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Difficulty:
85%
(hard)
Question Stats:
47% (02:06) correct
53%
(01:56)
wrong
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If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. The second smallest prime factor of p(12)+11 is
A. 2
B. 11
C. 13
D. 17
E. 211
A. 2
B. 11
C. 13
D. 17
E. 211
Solving
P(12)+11 = (2 x 3 x 5 x 7 x 11) +11
= 11 (2 x 3 x 5 x 7 +1)
=11(211)
Since 211 is prime, shouldn’t 11 be the 2nd smallest prime factor of the product?
P(12)+11 = (2 x 3 x 5 x 7 x 11) +11
= 11 (2 x 3 x 5 x 7 +1)
=11(211)
Since 211 is prime, shouldn’t 11 be the 2nd smallest prime factor of the product?
23 Dec 2012, 06:38
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nades09
\(p(12)+11= \)
\( =2*3*5*7*11+11=\)
\( = 11(2*3*5*7+1)=\)
\( = 11*211\).
Both 11 and 211 are primes: 11 is the smallest prime of p(12) + 11 and 211 is the second smallest prime of p(12) + 11.
Answer: E.
22 Dec 2012, 10:51
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nades09
11 is the first smallest prime factor. 211 is the second smallest prime factor
