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

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

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

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

Cheers,
Brent
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive [#permalink]
How is H^4 always positive? H can be (-4)^(1/4) in which case h^4 = -4
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive [#permalink]
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!!!!
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive [#permalink]
aks12194 wrote:
How is H^4 always positive? H can be (-4)^(1/4) in which case h^4 = -4

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

Numbers on the GMAT are real by default, so even roots from negative numbers are not defined.
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive [#permalink]
RB95 wrote:
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!!!!

Natural numbers = positive integers (or according to some non-negative integers). I think you meant real numbers instead.
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive [#permalink]
AbdurRakib wrote:
Is $$w + h^4$$ positive?

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

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Re: Is w + h^4 positive? (1) h is positive (2) w is positive [#permalink]
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.
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Is w + h^4 positive? (1) h is positive (2) w is positive [#permalink]
Bunuel wrote:
aks12194 wrote:
How is H^4 always positive? H can be (-4)^(1/4) in which case h^4 = -4

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

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

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
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Re: Is w + h^4 positive? (1) h is positive (2) w is positive [#permalink]
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Maxel wrote:
Bunuel wrote:
aks12194 wrote:
How is H^4 always positive? H can be (-4)^(1/4) in which case h^4 = -4

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

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

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

Yes, however, h^4 always means (h)^4.
Re: Is w + h^4 positive? (1) h is positive (2) w is positive [#permalink]
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