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#22066

algebra

estimation

medium

90 sec

In order to estimate the value of $P - Q$ where $P$ and $Q$ are real numbers with $P > Q > 0$ , a student rounded $P$ down by a small amount, rounded $Q$ up by the same amount, and then subtracted their rounded values. Which of the following statements is necessarily correct?

A.

Their estimate is larger than $P - Q$

B.

Their estimate is smaller than $P - Q$

C.

Their estimate equals $P - Q$

D.

Their estimate equals $Q - P$

E.

Their estimate is $0$