woohoo921 wrote:
parkhydel wrote:
The table shows the number of people who responded “yes” or “no” or “don't know” when asked whether their city council should implement environmental programs X and Y. If a total of 1,000 people responded to the question about both programs, what was the number of people who did not respond “yes” to implementing either of the two programs?
(1) The number of people who responded “yes” to implementing only Program X was 300.
(2) The number of people who responded “no” to implementing Program X and “no” to implementing Program Y was 100.
DS17700.02
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MartyTargetTestPrepI would be so appreciative to learn your view as to how you would best solve this problem if you have time.
Hi
woohoo921 Thanks for your post.
I will share with you a methodical approach to solve this question. For this, I will use some basic inferences (all inferred from the information given in the question) and the Venn Diagram representation of the given data.
So, following the basic principles of solving any Data Sufficiency question, let’s start with the question stem analysis.
QUESTION STEM ANALYSIS: The table shows the number of people who responded “yes” or “no” or “don't know” when asked whether their city council should implement environmental programs X and Y. If a total of 1,000 people responded to the question about both programs, what was the number of people who did not respond “yes” to implementing either of the two programs? Let’s first understand what is given here.
A total of 1000 people responded to some survey about two programs – X and Y. And all of them responded for each program in one of three ways - “yes”, “no” or “don’t know”. Now, the question wants us to find
the number of people who DID NOT respond ‘yes’ to either of the two programs.
That is, we want the number of people who
did NOT respond ‘yes’ to program X and did NOT respond “yes” to program Y. To understand this whole thing, let’s first understand what it means for a person who does NOT respond “yes” to a program.
- For program X, those who do not respond “Yes” implies they responded either “no” or “don’t know” – this is everything except “yes”. So, if we want the number of people not responding “yes”, we can find them by subtracting those who do respond “yes” from the total of 1000.
So, # people not responding Yes = 1000 - # of people responding “yes”
- Similarly, for program Y, those who do not respond “yes” can be found as 1000 - # of people responding “yes”.
Overall, we can say that to find
the number of people who DID NOT respond ‘yes’ to either of the two programs, we MUST find those who said “Yes” to either of the two programs. And then we’ll just subtract that number from 1000.
So, our required number =
{1000 - # of people who responded “yes” to either X or Y}.
NOTE: Now, there are chances of some people being common - those who said “yes” to both programs. That is why the number of people who said “yes” to either X or Y is
NOT just the sum of those who said “yes” to X and those who said “yes” to Y. The correct formula for
#people who responded “yes” to either X or Y is below: (#Responded “yes” to X) UNION (#Responded “yes” to Y).
Let’s now see what the statements give us, starting with the analysis of statement 1.
STATEMENT 1 ANALYSIS: The number of people who responded “yes” to implementing only Program X was 300. So, this statement tells us about those who responded “yes” to only program X. For using this effectively, let’s try to make the Venn Diagram for those who responded “yes” to
either program.
Here, ‘a’ and ‘c’ represent those who responded “yes” to ONLY program X and to ONLY program Y, respectively, and ‘b’ represents those who responded “yes” to both programs.
Now, statement 1 gives us the value for ‘a’ as 300.
- This implies b = 400 – a = 400 – 300 = 100
- And since we now know the value of b, the value of c = 300 – b = 200
So, the number of people who said “yes” to either of the two programs = a + b + c = 300 + 100 + 200 = 600.
And that is exactly what is needed. So, we can say the required number = 1000 - (a + b + c) = 1000 – 600 = 400.
Hence, a UNIQUE answer, which makes statement 1 alone
SUFFICIENT.
STATEMENT 2 ANALYSIS: The number of people who responded “no” to implementing Program X and “no” to implementing Program Y was 100. This statement tells us about the number of people who responded “NO” to both programs.
Note: Without any analysis, we can see that this statement gives us nothing about the people who respond “yes” to one or both of X and Y. So, it looks like this statement will not be of much use. Still, we will do the same analysis as we did in statement 1 and be sure of our answer.
Per statement 2, q = 100. These are the people who responded “no” to both programs.
- Now, p + q = 200, and q = 100. This implies p = 100.
- Similarly, q + r = 350 and q = 100. This implies r = 250.
- Combining the two inferences above, we get:
- #people who responded “no” to either of the two programs = p + q + r = 450.
But even after this analysis, does this provide us with any information about the number of people who responded “yes” to either of the two programs?
NO! That means the information in statement 2 alone is
INSUFFICIENT to provide a unique answer to the main question asked.
So, our correct answer choice is
option A.
Hope this helps!
Best,
Aditi Gupta
Quant expert,
e-GMAT _________________