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How many objects can be weighed

Source: 1959 AHSME Problem 19

August 13, 2013
AMCAMC 12

Problem Statement

With the use of three different weights, namely 1 lb., 3 lb., and 9 lb., how many objects of different weights can be weighed, if the objects is to be weighed and the given weights may be placed in either pan of the scale? <spanclass=latexbold>(A)</span> 15<spanclass=latexbold>(B)</span> 13<spanclass=latexbold>(C)</span> 11<spanclass=latexbold>(D)</span> 9<spanclass=latexbold>(E)</span> 7 <span class='latex-bold'>(A)</span>\ 15 \qquad<span class='latex-bold'>(B)</span>\ 13\qquad<span class='latex-bold'>(C)</span>\ 11\qquad<span class='latex-bold'>(D)</span>\ 9\qquad<span class='latex-bold'>(E)</span>\ 7