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
OAE
p(12)+11
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By the definition, p(12) = (11)(7)(5)(3)(2)j_shreyans wrote: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
OAE
So, p(12) + 11 = (11)(7)(5)(3)(2) + 11
= 11[(7)(5)(3)(2) + 1] I factored out the 11
= 11[210 + 1]
= 11(211)
NOTE: 11 is prime and 211 is prime
The second smallest prime factor of p(12)+11 is
p(12)+11 has only 2 prime factors: 11 and 211
So, the second smallest is 211 (the smallest is 11)
Answer: E
Cheers,
Brent
Last edited by Brent@GMATPrepNow on Thu Apr 19, 2018 3:00 pm, edited 2 times in total.
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Brent,Brent@GMATPrepNow wrote:
The second smallest prime factor of p(12)+11 is
p(12)+11 has only 2 prime factors: 11 and 211
So, the second smallest is 11
Cheers,
Brent
I think that you're misinterpreting the meaning of second smallest.
Of the two prime factors of p(12)+11, 11 is the smallest, so 211 is the second smallest.
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Good catch, Mitch.GMATGuruNY wrote:Brent,Brent@GMATPrepNow wrote:
The second smallest prime factor of p(12)+11 is
p(12)+11 has only 2 prime factors: 11 and 211
So, the second smallest is 11
Cheers,
Brent
I think that you're misinterpreting the meaning of second smallest.
Of the two prime factors of p(12)+11, 11 is the smallest, so 211 is the second smallest.
I read it as second largest the whole time.
I have edited my response.
Cheers,
Brent
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P(12) = 2 x 3 x 5 x 7 x 11j_shreyans wrote: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
OAE
Therefore, P(12)+11 = 2 x 3 x 5 x 7 x 11 + 11 = 11(2x3x5x7+1) = 11(211)
Only two primes therefore
first smallest- 11
Second smallest- 211
Answer: 211
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What a great question
I have heard the term "second smallest" in any GMAT question for the first time
first smallest -11
second smallest -211 is the answer.
I have heard the term "second smallest" in any GMAT question for the first time
first smallest -11
second smallest -211 is the answer.