For" for either topic was 40.[/b]
Since there were 100 voters, and 40 did NOT respond "For", the total number who DID respond "For" -- in other words, the total number of "For" voters -- was 60.
SUFFICIENT.

[b]Statement 2: The number of students who responded "Against" for both Topics was 20.[/b]
No way to determine the total number of "For" voters.
INSUFFICIENT.

The correct answer is [spoiler]A[/spoiler].[/quote]

We know from table that
Total "Against A" : 40
Total "Against B" : 20

so, total "against" : 40 + 20 - both
: 60 - both

We know from Statement 2 that "both against" : 20

so, total "against" : 60 - 20 = 40

so, total "for" : 100 - 40 = 60

so, both "for" : 40 + 30 - 60 = 10

Hence, answer should be D

Pl tell where I am wrong?

ranjeet75 wrote:
We know from table that
Total "Against A" : 40
Total "Against B" : 20

so, total "against" : 40 + 20 - both
: 60 - both

We know from Statement 2 that "both against" : 20

so, total "against" : 60 - 20 = 40

so, total "for" : 100 - 40 = 60

so, both "for" : 40 + 30 - 60 = 10

Hence, answer should be D

Pl tell where I am wrong?

Since every student voted twice, the total number of votes = 200.

Statement 2 implies that the AGAINST votes are distributed as follows:


There is no way to determine how the remaining votes are distributed.

The following distribution is possible:

In this case, the number of students who voted for both A and B is 20.

The following distribution also is possible:

In this case, the number of students who voted for both A and B is 0.

Since the number of students who voted for both A and B can be different values, INSUFFICIENT.