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Manager  Joined: 22 Apr 2011
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A “Sophie Germain” prime is any positive prime number p for  [#permalink]

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46 00:00

Difficulty:   95% (hard)

Question Stats: 35% (02:35) correct 65% (02:28) wrong based on 525 sessions

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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
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Posts: 64111
Re: A “Sophie Germain” prime is any positive prime number p for  [#permalink]

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18
1
17
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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1
+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.

Originally posted by geno5 on 15 May 2012, 22:33.
Last edited by geno5 on 15 May 2012, 23:47, edited 1 time in total.
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Re: A “Sophie Germain” prime is any positive prime number p for  [#permalink]

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1
1
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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Joined: 02 Sep 2009
Posts: 64111
Re: A “Sophie Germain” prime is any positive prime number p for  [#permalink]

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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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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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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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Thanks Banuel.

I read the premise wrongly. Manager  Joined: 08 Jun 2015
Posts: 99
A “Sophie Germain” prime is any positive prime number p for  [#permalink]

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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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taking prime number as p=23 , its 2p+1 =47 and 47 is a prime number.

Then why are we not considering unit digit of 47 (i.e 7) here.
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Re: A “Sophie Germain” prime is any positive prime number p for  [#permalink]

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warrior1991 wrote:

taking prime number as p=23 , its 2p+1 =47 and 47 is a prime number.

Then why are we not considering unit digit of 47 (i.e 7) here.
The question says:

A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime.

This means that it is 23 that is a Sophie Germain prime, not 47, because;

if p=23, 2p+1 is prime
but
if p=47, 2p+1 is not prime

Therefore, we won't consider 47 a Sophie Germain prime.
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Re: A “Sophie Germain” prime is any positive prime number p for  [#permalink]

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warrior1991 wrote:

taking prime number as p=23 , its 2p+1 =47 and 47 is a prime number.

Then why are we not considering unit digit of 47 (i.e 7) here.

Only p is the Sophie Germain prime, not the corresponding 2p + 1.
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Re: A “Sophie Germain” prime is any positive prime number p for  [#permalink]

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It's strange to ask for the "product of all the possible units digits" here, because then there's no reason to bother checking numbers with a units digit of "1" -- a product will be the same whether we include "1" or not. So you can save yourself a quarter of the work here and only check 3, 7 and 9, which was done perfectly in other solutions above.
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Re: A “Sophie Germain” prime is any positive prime number p for  [#permalink]

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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.

Hi Bunuel,

13 is a Sophie Prime and (13 *2 ) +1 equals 27 which is not prime. I think the ans should be 9.
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Re: A “Sophie Germain” prime is any positive prime number p for  [#permalink]

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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.

Hi Bunuel,

13 is a Sophie Prime and (13 *2 ) +1 equals 27 which is not prime. I think the ans should be 9.

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

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Here's my take.

Since the question talks about "Sophie Germain" Primes we have to check for same.
2, 3, 5, 11, 23, 29, 41, 53, 71, 83, 89 and so on are all "Sophie Germain" Primes. For these primes greater than 5 units digits are 1,3,9 which repeats, hence product is 1*3*9=27.

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GMATPREPSoft1 680(Q48,V35) June 26, 2019 A “Sophie Germain” prime is any positive prime number p for   [#permalink] 13 Jul 2019, 09:38

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