Difference between revisions of "2018 AMC 10B Problems/Problem 11"
m (→Solution 2 (Answer Choices)) |
m (→Solution 2 (Answer Choices)) |
||
Line 13: | Line 13: | ||
A) <math>p^2+16</math> isn't true when <math>p=5</math> | A) <math>p^2+16</math> isn't true when <math>p=5</math> | ||
− | B) <math>p^2+24</math> isn't true when p=7 | + | B) <math>p^2+24</math> isn't true when <math>p=7</math> |
C) <math>p^2+26</math> | C) <math>p^2+26</math> | ||
− | D) <math>p^2+46</math> isn't true when p=11 | + | D) <math>p^2+46</math> isn't true when <math>p=11</math> |
− | E) <math>p^2+96</math> isn't true when p=17 | + | E) <math>p^2+96</math> isn't true when <math>p=17</math> |
− | Therefore, <math>C</math> is the correct answer. | + | Therefore, <math>\framebox{C}</math> is the correct answer. |
==See Also== | ==See Also== |
Revision as of 21:41, 2 September 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 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) isn't true when
B) isn't true when
C)
D) isn't true when
E) isn't true when
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.