If n is an integer, is n positive? (1) (2n + 1)/(n + 1) is an integer

I must disagree with the reasoning on statement 1. Just because you gave 2 examples in which the statement holds true, that does not mean the statement does not hold true for any positive values of N. The message from this is: the only scenario in which you can use two examples to prove that a statement is sufficient or not, is when you (relating to this question) have a value of N for which the answer is YES and a value for N for which the answer is NO. Proving that the statement is insufficient. I guessed B on this question.

-update-

On statement 1 I reasoned that the only way for it to be true would be 2n=n meaning that n should equal 0.

Martijn is correct; plugging in numbers typically works best when you suspect that the statement is NOT SUFFICIENT. In these cases, all you need to do is find values that yield different (conflicting) answers to the target question.

Conversely, if the statement is SUFFICIENT, then plugging in values will only HINT at whether or not the statement is sufficient, but you won't be able to make any definitive conclusions.

For example, let's say we have the following target question: If n is a positive integer, is (2^n) - 1 prime?
Let's say statement 1 says: n is a prime number:

Now let's plug in some prime values of n:
If n = 2, then (2^n) - 1 = 2² - 1 = 3, and 3 IS prime
If n = 3, then case (2^n) - 1 = 2³ - 1 = 7, and 7 IS prime
If n = 5, then (2^n) - 1 = 2⁵ - 1 = 31, and 31 IS prime
At this point, it certainly APPEARS that statement guarantees that (2^n) - 1 is prime? Let’s try one more prime value of n.
If n = 7, then (2^n) - 1 = 2⁷ - 1 = 127, and 127 IS prime

So, can we be 100% certain that statement 1 is sufficient? No. The truth of the matter is that statement 1 is NOT SUFFICIENT. To see why, let’s examine the possibility that n = 11
If n = 11, then (2^n) - 1 = (2^11) - 1 = 2047, and 2047 is NOT prime


Here’s a different example:
Target question: Is x > 0?
Let's say statement 1 says: 5x > 4x

Now let's plug in some values of x that satisfy the condition that 5x > 4x.
x = 3, in which case x > 0
x = 0.5, in which case x > 0
x = 15, in which case x > 0
x = 1000, in which case x > 0

Once again, it APPEARS that statement 1 provides sufficient information to answer the target question. Can we be 100% certain? No. Perhaps we didn't plug in the right numbers (as was the case in the first example). Perhaps there's a number that we could have plugged in such that x < 0

If we want to be 100% certain that a statement is SUFFICIENT, we'll need to use a technique other than plugging in.
Here, we can take 5x > 4x, and subtract 4x from both sides to get x > 0 VOILA - we can now answer the target question with absolute certainty.
So, statement 1 is SUFFICIENT.

TAKEAWAY: Plugging in numbers is best suited for situations in which you suspect that the statement is not sufficient. In these situations, plugging in values can yield results that are 100% conclusive. Conversely, in situations in which the statement is sufficient, plugging in values can STRONGLY HINT at sufficiency, but the results are not 100% conclusive.

For more on this, you can watch our free video titled “Choosing Good Numbers: https://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1102 or you can read an article I wrote: https://www.gmatprepnow.com/articles/dat ... lug-values

Cheers,
Brent

Hi Brent,
I have quick question regarding your example is x>0. If I use x=-2 in the statement 5x>4x, so -10<-8 so X won't be smaller than zero. it should be insufficient. However, through simple algebra you proved that X>0. I'm confused. what did I miss?

Thanks

Plugging in x = -2 does not satisfy the given inequality 5x > 4x
We get: (5)(-2) > (4)(-2), which evaluates to -10 > -8, HOWEVER -10 is not greater than -8

Cheers,
Brent

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If n is an integer, is n positive?

1) (2n+1)/(n+1) is an integer

2) n=−n

There is one variable (n) in the original condition and 2 equations in the given conditions, so there is high chance (D) is the answer.
For condition 1, n=0,-2, so the answer is 'no' and is sufficient.
For condition 2, 2n=0, n=0, so the answer is 'no' and is sufficient, making the answer (D).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Hi Brent,

In the above statement 1, can n be -2? Because in the 3rd step above in which 1+ n/(n+1), if we replace n with -2, the answer will be 2. So technically n can be 0 or -2? However, the statement still prove to be sufficient.

We must always remember what the target question is asking.

Target question: Is n positive?

If n = 0, the answer to the target question is "NO, n is not positive"
If n = -2, the answer to the target question is "NO, n is not positive"

In order for a statement to be insufficient, we need DIFFERENT answers to the target question.

Does that help?

Cheers,
Brent

According to the first statement n has two values -2 and 0, but in 2nd statement, '-2' doesn't satisfy the condition. In data sufficiency questions, shouldn't n have values that justify both the statements?

From statement 2, we can conclude that x = 0 OR x = -2
So, we're not saying that x must equal -2

Since x = 0 satisfies both statements, the question isn't breaking any data sufficiency rules

Does that help?

Cheers,
Brent

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