Difference between revisions of "2018 AMC 10B Problems/Problem 11"
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Because squares of a non-multiple of 3 is always <math>1\mod 3</math>, the only expression is always a multiple of <math>3</math> is <math>\boxed{\textbf{(C) } p^2+26} </math>. This is excluding when <math>p=0\mod3</math>, which only occurs when <math>p=3</math>, then <math>p^2+26=35</math> which is still composite. | Because squares of a non-multiple of 3 is always <math>1\mod 3</math>, the only expression is always a multiple of <math>3</math> is <math>\boxed{\textbf{(C) } p^2+26} </math>. This is excluding when <math>p=0\mod3</math>, which only occurs when <math>p=3</math>, then <math>p^2+26=35</math> which is still composite. | ||
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+ | ==Solution 2 (Answer Choices)== | ||
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+ | Since the question asks which of the following will never be a prime number when p^2 is a prime number, a way to find the answer is by trying to find a value for <math>p</math> such that the statement above won't be true. | ||
+ | A) p^2+16 isn't true when p=5 | ||
+ | B) p^2+24 isn't true when p=7 | ||
+ | C) P^2+26 | ||
+ | D) p^2+46 isn't true when p=11 | ||
+ | E) p^2+96 isn't true when p=17. | ||
+ | Therefore, <math>C</math> is the correct answer. | ||
==See Also== | ==See Also== |
Revision as of 21:48, 22 August 2019
Which of the following expressions is never a prime number when is a prime number?
Solution 1
Because squares of a non-multiple of 3 is always , the only expression is always a multiple of
is
. This is excluding when
, which only occurs when
, then
which is still composite.
Solution 2 (Answer Choices)
Since the question asks which of the following will never be a prime number when p^2 is a prime number, a way to find the answer is by trying to find a value for such that the statement above won't be true.
A) p^2+16 isn't true when p=5
B) p^2+24 isn't true when p=7
C) P^2+26
D) p^2+46 isn't true when p=11
E) p^2+96 isn't true when p=17.
Therefore,
is the correct answer.
See Also
2018 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 | ||
All AMC 10 Problems and Solutions |
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