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If a+b>0 and a^b<0, which of the following must be true?

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If a+b>0 and a^b<0, which of the following must be true?  [#permalink]

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New post 10 Jan 2019, 08:15
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If a+b>0 and a^b<0, which of the following must be true?

I. a<0
II. b>0
III. |b|>|a|

A. I only
B. I&II only
C. I&III only
D. I,II&III
E. Noe of these
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Re: If a+b>0 and a^b<0, which of the following must be true?  [#permalink]

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New post 10 Jan 2019, 08:32
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If a+b>0 and a^b<0, which of the following must be true?

a+b > 0
a^b < 0 implies a is negative and b is odd(-ve/+ve)
but a+b > 0 implies b should be positive and have magnitude greater than a (since a is negative from above sentence)


I. a<0 True
II. b>0 true
III. |b|>|a| true

Option D is correct
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Re: If a+b>0 and a^b<0, which of the following must be true?  [#permalink]

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New post 10 Jan 2019, 08:37
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\(a^b < 0\) means that a must be negative and b odd
if a is negative and and a+b > 0 means that b must be positive
also |b| > |a|, otherwise a+b wouldn't be positive

D
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Re: If a+b>0 and a^b<0, which of the following must be true?  [#permalink]

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New post 10 Jan 2019, 09:13
1
akurathi12 wrote:
If a+b>0 and a^b<0, which of the following must be true?

I. a<0
II. b>0
III. |b|>|a|

A. I only
B. I&II only
C. I&III only
D. I,II&III
E. Noe of these


To test the statement, i took some values
a+b>0 and a^b<0 , for both these statements to be true, a < 0 and b > 0 should be true

if you take a=-1 and b= 3,
If you notice here a != b and b will always be > than a
if you notice here a^b<0, b has to have an odd integer > 1

Making answer as D.
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Re: If a+b>0 and a^b<0, which of the following must be true?  [#permalink]

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New post 10 Jan 2019, 21:20
akurathi12 wrote:
If a+b>0 and a^b<0, which of the following must be true?

I. a<0
II. b>0
III. |b|>|a|

A. I only
B. I&II only
C. I&III only
D. I,II&III
E. Noe of these


We have a^b <0

It is clear that a is negative because a positive number raised to any power is positive

We can consider the following cases

a = -2, b = +/- 1

a = -2 , b = +/- 3

a = - 1/8 , b = +/-1/3 and so on

Now, a + b > 0

Since, a < 0 , from the first condition, We can generate the following cases

a = -2, b = 3

a = -1/8. b = 1/3

It can be seen that a < 0, b > 0 and |b| > |a|

Choice D
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Re: If a+b>0 and a^b<0, which of the following must be true? &nbs [#permalink] 10 Jan 2019, 21:20
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