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.
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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!
_________________

B is the OA

in gre never assume that figure is drawn to scale
In this question we just have to compare the distance b/w:-
x and 5 ? a and b
clearly as we can see from the number line distance between x and is less than 5, and distance between a and b is greater than 5
therefore answer will be B

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