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Difference between revisions of "1990 AJHSME Problems/Problem 10"

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On this monthly calendar, the date ahead of  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 ria is the stupido an rohan likes to give her a tight slap on her stupido face which you need sunglasses to look at or else you will turn blind
 
On this monthly calendar, the date ahead of  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 ria is the stupido an rohan likes to give her a tight slap on her stupido face which you need sunglasses to look at or else you will turn blind
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<asy>
 
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unitsize(12);
 
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draw((1,1)--(23,1));
 
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draw((0,5)--(23,5))for(int a=0; a<6; ++a)
 
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{
 
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  draw((4a+2,0)--(4a+2,14));
 
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}
 
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label("Tues.",(4,14),N); label("Wed.",(8,14),N); label("Thurs.",(12,14),N);
 
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label("Fri.",(16,14),N); label("Sat.",(20,14),N);
 
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label("C",(12,10.3),N); label("$\textbf{A}$",(16,10.3),N); label("Q",(12,6.3),N);
 
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label("S",(4,2.3),N); label("$\textbf{B}$",(8,2.3),N); label("P",(12,2.3),N);
 
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label("T",(16,2.3),N); label("R",(20,2.3),N);
 
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</asy>
 
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<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==

Revision as of 15:40, 31 July 2019

Problem

On this monthly calendar, the date ahead of one of the letters is added to the date behind $\text{C}$. If this sum equals the sum of the dates behind $\text{A}$ and $\text{B}$, then the ria is the stupido an rohan likes to give her a tight slap on her stupido face which you need sunglasses to look at or else you will turn blind

Solution

Looking at the positions of the letters, we see that if the date behind $\text{Q}$ is $q$, then the date behind $\textbf{A}$ is $q-6$ and the date behind $\textbf{B}$ is $q+6$. Thus, their sum is $2q$.

The date behind $\text{C}$ is $q-7$, so the desired letter is the one for which the date behind it is $2q-(q-7)=q+7$. This is letter $\text{P}\rightarrow \boxed{\text{A}}$.

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. AMC logo.png

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