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USA - Middle School Tournaments
Math Invitational for Girls
2019 MIG
11
11
Part of
2019 MIG
Problems
(1)
2019 Individual #11
Source:
5/1/2022
An integer
N
N
N
which satisfies exactly three of the four following conditions is called two-good.
~
(I)
N
N
N
is divisible by
2
2
2
(II)
N
N
N
is divisible by
4
4
4
(III)
N
N
N
is divisible by
8
8
8
(IV)
N
N
N
is divisible by
16
16
16
~
How many integers between
1
1
1
and
100
100
100
, inclusive, are two-good?
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A
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6
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B
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7
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C
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8
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D
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9
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E
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10
<span class='latex-bold'>(A) </span>6\qquad<span class='latex-bold'>(B) </span>7\qquad<span class='latex-bold'>(C) </span>8\qquad<span class='latex-bold'>(D) </span>9\qquad<span class='latex-bold'>(E) </span>10
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6
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B
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7
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C
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8
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D
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9
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(
E
)
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10
2019 Individual