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a > 0 || (a + 2)(3a + 6)
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06 Apr 2018, 15:26
06 Apr 2018, 15:26
Expert Reply
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Question Stats:
74% (01:10) correct
25% (00:46) wrong based on 35 sessions
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a > 0
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.
Quantity A |
Quantity B |
\((a + 2)(3a + 6)\) |
\((3a + 2)(a + 6)\) |
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.
Drill 1
Question: 2
Page: 507
Question: 2
Page: 507
Re: a > 0 || (a + 2)(3a + 6)
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15 Apr 2018, 05:24
15 Apr 2018, 05:24
Expert Reply
Explanation
For Quantity A, you get \(3a^2 + 6a + 6a + 12\), or \(3a^2 + 12a + 12\).
For Quantity B, you get \(3a^2 + 18a + 2a + 12\), or \(3a^2 + 20a + 12\).
Remember to compare, not calculate.
Notice that the only difference between the quantities is that between 20a and 12a. Because a is positive, 20a must be greater than 12a, thus, Quantity B will always be greater.
For Quantity A, you get \(3a^2 + 6a + 6a + 12\), or \(3a^2 + 12a + 12\).
For Quantity B, you get \(3a^2 + 18a + 2a + 12\), or \(3a^2 + 20a + 12\).
Remember to compare, not calculate.
Notice that the only difference between the quantities is that between 20a and 12a. Because a is positive, 20a must be greater than 12a, thus, Quantity B will always be greater.
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Re: a > 0 || (a + 2)(3a + 6)
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23 Mar 2021, 05:04
23 Mar 2021, 05:04
sandy wrote:
a > 0
Quantity A |
Quantity B |
\((a + 2 |
3a + 6)\))(\((3a + 2)(a + 6)\) |
We can solve this question using matching operations (my favorite Quantitative Comparison strategy)
Given:
Quantity A: \((a + 2)(3a + 6)\)
Quantity B: \((3a + 2)(a + 6)\)
Expand and simplify both quantities to get:
Quantity A: \(3a^2 + 12a + 12\)
Quantity B: \(3a^2 + 20a + 12\)
Subtract \(3a^2\) from both quantities to get:
Quantity A: \(12a + 12\)
Quantity B: \(20a + 12\)
Subtract \(12\) from both quantities to get:
Quantity A: \(12a\)
Quantity B: \(20a\)
Subtract \(12a\) from both quantities to get:
Quantity A: \(0\)
Quantity B: \(8a\)
At this point, we can see that:
If a = 0, the quantities are equal
If a < 0, Quantity A is greater
If a > 0, Quantity B is greater
Answer: D
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