Difference between revisions of "2002 AMC 12B Problems/Problem 10"

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The answer is 30.
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==Problem==
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How many different integers can be expressed as the sum of three distinct members of the set <math>\{1,4,7,10,13,16,19\}</math>?
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<math>\mathrm{(A)}\ 13
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\qquad\mathrm{(B)}\ 16
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\qquad\mathrm{(C)}\ 24
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\qquad\mathrm{(D)}\ 30
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\qquad\mathrm{(E)}\ 35</math>
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==Solution==
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We can make all multiples of three between 1+4+7=12 and 13+16+19=48, inclusive. There are <math>\frac{48}{3}-\frac{12}{3}+1=13\Rightarrow \boxed{\mathrm{(A)}</math> integers we can form.
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==See also==

Revision as of 09:51, 5 February 2008

Problem

How many different integers can be expressed as the sum of three distinct members of the set $\{1,4,7,10,13,16,19\}$? $\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 16 \qquad\mathrm{(C)}\ 24 \qquad\mathrm{(D)}\ 30 \qquad\mathrm{(E)}\ 35$

Solution

We can make all multiples of three between 1+4+7=12 and 13+16+19=48, inclusive. There are $\frac{48}{3}-\frac{12}{3}+1=13\Rightarrow \boxed{\mathrm{(A)}$ (Error compiling LaTeX. ! File ended while scanning use of \boxed.) integers we can form.

See also

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