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.

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If w 0, what is the value of w?

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