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Algebra vs. Ballparking

Expert replies
by [email protected] » Mon Apr 22, 2013 5:02 am
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?
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Source: — Data Sufficiency |

by Anju@Gurome » Mon Apr 22, 2013 5:12 am
[email protected] wrote:1/(x+1)<1 => 1<(x+1)*1 => 1<x+1 => 1-1<x => x>0 - sufficient
There are two possibilities, (x + 1) is positive and (x + 1) is negative.

If (x + 1) > 0,
  • 1/(x + 1) < 1 ---> 1 < (x + 1) ---> x > 0
    So, this is true for all x > 0
And if (x + 1) < 0,
  • 1/(x + 1) < 1 ---> 1 > (x + 1) ---> x < 0
    So, this is true for all x < -1
Hence, any value of x which is either less than -1 and or greater than 0 satisfy statement 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

Backup Methods : General guide on plugging, estimation etc.
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