Difference between revisions of "1990 AJHSME Problems/Problem 10"
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==Problem== | ==Problem== | ||
+ | On this monthly calendar, the date behind one of the letters is added to the date behind <math>\text{C}</math>. If this sum equals the sum of the dates behind <math>\text{A}</math> and <math>\text{B}</math>, then the letter is | ||
− | + | <asy> | |
+ | unitsize(12); | ||
+ | draw((1,1)--(23,1)); | ||
+ | draw((0,5)--(23,5)); | ||
+ | draw((0,9)--(23,9)); | ||
+ | draw((0,13)--(23,13)); | ||
+ | for(int a=0; a<6; ++a) | ||
+ | { | ||
+ | draw((4a+2,0)--(4a+2,14)); | ||
+ | } | ||
+ | label("Tues.",(4,14),N); label("Wed.",(8,14),N); label("Thurs.",(12,14),N); | ||
+ | label("Fri.",(16,14),N); label("Sat.",(20,14),N); | ||
+ | label("C",(12,10.3),N); label("$\textbf{A}$",(16,10.3),N); label("Q",(12,6.3),N); | ||
+ | label("S",(4,2.3),N); label("$\textbf{B}$",(8,2.3),N); label("P",(12,2.3),N); | ||
+ | label("T",(16,2.3),N); label("R",(20,2.3),N); | ||
+ | </asy> | ||
+ | |||
+ | <math>\text{(A)}\ \text{P} \qquad \text{(B)}\ \text{Q} \qquad \text{(C)}\ \text{R} \qquad \text{(D)}\ \text{S} \qquad \text{(E)}\ \text{T}</math> | ||
==Solution== | ==Solution== | ||
− | + | Let the date behind <math>C</math> be <math>x</math>. Now the date behind <math>A</math> is <math>x+1</math>, and after looking at the calendar, the date behind <math>B</math> is <math>x+13</math>. Now we have <math>x+1+x+13=x+y</math> for some date <math>y</math>, and we desire for <math>y</math> to be <math>x+14</math>. Now we find that <math>y</math> is the date behind <math>P</math>, so the answer is <math>\boxed{(\text{A})}</math> ~motorfinn | |
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==See Also== | ==See Also== | ||
{{AJHSME box|year=1990|num-b=9|num-a=11}} | {{AJHSME box|year=1990|num-b=9|num-a=11}} | ||
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{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 10:51, 8 September 2019
Problem
On this monthly calendar, the date behind one of the letters is added to the date behind . If this sum equals the sum of the dates behind
and
, then the letter is
Solution
Let the date behind be
. Now the date behind
is
, and after looking at the calendar, the date behind
is
. Now we have
for some date
, and we desire for
to be
. Now we find that
is the date behind
, so the answer is
~motorfinn
See Also
1990 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.