Difference between revisions of "2012 AMC 12B Problems/Problem 6"

(Created page with "== Problem== In order to estimate the value of x-y where x and y are real numbers with x <math>\g</math> y")
 
(Problem)
Line 1: Line 1:
 
== Problem==
 
== Problem==
In order to estimate the value of x-y where x and y are real numbers with x <math>\g</math> y
+
In order to estimate the value of x-y where x and y are real numbers with x>y>0. Xiaoli rounded x up by a small amount, rounded y down by the same amount, and then subtracted. Which statement is always true?
 +
 
 +
 
 +
 
 +
==Solution==
 +
 
 +
Since the original equation x-y now becomes (x+k) - (y-k), where k is a constant. so simplified, the equation becomes: x-y+2k, which is greater than x-y, hence the answer is: A.

Revision as of 21:26, 23 February 2012

Problem

In order to estimate the value of x-y where x and y are real numbers with x>y>0. Xiaoli rounded x up by a small amount, rounded y down by the same amount, and then subtracted. Which statement is always true?


Solution

Since the original equation x-y now becomes (x+k) - (y-k), where k is a constant. so simplified, the equation becomes: x-y+2k, which is greater than x-y, hence the answer is: A.

Invalid username
Login to AoPS