Difference between revisions of "1970 AHSME Problems/Problem 34"
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\text{(E) an even multiple of } 7 \text{ greater than } 98 </math> | \text{(E) an even multiple of } 7 \text{ greater than } 98 </math> | ||
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We know that 13903 minus 13511 is equivalent to 392. Additionally, 14589 minus 13903 is equivalent to 686. Since we are searching for the greatest integer that divides these three integers and leaves the same remainder, the answer resides in the greatest common denominator of 686 and 392. Therefore, the answer is 98, or <math>\fbox{C}</math> | We know that 13903 minus 13511 is equivalent to 392. Additionally, 14589 minus 13903 is equivalent to 686. Since we are searching for the greatest integer that divides these three integers and leaves the same remainder, the answer resides in the greatest common denominator of 686 and 392. Therefore, the answer is 98, or <math>\fbox{C}</math> | ||
Revision as of 15:58, 11 March 2017
Problem
The greatest integer that will divide 
, 
and 
and leave the same remainder is
Solution
We know that 13903 minus 13511 is equivalent to 392. Additionally, 14589 minus 13903 is equivalent to 686. Since we are searching for the greatest integer that divides these three integers and leaves the same remainder, the answer resides in the greatest common denominator of 686 and 392. Therefore, the answer is 98, or 
See also
| 1970 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 33 |
Followed by Problem 35 | |
| 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 • 31 • 32 • 33 • 34 • 35 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
