Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 11"
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+ | Notice that <math>252=2^2\cdot 3^2\cdot 7</math>. Because <math>b=2a</math> and <math>d=4a,</math> it is invalid for <math>a</math> to be a multiple of <math>2</math>. With similar reasoning, <math>a</math> must have at most one factor of <math>3</math>. Thus, <math>a=\boxed{21}</math>. | ||
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+ | (With <math>a=21</math>, we have <math>b=42, c=63, d=84,</math> which is valid) | ||
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+ | ~Apple321 |
Revision as of 22:57, 10 July 2021
Problem
If and
,
,
, and
are divisors of
, what is the maximum value of
?
Solution
must be a number such that
,
,
. Thus, we must have
. This implies the maximum value of
is
~Bradygho
Notice that . Because
and
it is invalid for
to be a multiple of
. With similar reasoning,
must have at most one factor of
. Thus,
.
(With , we have
which is valid)
~Apple321