Difference between revisions of "1999 AHSME Problems/Problem 4"
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Crossing off numbers that are not <math>1</math> more than a multiple of <math>4</math> (in other words, numbers that are <math>1</math> less than a multiple of <math>4</math>, since all numbers are odd), we get: | Crossing off numbers that are not <math>1</math> more than a multiple of <math>4</math> (in other words, numbers that are <math>1</math> less than a multiple of <math>4</math>, since all numbers are odd), we get: | ||
| − | <math>29, 49, 89</math> | + | <math>29, 49, 89.</math> |
Noting that <math>49</math> is not prime, we have only <math>29</math> and <math>89</math>, which give a sum of <math>118</math>, so the answer is <math>\boxed{A}</math>. | Noting that <math>49</math> is not prime, we have only <math>29</math> and <math>89</math>, which give a sum of <math>118</math>, so the answer is <math>\boxed{A}</math>. | ||
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==See Also== | ==See Also== | ||
Latest revision as of 16:15, 19 December 2018
Problem
Find the sum of all prime numbers between 
and 
that are simultaneously greater than a multiple of 
and less than a multiple of 
.
Solution
Numbers that are less than a multiple of all end in or 
.
No prime number ends in , since all numbers that end in are divisible by 
. Thus, we are only looking for numbers that end in .
Writing down the ten numbers that so far qualify, we get 
.
Crossing off multiples of 
gives 
.
Crossing off numbers that are not more than a multiple of (in other words, numbers that are less than a multiple of , since all numbers are odd), we get:
Noting that 
is not prime, we have only 
and 
, which give a sum of 
, so the answer is 
.
See Also
| 1999 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
