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a > 0
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02 Oct 2018, 05:46
02 Oct 2018, 05:46
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Question Stats:
46% (00:19) correct
53% (00:13) wrong based on 97 sessions
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a > 0
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(a^4a^5\) |
\((a^3)^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Re: a > 0
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04 Oct 2018, 14:20
04 Oct 2018, 14:20
1
amorphous wrote:
a > 0
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(a^4a^5\) |
\((a^3)^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Applying the Product Law, \(a^4a^5 = a^9\)
Applying the Power of a Power Law, \((a^3)^2 = a^6\)
So, we have:
Quantity A: \(a^9\)
Quantity B: \(a^6\)
Since a is POSITIVE, we know that \(a^6\) is POSITIVE, which means we can safely divide both quantities by \(a^6\)
When we do this, we get:
Quantity A: \(a^3\)
Quantity B: 1
Let's test some values of m
If m = 1, we get:
Quantity A: 1³ = 1
Quantity B: 1
In this case, the two quantities are EQUAL
If m = 2, we get:
Quantity A: 2³ = 8
Quantity B: 1
In this case, Quantity A is GREATER
Answer: D
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Re: a > 0
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14 Oct 2020, 22:38
14 Oct 2020, 22:38
1
Quantity A: a^4 X a^5 = a^4+5 = a^9.
Quantity B: (a^3)^2 = a^3X2 = a^6.
There is a nice rule which says, if base is between 0 and 1, value of the base and exponent is inversely proportional to the magnitude of the exponent.
Given a>0, we don't if 'a' is a decimal between 0 and 1 or an integer.
If 'a' is a decimal between 0 and 1 then Quantity B will be greater.
If 'a' is an integer then Quantity A will be greater.
Therefore we cannot determine the relationship between the two quantities hence the answer is D.
Quantity B: (a^3)^2 = a^3X2 = a^6.
There is a nice rule which says, if base is between 0 and 1, value of the base and exponent is inversely proportional to the magnitude of the exponent.
Given a>0, we don't if 'a' is a decimal between 0 and 1 or an integer.
If 'a' is a decimal between 0 and 1 then Quantity B will be greater.
If 'a' is an integer then Quantity A will be greater.
Therefore we cannot determine the relationship between the two quantities hence the answer is D.
