# Difference between revisions of "2012 AMC 10B Problems/Problem 6"

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== Problem 6 == | == Problem 6 == | ||

− | 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 her rounded values. Which of the following statements is necessarily correct? | + | In order to estimate the value of <math>x-y</math> where <math>x</math> and <math>y</math> are real numbers with <math>x > y > 0</math>, Xiaoli rounded <math>x</math> up by a small amount, rounded <math>y</math> down by the same amount, and then subtracted her rounded values. Which of the following statements is necessarily correct? |

− | |||

− | |||

− | |||

+ | A) Her estimate is larger than <math>x-y</math> | ||

+ | B) Her estimate is smaller than <math>x-y</math> | ||

+ | C) Her estimate equals <math>x-y</math> | ||

+ | D) Her estimate equals <math>y - x</math> | ||

+ | E) Her estimate is <math>0</math> | ||

== Solutions == | == Solutions == |

## Revision as of 18:08, 8 December 2012

## Problem 6

In order to estimate the value of where and are real numbers with , Xiaoli rounded up by a small amount, rounded down by the same amount, and then subtracted her rounded values. Which of the following statements is necessarily correct?

A) Her estimate is larger than B) Her estimate is smaller than C) Her estimate equals D) Her estimate equals E) Her estimate is

## Solutions

Say Z=is the amount rounded up by and down by.

*Xiaoli rounded x up by a small amount, rounded y down by the same amount, and then subtracted her rounded values*.

Which translates to:

==

This is bigger than the original amount of .

Therefore, her estimate is larger than

or