1986 AMC 12 Problem 4

Attempt Problem 4 of the 1986 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1986 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Let

S

be the statement

“If the sum of the digits of the whole number

n

is divisible by

6,

then

n

is divisible by

6.

”

A value of

n

which shows

S

to be false is

30

33

40

42

none of these

A counterexample must satisfy the hypothesis but not the conclusion

Divisibility by

6

requires both divisibility by

2

and by

3

The digit sum of

33

6,

which is divisible by

6.

However,

33

is odd, so it is not divisible by

6.

Thus

33

makes the implication false.

Therefore the correct answer is B.

Problem 4 in other years