Difference between revisions of "1986 AHSME Problems/Problem 4"
(Created page with "==Problem== Let S be the statement "If the sum of the digits of the whole number <math>n</math> is divisible by <math>6</math>, then <math>n</math> is divisible by <math>6</mat...") |
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==Solution== | ==Solution== | ||
− | + | For a counterexample, we need a number whose digit sum is divisible by <math>6</math>, but which is not itself divisible by <math>6</math>. <math>33</math> satisfies these conditions, as <math>3+3=6</math> but <math>6</math> does not divide <math>33</math>, so the answer is <math>\boxed{B}</math>. | |
== See also == | == See also == |
Latest revision as of 17:05, 1 April 2018
Problem
Let S be the statement "If the sum of the digits of the whole number is divisible by , then is divisible by ."
A value of which shows to be false is
Solution
For a counterexample, we need a number whose digit sum is divisible by , but which is not itself divisible by . satisfies these conditions, as but does not divide , so the answer is .
See also
1986 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 |
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