fcabanski wrote:The Data Sufficiency section is not about proving sufficiency. It's about selecting the correct answer. If you select the correct answer but don't prove your reasoning, you still get the credit for a correct answer. Examining values for x and y, and examining trends, is good enough for proving, to the test taker, that statement 2 is sufficient.
I challenge you to find an exception for this problem (that shows statement 2 is not sufficient).
May be it was not clear from my previous post but I was trying to make a general point about DS problems not specific to this problem. And I never said that you have to show the proof of sufficiency to someone! I was trying to say that by not finding an exception you can never be 100% sure that a statement is sufficient (not only for this problem). Only by identifying a trend for some examples without any logical basis we cannot claim a statement always holds because it may very well be that there is an exception to the trend which we didn't consider.
In some cases (like this) we can get lucky and identify the correct answer but if students are taught this method of marking a statement sufficient by not finding an exception, they may not be always so lucky.
Also I've tried to provide an example of how people can make the mistake.
If that was not sufficient, here is another...
If p is a positive integer, is 2^p - 1 prime?
1. p < 5
2. p is prime
For statement 1, if p = 1, (2^p - 1) = 1 is not prime
And if p = 2, (2^p - 1) = 3 is a prime
So, statement 1 is
not sufficient as we have found a contradiction.
[
Now if a student is taught to mark a statement sufficient by not finding an exception, he/she will approach as follows...]
For statement 2, let's check some values for p,
for p = 2, (2^2 - 1) = 4 - 1 = 3 is a prime
for p = 3, (2^3 - 1) = 8 - 1 = 7 is a prime
for p = 5, (2^5 - 1) = 32 - 1 = 31 is a prime
for p = 7, (2^7 - 1) = 128 - 1 = 127 is a prime
...
Looks like there is a trend. So 2^p - 1 is always prime.
So, statement 2 is
sufficient as we have not found a contradiction.
But in this case that logic fails!
Because for p = 11, 2^p - 1 = 2048 - 1 = 2047 = 23*89 is not prime.
So, actually statement 2 is
not sufficient.
I hope now I'm being clear about the point I'm trying to make.
