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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]

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15 May 2012, 21:48
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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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15 May 2012, 23:33
+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 16 May 2012, 00:47, edited 1 time in total.

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16 May 2012, 00:14
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]

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16 May 2012, 00:38
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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.

Hope it's clear.
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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink]

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29 Oct 2013, 12:37
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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink]

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11 Jan 2014, 09:06
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.

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]

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11 Jan 2014, 09:09
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.

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]

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11 Jan 2014, 09:21
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.

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]

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11 Jan 2014, 09:26
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Expert's post
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]

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11 Jan 2014, 10:34
Thanks Banuel.

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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink]

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21 Feb 2015, 19:02
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A “Sophie Germain” prime is any positive prime number p for [#permalink]

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19 Jul 2015, 11:01
I see - I misunderstood the question at first...

It's asking for all of the possible UNIQUE units digits, not all of the units digits of SG primes multiplied out.

For example, 11, 23, 29, 53... are primes. Unique units are only 1, 3, and 9, which multiply to 27.

If interpreted literally, it would go on forever (i.e. answer = infinite).

Knowing this and the answer choices, there's only one intended Q&A combo possible - unique units and not infinite.

I do think, however, that they should have worded it more clearly as it is ambiguous.

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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink]

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21 Aug 2016, 11:41
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A "Sophie Germain" prime is [#permalink]

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22 Aug 2016, 12:00
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: 37
B: 21
C: 27
D: 18
E: 9

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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink]

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22 Aug 2016, 12:51
RaghavSingla 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: 37
B: 21
C: 27
D: 18
E: 9

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Merging topics. Please refer to the discussion above.
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A “Sophie Germain” prime is any positive prime number p for [#permalink]

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06 Sep 2016, 23:47
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.

Hope it's clear.

Need your help in understanding the question. Does not this question ask for product of "unit digits of Sophie prime numbers" and not unit digits of prime numbers.
In that case, the Sophie prime numbers greater than 5 are 7,11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be E.

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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink]

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06 Sep 2016, 23:53
abani 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.

Hope it's clear.

Need your help in understanding the question. Does not this question ask for product of "unit digits of Sophie prime numbers" and not unit digits of prime numbers.
In that case, the Sophie prime numbers greater than 5 are 7,11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be E.

I went through the post and understood it. English is tough

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Re: A “Sophie Germain” prime is any positive prime number p for [#permalink]

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12 Sep 2017, 04:10
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Re: A “Sophie Germain” prime is any positive prime number p for   [#permalink] 12 Sep 2017, 04:10
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