Is w + h^4 positive? (1) h is positive (2) w is positive

Question

Is  w + h^4  positive?

(1) h is positive
(2) w is positive

adiagr · Accepted Answer

Key to this question is to understand that  h^4  is always positive.

Then Statement (1) cannot guarantee that  w + h^4

Say h is 1 and w is -2, then given statement is negative. 
say h is 2 and w is 1 then given statement is positive.

So not sufficient.

Statement (2) says w is positive. Now  h^4  is always positive

so the combined expression  will  be positive.

Sufficient.

B is the answer.

ScottTargetTestPrep · Answer

We need to determine whether w+h^4 is positive. First, we know that h^4 is always non-negative.

Let’s look at the 2 possibilities for the value of w+h^4:

1) If w is positive, then (w + h^4) will be positive.

2) If w is negative, then h^4 must be greater than |w| in order for (w + h^4) to be positive. For example if w = -4, then h^4 must be greater than 4 in order for (w + h^4) to be positive.

Statement One Alone:

h is positive

Since we already know that h^4 is positive and do not have any information about w, we do not have enough information to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

w is positive

Since we know that h^4 is non-negative, also knowing that w is positive is enough information to determine that w + h^4 is positive. Statement two is sufficient to answer the question.

Answer: B

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=HiQXD56Iduk

BrentGMATPrepNow · Answer

Target question :    Is w + h⁴ positive?

Statement 1 : h is positive   
Let's TEST some values.
There are several values of w and h that satisfy statement 1. Here are two: 
Case a: w = 1 and h = 1. In this case,  w + h⁴ = 1 + 1⁴ = 2. So, w + h⁴ IS positive 
Case b: w = -3 and h = 1. In this case,  w + h⁴ = -3 + 1⁴ = -2. So, w + h⁴ is NOT positive 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : w is positive  
Important concept: (any number)^(even integer) =   a value greater than or equal to 0  
Statement 2 tells us that w is  some positive number 
We can write:  w  +  h⁴  = ( some positive number ) + (   a value greater than or equal to 0  )
We can see that  w + h⁴ positive is definitely positive 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

aks12194 · Answer

How is H^4 always positive? H can be (-4)^(1/4) in which case h^4 = -4

RB95 · Answer

aks12194

(-4)^1/4 is basically 4th root of a negative number. This means that the number (h) is a complex number.
NOTE: ALL NUMBERS ON GMAT ARE NATURAL NUMBERS. HENCE h^4 is always positive or 0!!!!

Bunuel · Answer

(-4)^{(\frac{1}{4})} = \sqrt {-4} .

Numbers on the GMAT are real by default, so even roots from negative numbers are not defined.

Bunuel · Answer

Natural numbers = positive integers (or according to some non-negative integers). I think you meant real numbers instead.

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=LU_UWRnVL8c

WannaManaConsult · Answer

Doesn't matter for this question but I just want to point out h^4 doesn't have to be positive; it can be 0.

Maxel · Answer

Bunuel 
can you explain why h^4 is always positive here since the interger h is not inside parentheses?
we know that, -2^4= -16 AND (-2)^4= 16

Bunuel · Answer

Yes, however, h^4 always means (h)^4.

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Is w + h^4 positive? (1) h is positive (2) w is positive

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Is w + h^4 positive? (1) h is positive (2) w is positive

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