Is x positive?
1) 1/(x+1)<1
2) x-1 is a perfect square
statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;
EACH statement ALONE is sufficient to answer the question asked;
statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
I knew that 2 is alone sufficient. But...
1 statement
1 way of solving - 1/(x+1)<1 => 1<(x+1)*1 => 1<x+1 => 1-1<x => x>0 - sufficient
2 way of solving -
if x = 3 => 1/3+1<1 =>1/4<1 - is true
if x=-2 => 1/-2+1 => -1<1 - is true
So insufficient
What is true about first statement?
Algebra vs. Ballparking
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There are two possibilities, (x + 1) is positive and (x + 1) is negative.[email protected] wrote:1/(x+1)<1 => 1<(x+1)*1 => 1<x+1 => 1-1<x => x>0 - sufficient
If (x + 1) > 0,
- 1/(x + 1) < 1 ---> 1 < (x + 1) ---> x > 0
So, this is true for all x > 0
- 1/(x + 1) < 1 ---> 1 > (x + 1) ---> x < 0
So, this is true for all x < -1
As x can be positive as well as negative, statement 1 is insufficient.
You've considered only the first scenario, i.e. (x + 1) is positive.
Hope that helps.
Anju Agarwal
Quant Expert, Gurome
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Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §