IMO D

-1<x<1


1. x>x^2


This is possible only if x is between 0 and 1 . Between 0 and -1, x<x^2

Although we dont have to consider x>1, x<-1 , even in those situations x^2 >x

0<x<1

Sufficient

2. x>x^3

Again this is possible only if x is between 0 and 1 considering range of x of -1<x<1

We also know that x >x^3 when x is less than -1 but we dont have to consider that possibilities as x is only between 1 and -1

Between 0 and -1, x^3>x

Sufficient


D

maihuna wrote:
Pick a no is not a good strategy, all the mod questions are solvable step by step, I have recently paid huge price to such ad-hoc methods when I ended up scoring a mere 47 in quant and so ruining up my chance to apply for an mba this year. Oppurtunity cost is too much, in practice look for a method that is guaranteed to work and dont waste time tricking on other questions.....

Well I dont agree with the fact that picking a number is not a good strategy or that one should always solve DS questions with one guaranteed method. I feel one should have a basket of methods and shortcuts when they attack a DS question. Because there are times where one approach or method would fail or you'll have no idea on how to apply that approach to a particular question. In such cases it is usually good if you have a backup method.

For instance look at this question, it barely takes a few seconds to solve this question if you plug in numbers. But if you do it algebraically chances are that you might end up messing up one step and get an incorrect answer.

A lot of people do have difficulty using methods like picking numbers because we are not used to solving questions using this approach. For most of us (me atleast) since school days it has been drilled in our heads that we have to use algebraic methods and solve a question step by step.
So its just a matter of practice to gain proficiency and to be comfortable with such methods. Otherwise these methods are extremely useful and can save a lot of time.

Though Im not saying algebraic methods are bad either. They are very helpful in understanding the logic behind the questions. But I find them a bit more time consuming.

So maihuna dont hate picking numbers method they can be quite useful

Btw my answer is also D. Same approach as mehravikas.

Pick a no is not a good strategy, all the mod questions are solvable step by step, I have recently paid huge price to such ad-hoc methods when I ended up scoring a mere 47 in quant and so ruining up my chance to apply for an mba this year. Oppurtunity cost is too much, in practice look for a method that is guaranteed to work and dont waste time tricking on other questions.....

as for as part b is concerned, dont factorize x^2-1 to durther cases just consider it this way: for 0<x<1 x^2<1 for other values x^2>1 it will help minimizing number of cases to be considered.

Maihuna,
I appreciate your feedback & thoughts but did u even look at my first solution? Anyways I was picking numbers to help explain to Pakaswa one of his cases in his stmt II analysis. This is not a modulus question right and Yes using number line concepts works good for most abs value problems.

Different paths lead to different destinations...-> Pick what works


Irrespective of all that, I completely agree with what Mals said above. Picking numbers is a GREAT STRATEGY. If u can't think of an algebric approach then u almost always have to do this(much better than staring at the problem hoping an algebric solution will click in our brains). For eg: Picking numbers works wonders for remainder problems.

If u use smart numbers according to the constraints given in the problem then with practice "picking numbers" may even be one of the fastest ways to prove suff/insuff.

Even if u prove something algebrically still u can pick numbers to double check ur algebric deduction.

Take this more as a friendly request:
DONT AVOID THIS STRATEGY COMPLETELY

Above all go with what u feel most comfortable with since different strategies work for different people. As long as u can get to the answer within the required time then any strategy is GOOD on the GMAT.

Just my 3 cents since I went over...

Good luck.


Regards,
CR

This has been one interesting discussion and we are very much benefited by this.
Echoing, Mals and Cramya, I too feel that having more than 1 strategy to solve a problem is definetly very important.
I have this ad-hoc thumb rule which I have tested.
If I can recognize a problem and nail down the strategy I want to use within the first 30 seconds of seeing a problem, then I can "most likely" solve the problem within 2 mins. Else, I would most likely take 3 or 4 mins.
So having a bag of tricks for solving a problem is very very useful.

my 2 cents.

-V

pakaskwa wrote:If -1<x<1, is x>0?
(1) x^2<x
(2) x^3<x

A friend of mine asked me this question, and we don't know the OA.

For (1) x^2 is a positive number less than x, so x is also positive. Sufficient

For (2) in the given interval for x, x^3 < x will be true when x is positive. Sufficient.

Take D from me.

if at first you don't succeed ...... try it in excel

x x^2 x^2 < x x^3 x^3 < x
-0.9 0.81 No -0.729 No
-0.8 0.64 No -0.512 No
-0.7 0.49 No -0.343 No
-0.6 0.36 No -0.216 No
-0.5 0.25 No -0.125 No
-0.4 0.16 No -0.064 No
-0.3 0.09 No -0.027 No
-0.2 0.04 No -0.008 No
-0.1 0.01 No -0.001 No
0 0 No 0 No
0.1 0.01 Yes 0.001 Yes
0.2 0.04 Yes 0.008 Yes
0.3 0.09 Yes 0.027 Yes
0.4 0.16 Yes 0.064 Yes
0.5 0.25 Yes 0.125 Yes
0.6 0.36 Yes 0.216 Yes
0.7 0.49 Yes 0.343 Yes
0.8 0.64 Yes 0.512 Yes
0.9 0.81 Yes 0.729 Yes


so we know x > 0 when each of the above conditions are satisfied. Moreover, there is no fear that x=0 since conditions wouldn't hold. So I'm going with D (which was my original answer but to add something new to this thread I added table above).