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a < 0 < b

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a < 0 < b [#permalink]  15 Feb 2017, 08:46
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Question Stats:

74% (00:39) correct 25% (00:35) wrong based on 226 sessions

$$a < 0 < b$$

 Quantity A Quantity B $$a^{-10}$$ $$b^{-5}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: a < 0 < b [#permalink]  21 Feb 2017, 16:32
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Explanation

The best strategy to solve these problems is by plugging values

Put a = -1 and b = 1, then we have

Quantity A is $$-1^{10} = 1$$

Quantity B is $$1^5 =1$$

Clearly, the quantities are equal. Now put a = -2 and b = 1

Quantity A is $$-2^{10} = 1024$$

Quantity B is $$1^5 =1$$

Now Quantity A is greater. Clearly, both A and C cannot be right at the same time so option D is the correct choice!
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Re: a < 0 < b [#permalink]  10 Aug 2017, 08:35
But the question states a^-10 power and b^-5... and a < 0 < b

-1^-10 = -1
1^-5 = 1

In what circumstance can A and B be equal if you raise them to a negative power?

Ok, I am an idiot - I was playing with the equation in my calculator, which is why it was driving me nuts... because I was almost positive it was wrong... I was inputting -1^-10, and not (-1)^-10... You are correct.
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Re: a < 0 < b [#permalink]  19 May 2018, 09:38
I think the entity A will be a faction with a negative sign and entity B will be postive ..becasue the entity A is negative in nature ?

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Re: a < 0 < b [#permalink]  19 May 2018, 16:36
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IshanGre wrote:
I think the entity A will be a faction with a negative sign and entity B will be postive ..becasue the entity A is negative in nature ?

$$a$$ is a negative number may or maynot be a fraction. However it is raised to even power.
If $$a$$ is a fraction then $$a^{-10}$$ is a number greater than 1.
if $$|a| > 1$$ then $$a^{-10}$$ is a fraction.

However in both cases they are positive.
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Re: a < 0 < b [#permalink]  21 May 2018, 06:13
sandy wrote:
IshanGre wrote:
I think the entity A will be a faction with a negative sign and entity B will be postive ..becasue the entity A is negative in nature ?

$$a$$ is a negative number may or maynot be a fraction. However it is raised to even power.
If $$a$$ is a fraction then $$a^{-10}$$ is a number greater than 1.
if $$|a| > 1$$ then $$a^{-10}$$ is a fraction.

However in both cases they are positive.

I can see but the question stem says that the a is raised to the power of negative 10? pls elaborate
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Re: a < 0 < b [#permalink]  21 May 2018, 12:19
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Say a=$$\frac{-1}{2}$$ then $$a^{-10}=(\frac{-1}{2})^{-10}= 2^{10}$$.

Also a=$$-2$$ then $$a^{-10}=(-2)^{-10}= (\frac{-1}{2})^{10}=\frac{1}{2^{10}}$$.

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Re: a < 0 < b [#permalink]  16 Jul 2018, 17:53
How is it not B?

When we set a = -1 and b = 1:
qty1) -1^-10) = -1/1^10 = -1
qty2) 1^5 = 1

Thus QTY 2 is bigger.

Lets make a=-2 and b=2:
qty1) -2^-10 = -1/2^10
qty2) 2^5 = 32

Clearly a negative fraction is smaller than 32 making qty 2 greater again.

This has to mean that B is the answer. Why would it be D?
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Re: a < 0 < b [#permalink]  17 Jul 2018, 13:29
Expert's post

$$a^{-10} = \frac{1}{a^{10}}$$ and if $$a$$ is $$-1 = 1^{10} = 1$$. So a ends up being positive.
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Re: a < 0 < b [#permalink]  03 Jan 2019, 17:45
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a < 0 < b
A = a^-10 = (1/a)^10 because a has power 10 which is even, A is positive.
B = b^-5 = (1/b)^5 B is positive, because b>0.

If a = -1 -> A =1
If b = 1 -> B =1
So A and B are equal

If a = -1/2 -> A =2^10
If b = 1 -> B =1
So A is bigger than A

If a = -1 -> A =1
If b = 1/2 -> B =2^5
So B is bigger than A.

So we are not able to construe which one is bigger or smaller, etc. The answer is D.
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Re: a < 0 < b [#permalink]  25 May 2019, 09:30
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Carcass wrote:

$$a < 0 < b$$

 Quantity A Quantity B $$a^{-10}$$ $$b^{-5}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Let's test some values of a and b

case i: If a < 0 < b, then it COULD be the case that a = -1 and b = 1
We get:

QUANTITY A: $$a^{-10}=(-1)^{-10}=\frac{1}{(-1)^{10}}=\frac{1}{1}=1$$

QUANTITY B: $$b^{-5}=1^{-5}=\frac{1}{1^5}=\frac{1}{1}=1$$

In this case, the two quantities are equal

case ii: If a < 0 < b, then it COULD be the case that a = -1 and b = 2
We get:

QUANTITY A: $$a^{-10}=(-1)^{-10}=\frac{1}{(-1)^{10}}=\frac{1}{1}=1$$

QUANTITY B: $$b^{-5}=2^{-5}=\frac{1}{2^5}=\frac{1}{32}$$

In this case, Quantity A is greater

Cheers,
Brent
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Re: a < 0 < b [#permalink]  22 Jan 2020, 06:25
testing nos is the best strategy here
Re: a < 0 < b   [#permalink] 22 Jan 2020, 06:25
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