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# a and b are integers.

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Founder
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a and b are integers. [#permalink]  24 May 2017, 01:27
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Expert's post
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Question Stats:

66% (00:27) correct 33% (00:37) wrong based on 128 sessions

$$a$$ and $$b$$ are integers.

$$a^2=b^3$$

 Quantity A Quantity B a b

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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GRE Instructor
Joined: 10 Apr 2015
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Kudos [?]: 4499 [1] , given: 69

Re: a and b are integers. [#permalink]  24 May 2017, 05:57
1
KUDOS
Expert's post
Carcass wrote:

a and b are integers.

$$a^2=b^3$$

 Quantity A Quantity B a b

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.

There are many values of a and b that satisfy the equation a² = b³
So, let's TEST a few options.

One pair of values is a = 0 and b = 0, since 0² = 0³
In this case, we get:
Quantity A: 0
Quantity B: 0
Here, the quantities are EQUAL

Another pair of values is a = 8 and b = 4, since 8² = 4³
In this case, we get:
Quantity A: 8
Quantity B: 4
Here, Quantity A is GREATER

[Reveal] Spoiler:
D

Cheers,
Brent
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GRE 1: Q142 V146
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Kudos [?]: 94 [0], given: 99

Re: a and b are integers. [#permalink]  18 May 2018, 03:32
GreenlightTestPrep wrote:
Carcass wrote:

a and b are integers.

$$a^2=b^3$$

 Quantity A Quantity B a b

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.

There are many values of a and b that satisfy the equation a² = b³
So, let's TEST a few options.

One pair of values is a = 0 and b = 0, since 0² = 0³
In this case, we get:
Quantity A: 0
Quantity B: 0
Here, the quantities are EQUAL

Another pair of values is a = 8 and b = 4, since 8² = 4³
In this case, we get:
Quantity A: 8
Quantity B: 4
Here, Quantity A is GREATER

[Reveal] Spoiler:
D

Cheers,
Brent

I was unable to come up with

Another pair of values is a = 8 and b = 4, since 8² = 4³
In this case, we get:
Quantity A: 8
Quantity B: 4
Here, Quantity A is GREATER
Founder
Joined: 18 Apr 2015
Posts: 13371
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Kudos [?]: 3402 [0], given: 12227

Re: a and b are integers. [#permalink]  18 May 2018, 11:32
Expert's post
$$8^2 = 64$$

$$4^3 = 64$$

So $$a^2 = b^3$$; $$64 = 64$$

But $$a = 8$$ and $$b = 4$$ and $$a \neq b$$

Hope now is clear.

Regards
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Intern
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Posts: 28
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Kudos [?]: 20 [1] , given: 0

Re: a and b are integers. [#permalink]  15 Jun 2019, 22:35
1
KUDOS
Carcass wrote:

$$a$$ and $$b$$ are integers.

$$a^2=b^3$$

 Quantity A Quantity B a b

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.

------------CONCEPT---------------
If a = -ve --> b = +ve
If a = +ve --> b= +ve

i.e. b will have same value for 2 values of a and hence can be greater as well as smaller than a.
Re: a and b are integers.   [#permalink] 15 Jun 2019, 22:35
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