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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  [#permalink]

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15 Jun 2016, 03:15
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86% (00:27) correct 14% (00:25) wrong based on 1154 sessions

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Is $$w + h^4$$ positive?

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

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Md. Abdur Rakib

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Re: Is w + h^4 positive? (1) h is positive (2) w is positive  [#permalink]

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15 Jun 2016, 03:19
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AbdurRakib wrote:
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.

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Re: Is w + h^4 positive? (1) h is positive (2) w is positive  [#permalink]

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06 Dec 2016, 08:19
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AbdurRakib wrote:
Is $$w + h^4$$ positive?
1) h is positive
2) w is positive

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.

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Re: Is w + h^4 positive? (1) h is positive (2) w is positive  [#permalink]

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12 Dec 2016, 14:24
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
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive  [#permalink]

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13 Dec 2016, 04:55
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? (1) h is positive (2) w is positive  [#permalink]

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Updated on: 21 May 2019, 07:25
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

Originally posted by Mo2men on 28 Jul 2017, 15:54.
Last edited by Mo2men on 21 May 2019, 07:25, edited 1 time in total.
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive  [#permalink]

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18 Sep 2017, 03:56
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
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive  [#permalink]

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12 Jan 2018, 04:48
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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Re: Is w + h^4 positive? (1) h is positive (2) w is positive  [#permalink]

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28 Jan 2018, 09:13
niks18 amanvermagmat

Quote:
Is $$w + h^4$$ positive?
1) h is positive
2) w is positive

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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Re: Is w + h^4 positive? (1) h is positive (2) w is positive  [#permalink]

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28 Jan 2018, 09:19
niks18 amanvermagmat

Quote:
Is $$w + h^4$$ positive?
1) h is positive
2) w is positive

Hi Experts,
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 ger result as 2, and is YES

Is my number picking approach correct?

In a Yes/No question if you get Yes/No with two plug-in then that should be sufficient.
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive  [#permalink]

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21 May 2019, 05:02
AbdurRakib wrote:
Is $$w + h^4$$ positive?

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

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
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive  [#permalink]

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22 May 2019, 08:00
AbdurRakib wrote:
Is $$w + h^4$$ positive?

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

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
Re: Is w + h^4 positive? (1) h is positive (2) w is positive   [#permalink] 22 May 2019, 08:00
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