If n is an integer is n - 1 0?

Question

If n is an integer is n - 1 > 0

(1) n^2 - n > 0
(2) n^2 = 9

Bunuel · Answer

If n is an integer is n - 1 > 0

Is n - 1 > 0? --> is n > 1?

(1) n^2 - n > 0 --> n(n - 1) > 0 --> n < 0 or n > 1. Not sufficient.

(2) n^2 = 9 --> n = 3 or n = -3. Not sufficient.

(1)+(2) n could still be 3 or -3. Not sufficient.

Answer: E.

Solving inequalities:
https://gmatclub.com/forum/x2-4x-94661.html#p731476 (check this one first)
https://gmatclub.com/forum/inequalities-trick-91482.html
https://gmatclub.com/forum/data-suff-ine ... 09078.html
https://gmatclub.com/forum/range-for-var ... me#p873535
https://gmatclub.com/forum/everything-is ... me#p868863

Hope it helps.

kyro · Answer

1) n^2-n>0 : in this case if n is -ve thn this case is always true, but the eqn n-1>0 becomes invalid, hence insufficient.
2) n^2=9 => n=3 or n=-3, hence insufficient.
both are insufficient.

rakp · Answer

Thanks for the replies but I still have a doubt. Shouldn't the answer be C?
 1) n^2 - n > 0 --> n(n-1)>0, doesn't this mean that n>0 or n>1 so when we combine this with n= +3 or n= -3 then the answer is +3?

Please elaborate.
Thank you!

Bunuel · Answer

The range n > 0 or n > 1 does not make any sense. (1) n^2 - n > 0 --> n(n-1)>0 --> the roots are 0 and 1 --> ">" sign indicates that the solution lies to the left of the smaller root and to the right of the larger root: n<0 or n>1. Not sufficient. Solving inequalities: x2-4x-94661.html#p731476 ( check this one first ) inequalities-trick-91482.html data-suff-inequalities-109078.html range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535 everything-is-less-than-zero-108884.html?hilit=extreme#p868863 Hope it helps.

carriehoang0410 · Answer

Ans is C
(1) n^2 - n > 0 , so n > 0 or n - 1>0 ----> insufficient
(2) n^2 = 9, so n= 3 or n = -3 -----> insufficient
Combine: we have n=3, hence n -1 . 0

Bunuel · Answer

The red part is not correct. Refer to my previous post.

atalpanditgmat · Answer

Bunuel could you please illustrate this concept thoroughly. I am having trouble understanding this one. n^2 - n > 0 --> n(n-1)>0 --> n<0 or n>1. Normally, we take it as n>0 and n>1. Needed extra light...
Thanks in advance.

Kris01 · Answer

Hello atalpanditgmat,

Here are my two cents on this.

In case of n(n-1)>0, we need to find solutions so that the product of n and n-1 is positive. This is possible only if both the values are positive or negative.
This can happen under two conditions.
n>1 so that n and n-1 are positive
n<0 so that n and n-1 are negative.

Now, discussing your doubt in details, suppose the equation to be x(y-1)>0. In such an equation, x >0 and y>1, so that the product of x and y-1 is positive. The other possibility is x<0 and y<1 so that the product of two negatives turns out positive. When, the same number is being considered, we cannot consider the variable in each of the expressions(like n and (n-1)) independent of each other as in case of x and y.

Hope this helps.

atalpanditgmat

Bunuel could you please illustrate this concept thoroughly. I am having trouble understanding this one. n^2 - n > 0 --> n(n-1)>0 --> n<0 or n>1. Normally, we take it as n>0 and n>1. Needed extra light...
Thanks in advance.

Bunuel · Answer

Check here: if-n-is-an-integer-is-n-131293.html#p1080057 Hope it helps.

niyantg · Answer

Hello Bunuel Please Clarify how did you get : n<0 or n>1 . from n(n-1)>0 If i Try frm eq : n(n-1)>0 We can say that either both are positive : n>0 or (n-1)>0 -> n>1 ... SO probably on combining these 2 equations we will get : n>1 or both are negative : n<0 or (n-1)<0 -> n<1 .. here on combining we can get : n<1 Please tell me where am i wrong ?

Bunuel · Answer

n(n-1)>0 means that the multiples have the same sign: n>0 and n-1>0 --> n>0 and n>1 --> n>1 (both to hold true n must be greater than 1); n<0 and n-1<0 --> n<0 and n<1 --> n<0 (both to hold true n must be less than 0). There are other approaches possible which are explained in the posts below: Theory on Inequalities: x2-4x-94661.html#p731476 inequalities-trick-91482.html data-suff-inequalities-109078.html range-for-variable-x-in-a-given-inequality-109468.html everything-is-less-than-zero-108884.html graphic-approach-to-problems-with-inequalities-68037.html All DS Inequalities Problems to practice: search.php?search_id=tag&tag_id=184 All PS Inequalities Problems to practice: search.php?search_id=tag&tag_id=189 700+ Inequalities problems: inequality-and-absolute-value-questions-from-my-collection-86939.html Also check our new set, 50 GMAT Data Sufficiency Questions on Inequalities : 50-gmat-data-sufficiency-questions-on-inequalities-167841.html Hope it helps.

MrWallSt · Answer

Also an alternative solution to the problem is the following:

Statement 1:

n^2-n>0 --> n^2>n (you can always use addition in inequalities) --> 1>1/n (we can divide by n^2 since we know that it is positive since any number squared is positive).

So from this statement we know that 1/n is less than 1. That means that n>1, since 1 divided by a number greater than 1 results in a fraction or n is negative. This is not enough to answer the question

Statement 2:

This statement tells us that n is -3 or 3. Not enough to answer the question either. When we combine both statements we still can not answer, therefore making the answer E.

If this was helpful, any kudos would be appreciated.

CEdward · Answer

If n is an integer is n - 1 > 0

(1) n^2 - n > 0 --> n(n-1) > 0 
n>2 WORKS
n<0 DOES NOT
Insufficient.

(2) n^2 = 9
|n| = 3 --> n = 3,-3 
Insufficient

Combo pack: 
Nothing has changed from st2 even after accounting for st1. n = 3,-3 
Insufficient.

If n is an integer is n - 1 > 0?

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