Difference between revisions of "1990 AJHSME Problems/Problem 10"
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==Problem== | ==Problem== | ||
| − | On this monthly calendar, the date | + | 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> | <asy> | ||
unitsize(12); | unitsize(12); | ||
draw((1,1)--(23,1)); | draw((1,1)--(23,1)); | ||
| − | draw((0,5)--(23,5)) | + | draw((0,5)--(23,5))for(int a=0; a<6; ++a) |
| − | |||
| − | |||
| − | for(int a=0; a<6; ++a) | ||
{ | { | ||
draw((4a+2,0)--(4a+2,14)); | draw((4a+2,0)--(4a+2,14)); | ||
Revision as of 15:39, 31 July 2019
Problem
On this monthly calendar, the date ahead of one of the letters is added to the date behind 
. If this sum equals the sum of the dates behind 
and 
, 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
unitsize(12);
draw((1,1)--(23,1));
draw((0,5)--(23,5))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);
(Error making remote request. Unknown error_msg)
Solution
Looking at the positions of the letters, we see that if the date behind 
is 
, then the date behind 
is 
and the date behind 
is 
. Thus, their sum is 
.
The date behind is 
, so the desired letter is the one for which the date behind it is 
. This is letter 
.
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. 
