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This week's question:
|x – 5| – |a – b|
|b – a| – |5 – x|
Compare Quantity A and Quantity B using the information given above, and select one of the following answer choices: 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.
Please post your answer, along with the explanation, below. Get cracking!
Edit: This challenge is now closed
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Quantity B is greater. A=|x-5|-|a-b| = (x-5)-(-(a-b)
since x>5, so the mod will always open positive. since a<b, |a-b| will always open negetive.
so A= x-5+a-b ............(i)
B=|b-a|-|5-x| = (b-a)-(-(5-x) same logic as above.
so B= b-a+5-x ...............(ii)
so A= -(B) ............... from (i) and (ii) now, numerical value of b-a is greater than 5 since 0 and 5 lies between a and b. numerical value of 5-x is less than 5 since x lies between 5 and 10. so, B is a positive quantity or A is a negetive quantity.
|5-x|-->X varies from 5 to 10 therefore |5-x| varies from 0 to 5 |b-a|--> B varies from 5 to 10 and is greater then X ..and A is less than 0.Therefore |b-a| is either greater then 10 or greater than 5.Which means greater than 5 covers the entire range. Hence ,|b-a|-|5-x| is always positive...(1)
Quantity A Since x > 0 , |x-5| is the same range as |5-x| varying from 0 to 5 |a-b| again as |b-a| varies from 5 to 10 Hence . |b-a|-|5-x| is < 0 ....(2)
Therefore Clearly , Quantity B is greater then Quantity A.