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A “Sophie Germain” prime is any positive prime number p for

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A “Sophie Germain” prime is any positive prime number p for [#permalink] New post 15 May 2012, 20:48
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A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 5 is

A. 3
B. 7
C. 21
D. 27
E. 189
[Reveal] Spoiler: OA

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Re: Sophie Germain [#permalink] New post 15 May 2012, 22:33
+1 D

1*3*9=27, Rest of the Digits cannot be prime.

even cannot be prime. 5 not prime and (7)*2+1=15 not prime.
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Last edited by geno5 on 15 May 2012, 23:47, edited 1 time in total.
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Re: Sophie Germain [#permalink] New post 15 May 2012, 23:14
Hey geno
Can you elabotare how you got the answer?
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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink] New post 15 May 2012, 23:38
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alchemist009 wrote:
A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 5 is

A. 3
B. 7
C. 21
D. 27
E. 189


A prime number greater than 5 can have only the following four units digits: 1, 3, 7, or 9.

If the units digit of p is 1 then the units digit of 2p+1 would be 3, which is a possible units digit for a prime. For example consider p=11=prime --> 2p+1=23=prime;

If the units digit of p is 3 then the units digit of 2p+1 would be 7, which is a possible units digit for a prime. For example consider p=23=prime --> 2p+1=47=prime;

If the units digit of p is 7 then the units digit of 2p+1 would be 5, which is NOT a possible units digit for a prime;

If the units digit of p is 9 then the units digit of 2p+1 would be 9, which is a possible units digit for a prime. For example consider p=29=prime --> 2p+1=59=prime.

The product of all the possible units digits of Sophie Germain primes greater than 5 is 1*3*9=27.

Answer: D.

Hope it's clear.
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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink] New post 29 Oct 2013, 11:37
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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink] New post 11 Jan 2014, 08:06
Bunuel wrote:
alchemist009 wrote:
A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 5 is

A. 3
B. 7
C. 21
D. 27
E. 189


A prime number greater than 5 can have only the following four units digits: 1, 3, 7, or 9.

If the units digit of p is 1 then the units digit of 2p+1 would be 3, which is a possible units digit for a prime. For example consider p=11=prime --> 2p+1=23=prime;

If the units digit of p is 3 then the units digit of 2p+1 would be 7, which is a possible units digit for a prime. For example consider p=23=prime --> 2p+1=47=prime;

If the units digit of p is 7 then the units digit of 2p+1 would be 5, which is NOT a possible units digit for a prime;

If the units digit of p is 9 then the units digit of 2p+1 would be 9, which is a possible units digit for a prime. For example consider p=29=prime --> 2p+1=59=prime.

The product of all the possible units digits of Sophie Germain primes greater than 5 is 1*3*9=27.

Answer: D.

Hope it's clear.


Why 7 is not considered for the final answer?
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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink] New post 11 Jan 2014, 08:09
Expert's post
kinjiGC wrote:
Bunuel wrote:
alchemist009 wrote:
A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 5 is

A. 3
B. 7
C. 21
D. 27
E. 189


A prime number greater than 5 can have only the following four units digits: 1, 3, 7, or 9.

If the units digit of p is 1 then the units digit of 2p+1 would be 3, which is a possible units digit for a prime. For example consider p=11=prime --> 2p+1=23=prime;

If the units digit of p is 3 then the units digit of 2p+1 would be 7, which is a possible units digit for a prime. For example consider p=23=prime --> 2p+1=47=prime;

If the units digit of p is 7 then the units digit of 2p+1 would be 5, which is NOT a possible units digit for a prime;

If the units digit of p is 9 then the units digit of 2p+1 would be 9, which is a possible units digit for a prime. For example consider p=29=prime --> 2p+1=59=prime.

The product of all the possible units digits of Sophie Germain primes greater than 5 is 1*3*9=27.

Answer: D.

Hope it's clear.


Why 7 is not considered for the final answer?


If the units digit of p is 7 then the units digit of 2p+1 would be 5, which is NOT a possible units digit for a prime greater than 5.
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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink] New post 11 Jan 2014, 08:21
Bunuel wrote:
kinjiGC wrote:
Bunuel wrote:
A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 5 is

A. 3
B. 7
C. 21
D. 27
E. 189

A prime number greater than 5 can have only the following four units digits: 1, 3, 7, or 9.

If the units digit of p is 1 then the units digit of 2p+1 would be 3, which is a possible units digit for a prime. For example consider p=11=prime --> 2p+1=23=prime;

If the units digit of p is 3 then the units digit of 2p+1 would be 7, which is a possible units digit for a prime. For example consider p=23=prime --> 2p+1=47=prime;

If the units digit of p is 7 then the units digit of 2p+1 would be 5, which is NOT a possible units digit for a prime;

If the units digit of p is 9 then the units digit of 2p+1 would be 9, which is a possible units digit for a prime. For example consider p=29=prime --> 2p+1=59=prime.

The product of all the possible units digits of Sophie Germain primes greater than 5 is 1*3*9=27.

Answer: D.

Hope it's clear.


Why 7 is not considered for the final answer?


If the units digit of p is 7 then the units digit of 2p+1 would be 5, which is NOT a possible units digit for a prime greater than 5.


It might be simple, but I have a doubt here. The question asks product of all the possible unit digits of Sophie Germain primes.

As 47 is a sophie germain prime number and prime number and 47 is > than 5, so 7 being the unit digit should be included in the product to get the final answer. That is why I marked 189.
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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink] New post 11 Jan 2014, 08:26
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kinjiGC wrote:
Bunuel wrote:
kinjiGC wrote:
Why 7 is not considered for the final answer?


If the units digit of p is 7 then the units digit of 2p+1 would be 5, which is NOT a possible units digit for a prime greater than 5.


It might be simple, but I have a doubt here. The question asks product of all the possible unit digits of Sophie Germain primes.

As 47 is a sophie germain prime number and prime number and 47 is > than 5, so 7 being the unit digit should be included in the product to get the final answer. That is why I marked 189.


A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. 47 is NOT a “Sophie Germain” prime because 2p+1=95, which is NOT a prime. Again, a “Sophie Germain” prime cannot have 7 as its units digit because the units digit of 2p+1 in this case would be 5. No prime greater than 5 has 5 as its units digit.

Hope it's clear.
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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink] New post 11 Jan 2014, 09:34
Thanks Banuel.

I read the premise wrongly. :cry:
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Re: A “Sophie Germain” prime is any positive prime number p for   [#permalink] 11 Jan 2014, 09:34
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