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N is the product of 5 consecutive prime numbers. If N is divisible by
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16 Jul 2023, 23:00
16 Jul 2023, 23:00
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N is the product of 5 consecutive prime numbers. If N is divisible by 10, then which of the following must be a divisor of N?
Indicate all that apply
A. 2
B. 6
C. 12
D. 14
E. 22
F. 30
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Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
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Indicate all that apply
A. 2
B. 6
C. 12
D. 14
E. 22
F. 30
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
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Re: N is the product of 5 consecutive prime numbers. If N is divisible by
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07 Aug 2023, 22:44
07 Aug 2023, 22:44
Expert Reply
OE
As ๐ is the product of 5 consecutive prime numbers, and ๐ is also divisible by 10,
thus ๐ will definitely include 2 and 5
Therefore, only 5 consecutive integers will be 2, 3, 5,7, 11.
โ ๐ = 2 ร 3 ร 5 ร 7 ร 11
Thus, among the options, the number which can completely divide ๐ will be the
divisor of ๐. Hence; the following will definitely be the divisors of ๐;
2, 6, 14, 22, 30
Ans. (A, B, D, E, F)
_________________
As ๐ is the product of 5 consecutive prime numbers, and ๐ is also divisible by 10,
thus ๐ will definitely include 2 and 5
Therefore, only 5 consecutive integers will be 2, 3, 5,7, 11.
โ ๐ = 2 ร 3 ร 5 ร 7 ร 11
Thus, among the options, the number which can completely divide ๐ will be the
divisor of ๐. Hence; the following will definitely be the divisors of ๐;
2, 6, 14, 22, 30
Ans. (A, B, D, E, F)
_________________
Intern
Joined: 15 Oct 2022
Posts: 14
Location: India
Concentration: Technology, Finance
GPA: 3.52
WE:Analyst (Computer Software)
Re: N is the product of 5 consecutive prime numbers. If N is divisible by
[#permalink]
08 Aug 2023, 19:04
08 Aug 2023, 19:04
Given that N is the product of 5 consecutive primes and N is a multiple of 10 (5x2). Hence, N will definitely include 2 & 5.
Since N will include 2 (smallest prime), ideally N should be equal to 2 x 3 x 5 x 7 x 11.
Therefore, the following amongst the options must be a divisor:
A) 2,
B) 6 (2 x 3)
D) 14 (2 x 7)
E) 22 (2 x 11)
F) 30 (2 x 3 x 5)
Since N will include 2 (smallest prime), ideally N should be equal to 2 x 3 x 5 x 7 x 11.
Therefore, the following amongst the options must be a divisor:
A) 2,
B) 6 (2 x 3)
D) 14 (2 x 7)
E) 22 (2 x 11)
F) 30 (2 x 3 x 5)
gmatclubot
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