2012 AMC 12B Problems/Problem 6

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 her rounded values. Which of the following statements is necessarily correct?

(A) Her estimate is larger than $x-y$ .

(B) Her estimate is smaller than $x-y$ .

(C) Her estimate equals $x-y$ .

(D) Her estimate equals $y-x$ .

(E) Her estimate is $0$ .

Solution

The original expression $x-y$ now becomes $(x+k) - (y-k)=(x-y)+2k>x-y$ , where $k$ is a positive constant, hence the answer is (A).

2012 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

2012 AMC 12B Problems/Problem 6

Problem

Solution

See Also