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A “trio-prime” is any number made up of three factors, not including itself and 1, that are consecutive primes. How many “trio-primes” are less than 1,000?
(A) 2
(B) 3
(C) 4
(D) 7
(E) 11
(A) 2
(B) 3
(C) 4
(D) 7
(E) 11
Luckisnoexcuse
Current Student
Joined: 18 Aug 2016
Last visit: 16 Apr 2022
Posts: 520
Given Kudos: 198
Concentration: Strategy, Technology
Schools: Kenan-Flagler '20 (M)
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
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01 Aug 2017, 00:15
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Bunuel
A “trio-prime” is any number made up of three factors, not including itself and 1, that are consecutive primes. How many “trio-primes” are less than 1,000?
(A) 2
(B) 3
(C) 4
(D) 7
(E) 11
(A) 2
(B) 3
(C) 4
(D) 7
(E) 11
Total factors of Trio Primes are 3 (excluding 1 and itself)
2,3,5,7,11,13
Since 7*11*13 = 1001
we have 2,3,5,7,11
So numbers with consecutive primes will be 2*3*5, 3*5*7, 5*7*11
3
B
31 Mar 2020, 02:48
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Bunuel
A “trio-prime” is any number made up of three factors, not including itself and 1, that are consecutive primes. How many “trio-primes” are less than 1,000?
(A) 2
(B) 3
(C) 4
(D) 7
(E) 11
(A) 2
(B) 3
(C) 4
(D) 7
(E) 11
Solution:
- • Let n be a trio-prime number
- o \(n =p*q*r\) , where p, q, and r are consecutive primes other than 1 or n,
- o \(p*q*r < 1000\)
- o \(2*3*5 = 30 < 1000\)
o \(3*5*7 = 105 <1000\)
o \(5*7*11 = 385 < 1000\)
o \(7*11*13 = 1001 > 1000\)
- All other combinations will be more than 1000
