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a and b are integers greater than zero.

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a and b are integers greater than zero. [#permalink] New post 18 Sep 2018, 10:35
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a and b are integers greater than zero.

Quantity A
Quantity B
\(\frac{a}{b}\)
\(a^2\)


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 and b are integers greater than zero. [#permalink] New post 18 Sep 2018, 21:16
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Take a=b=1 qty A and qty B will be equal.
Take a=2, b=1 qty A < qty B
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Re: a and b are integers greater than zero. [#permalink] New post 21 Aug 2020, 06:34
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Carcass wrote:


a and b are integers greater than zero.

Quantity A
Quantity B
\(\frac{a}{b}\)
\(a^2\)



Another approach is to use matching operations (my favorite Quantitative Comparison strategy)

Given:
Quantity A: a/b
Quantity B: a²

Since we're told b is POSITIVE, we can safely multiply both quantities by b to get:
Quantity A: a
Quantity B: a²b

Since we're told a is POSITIVE, we can safely divide both quantities by a to get:
Quantity A: 1
Quantity B: ab

At this point we can see that...
- if a = 1 and b = 1, but then the two quantities are equal
- if a = 2 and b = 2, but then Quantity B is greater

Answer: D

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Re: a and b are integers greater than zero. [#permalink] New post 21 Aug 2020, 06:50
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GreenlightTestPrep wrote:

Another approach is to use matching operations (my favorite Quantitative Comparison strategy)

Given:
Quantity A: a/b
Quantity B: a²

Since we're told b is POSITIVE, we can safely multiply both quantities by b to get:
Quantity A: a
Quantity B: a²b

Since we're told a is POSITIVE, we can safely divide both quantities by a to get:
Quantity A: 1
Quantity B: ab

At this point we can see that...
- if a = 0.5 and b = 0.5, but then Quantity A is greater
- if a = 2 and b = 2, but then Quantity B is greater

Answer: D


Even though the answer is right, we shouldn't plug-in decimals, since we have the condition that \(a\) and \(b\) are integers.
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Re: a and b are integers greater than zero. [#permalink] New post 21 Aug 2020, 06:54
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AskMathQuestions wrote:
Even though the answer is right, we shouldn't plug-in decimals, since we have the condition that \(a\) and \(b\) are integers.


Good point!
I edited my solution so that we test a = 1 and b = 1 instead.

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Re: a and b are integers greater than zero.   [#permalink] 21 Aug 2020, 06:54
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a and b are integers greater than zero.

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