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

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.

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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
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Is w+h^4
For any sign of h, h^4 is always positive
3 cases for w
1, If W is negative, h should be greater to result positive
2, W and H positive
3, If W is negative and greater than h , negative result

1, Insufficient
2, Sufficient

B

Here is my solution:

Question: Is \(w+h^{4}\) positive ?

Statement 1: h is positive.

\(h^{4}\) is always positive (even power).
So we need to know the value of w.
Not sufficient.

Statement 2: w is positive

Both w and h are positive.
Sufficient.

Hence B.
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Is \(w + h^4\) positive?

h^4 is always positive value regardless of value of h

1) h is positive

Let h =1 & w=0........Answer is Yes

Let h =1 & w=-10........Answer is No

Insufficient

2) w is positive

h^4 + w =positive or zero+Positive =Positive value..............Answer is Yes

Sufficient

Answer: B

As h has an even power which is 4 it will always turn out to be positive even if h is negative so the deciding factor here is w. Hence answer is B

Here since h has got even power, so h got to be positive. So now the question is whether w is positive or negative.
STMT 1 - h is positive . Not sufficient , Since we need info related to W
STMT2 - w is positive . Sufficient . Answer is B
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niks18 amanvermagmat




Can I plug in below two values for St 1 (we already know that \(h^4\) is always positive irrespective of value of h)
If w = -1 and h=1 then we get result as 0 and ans to Q is NO (0 is neither positive, nor negative)
If w=1 and h=1 then we get result as 2, ans is YES

Is my number picking approach correct?
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Hi adkikani

In a Yes/No question if you get Yes/No with two plug-in then that should be sufficient.

Considering expression w + (h^4) the RED portion is always +ve we have to find whether w is >=0 or not?

Statement 1. Insufficient
Statement 2. Sufficient, w>0

my approach

1. if h is positive, it can happen that w is positive -- in which case the question stem is true but if w has an unusually large negative value..then the argument does not hold.

2. sufficient; coz h can be negative but an even power turns it positive

What if H is a complex number. For example h= sqt( i ). Then we need both to solve. Answer should be C

No where have the mentioned These are integers.

Regards
Rit

Posted from my mobile device

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

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!!!!

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

Numbers on the GMAT are real by default, so even roots from negative numbers are not defined.
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Natural numbers = positive integers (or according to some non-negative integers). I think you meant real numbers instead.
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Bunuel

Yes- Thanks for pointing it out.. I meant REAL NUMBERS