Difference between revisions of "1992 AJHSME Problems/Problem 13"

(Created page with "== Problem == Five test scores have a mean (average score) of <math>90</math>, a median (middle score) of <math>91</math> and a mode (most frequent score) of <math>94</math>. T...")
 
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Because there was an odd number of scores, <math> 91 </math> must be the middle score. Since there are two scores above <math> 91 </math> and <math> 94 </math> appears the most frequent (so at least twice) and <math> 94>91 </math>, <math> 94 </math> appears twice. Also, the sum of the five numbers is <math> 90 \times 5 =450 </math>. Thus, the sum of the lowest two scores is <math> 450-91-94-94= \boxed{\text{(B)}\ 171} </math>.
 
Because there was an odd number of scores, <math> 91 </math> must be the middle score. Since there are two scores above <math> 91 </math> and <math> 94 </math> appears the most frequent (so at least twice) and <math> 94>91 </math>, <math> 94 </math> appears twice. Also, the sum of the five numbers is <math> 90 \times 5 =450 </math>. Thus, the sum of the lowest two scores is <math> 450-91-94-94= \boxed{\text{(B)}\ 171} </math>.
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==See Also==
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{{AJHSME box|year=1992|num-b=12|num-a=14}}

Revision as of 21:36, 22 December 2012

Problem

Five test scores have a mean (average score) of $90$, a median (middle score) of $91$ and a mode (most frequent score) of $94$. The sum of the two lowest test scores is

$\text{(A)}\ 170 \qquad \text{(B)}\ 171 \qquad \text{(C)}\ 176 \qquad \text{(D)}\ 177 \qquad \text{(E)}\ \text{not determined by the information given}$

Solution

Because there was an odd number of scores, $91$ must be the middle score. Since there are two scores above $91$ and $94$ appears the most frequent (so at least twice) and $94>91$, $94$ appears twice. Also, the sum of the five numbers is $90 \times 5 =450$. Thus, the sum of the lowest two scores is $450-91-94-94= \boxed{\text{(B)}\ 171}$.

See Also

1992 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
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All AJHSME/AMC 8 Problems and Solutions
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