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|x - 5|
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22 Mar 2018, 13:10
22 Mar 2018, 13:10
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Question Stats:
57% (01:56) correct
42% (01:49) wrong based on 202 sessions
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Quantity A |
Quantity B |
\(|x - 5| - |a - b|\) |
\(|b - a| - |5 - x|\) |
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
Re: |x - 5|
[#permalink]
26 Mar 2018, 04:22
26 Mar 2018, 04:22
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Answer is choice B. Here's how:
Firstly, it is not mentioned that the figure not drawn to scale, which means, it is drawn to scale.
As we know |a-b| = |b-a|, and |x-5| = |5-x|
So we can simplify Quantity B as follows:
Quantity A: |x-5| - |a-b|
Quantity B: |a-b| - |x-5|
Now, we need to see whether |x-5| is greater or |a-b|. As we know |x-y| gives distance between x and 5, while |a-b| gives distance between a and b, therefore. After looking at the number line we can see that clearly distance between a and b is greater than distance between x and 5.
Thus, Quantity B is greater.
Firstly, it is not mentioned that the figure not drawn to scale, which means, it is drawn to scale.
As we know |a-b| = |b-a|, and |x-5| = |5-x|
So we can simplify Quantity B as follows:
Quantity A: |x-5| - |a-b|
Quantity B: |a-b| - |x-5|
Now, we need to see whether |x-5| is greater or |a-b|. As we know |x-y| gives distance between x and 5, while |a-b| gives distance between a and b, therefore. After looking at the number line we can see that clearly distance between a and b is greater than distance between x and 5.
Thus, Quantity B is greater.
General Discussion
Re: |x - 5|
[#permalink]
22 Mar 2018, 16:43
22 Mar 2018, 16:43
1
Answer: C
a < 0 < 5 < b < x < 10
| x - 5| - |a - b|
|b - a| - |5 - x|
Comparing the two equations is better than evaluating their value, because they seem similar.
A: x is something between 5 and 10 so x -5 is positive, so |x-5| equals x-5
a is negative, b is positive, (a - b) is negative, so |a - b| = -(a - b)
| x - 5| - |a - b| = x - 5 - a + b
B: x is positive and more than 5, 5-x is negative, so |5-x| equals -(5-x)
b is positive and a is negative, (b-a) is positive, so |b-a| equals b-a
|b - a| - |5 - x| = b - a - 5 + x
They are both equal!
a < 0 < 5 < b < x < 10
| x - 5| - |a - b|
|b - a| - |5 - x|
Comparing the two equations is better than evaluating their value, because they seem similar.
A: x is something between 5 and 10 so x -5 is positive, so |x-5| equals x-5
a is negative, b is positive, (a - b) is negative, so |a - b| = -(a - b)
| x - 5| - |a - b| = x - 5 - a + b
B: x is positive and more than 5, 5-x is negative, so |5-x| equals -(5-x)
b is positive and a is negative, (b-a) is positive, so |b-a| equals b-a
|b - a| - |5 - x| = b - a - 5 + x
They are both equal!
