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

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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

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.

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

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29 Oct 2013, 12:37

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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.

Answer: D.

Hope it's clear.

Why 7 is not considered for the final answer? _________________

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

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11 Jan 2014, 09:09

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. _________________

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.

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. _________________

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.

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

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21 Feb 2015, 19:02

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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