If w 0, what is the value of w?

Question

If  w ≠ 0 , what is the value of  w ?

(1)  w^2 – w^3 > 0

(2)  w^4 = \frac{1}{256}

LetsDoIt2022 · Answer

Statement 1 : -> w < 0 as we'd add (subtract the negative w^3 ) to the always positive w^2 resulting in a positive number. -> and 0 < w < 1 as we will always subtract a fraction smaller than w^2 , resulting in a positive number. INSUFFICIENT Statement 2 : -> w can be either -\frac{1}{4} or \frac{1}{4} . INSUFFICIENT Combined : The two values Statement 2 gives us are both valid under Statement 1. INSUFFICIENT -> Answer E

gmatophobia · Answer

Statement 1

We can conclude that w < 1 , however the exact value of w is cannot be found.

Hence the statement is not sufficient.

Statement 2

w can be  \frac{-1}{4}  or  \frac{1}{4}

Hence, this statement can be eliminated.

Combination

Even when we combine, both the statements of Statement 2 hold true.

Hence   E

Can,Will · Answer

gmatophobia  can you elaborate statement 1?
 we have w>0 and w<1 that is 0<w<1

Can,Will · Answer

@brantgmatprepnow

please elaborate statement 1

chetan2u · Answer

If  w ≠ 0 , what is the value of  w ?

(1)  w^2 – w^3 > 0……..w^2(1-w)>0  
Now  w^2>0 , so  1-w>0  or  w<1 
w could be anything less than 1. 
Insufficient

(2)  w^4 = \frac{1}{256}……….w^4=(\frac{1}{6}^4=(\frac{1}{-6})^4 
So w is either  \frac{1}{6}  or  \frac{1}{-6} 
Insufficient

Combined 
Even after combining, w can be either  \frac{1}{6}  or  \frac{1}{-6}

gmatophobia · Answer

Hey  AnujL

In statement 1 we have

w^2–w^3  > 0

Let's take  w^2  common

w^2(1-w) > 0

We see the product of two numbers is greater than 0 (i.e. positive), this can happen in two scenarios

1) Both numbers are negative
2) Both numbers are positive

Extending the concept here, either both  w^2  & (1-w) should be negative or both should be positive.

However,  w^2  cannot be negative (because square of any real number is non - negative), so we can rule out case 1 ( both numbers are negative ). Hence, the only scenario under which this expression can be true is when both  w^2  and (1-w) are positive.

We know  w^2  is positive in this case

Therefore 1 - w should be positive as well.

1-w > 0

i.e. w < 1

Note : w can be anything (i.e. it can be positive or it can be negative). We don't have any restriction on w except that the value of w should be less than 1 and it cannot be 0.

Hope this clarifies.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If w 0, what is the value of w?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If w 0, what is the value of w?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards