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If r is a positive integer, does r have exactly four distinct positive

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If r is a positive integer, does r have exactly four distinct positive [#permalink]

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New post 26 Sep 2017, 10:53
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If r is a positive integer, does r have exactly four distinct positive factors?

(1) r is the product of two different prime numbers

(2) r = 6
[Reveal] Spoiler: OA

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Re: If r is a positive integer, does r have exactly four distinct positive [#permalink]

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New post 26 Sep 2017, 11:11
HKD1710 wrote:
If r is a positive integer, does r have exactly four distinct positive factors?

(1) r is the product of two different prime numbers

(2) r = 6


Statement 1: \(r=p_{1}*p_{2}\), where \(p_{1}\) & \(p_{2}\) are two different prime nos.

therefore no of factors \(= (1+1)*(1+1) = 4\). Sufficient

Statement 2: directly provides the value of r, hence we can definitely calculate number of factors (either Yes or NO). Hence Sufficient

Although not required but just FYI \(r=6=2*3\). Hence no of factors \(= (1+1)*(1+1) =4\)

Option D

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Re: If r is a positive integer, does r have exactly four distinct positive [#permalink]

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New post 27 Sep 2017, 00:45
niks18 wrote:
HKD1710 wrote:
If r is a positive integer, does r have exactly four distinct positive factors?

(1) r is the product of two different prime numbers

(2) r = 6


Statement 1: \(r=p_{1}*p_{2}\), where \(p_{1}\) & \(p_{2}\) are two different prime nos.

therefore no of factors \(= (1+1)*(1+1) = 4\). Sufficient

Statement 2: directly provides the value of r, hence we can definitely calculate number of factors (either Yes or NO). Hence Sufficient

Although not required but just FYI \(r=6=2*3\). Hence no of factors \(= (1+1)*(1+1) =4\)

Option D



Hi ,

I suppose the answer should be B.
In option A it is given that it is the product of 2 different prime numbers but that prime numbers can itself have some powers .example 2^3 . 3^5 then in this case the number of factors are (3+1)(5+1) that is a total of 24.Hence this option is not sufficient.

Experts please clarify if my understanding is correct.

Regards,
Sandeep

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Re: If r is a positive integer, does r have exactly four distinct positive [#permalink]

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New post 27 Sep 2017, 01:07
sandeep211986 wrote:
niks18 wrote:
HKD1710 wrote:
If r is a positive integer, does r have exactly four distinct positive factors?

(1) r is the product of two different prime numbers

(2) r = 6


Statement 1: \(r=p_{1}*p_{2}\), where \(p_{1}\) & \(p_{2}\) are two different prime nos.

therefore no of factors \(= (1+1)*(1+1) = 4\). Sufficient

Statement 2: directly provides the value of r, hence we can definitely calculate number of factors (either Yes or NO). Hence Sufficient

Although not required but just FYI \(r=6=2*3\). Hence no of factors \(= (1+1)*(1+1) =4\)

Option D



Hi ,

I suppose the answer should be B.
In option A it is given that it is the product of 2 different prime numbers but that prime numbers can itself have some powers .example 2^3 . 3^5 then in this case the number of factors are (3+1)(5+1) that is a total of 24.Hence this option is not sufficient.

Experts please clarify if my understanding is correct.

Regards,
Sandeep


Hi sandeep211986

My interpretation of statement 1 is that r is simply a product of two prime nos. if prime nos are raised to any power, then it will not be a prime number but it will simply be a composite number/integer. But as per the language of statement 1 it mentions only prime numbers. for example the illustration you have chosen r becomes 1944 and 1944 is not a product of only two prime nos but can be represented as a product of multiple numbers.

I guess the owner of the topic HKD1710 can throw some light on the language of statement 1 :-)

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Re: If r is a positive integer, does r have exactly four distinct positive [#permalink]

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New post 27 Sep 2017, 12:10
sandeep211986 wrote:
niks18 wrote:
HKD1710 wrote:
If r is a positive integer, does r have exactly four distinct positive factors?

(1) r is the product of two different prime numbers

(2) r = 6


Statement 1: \(r=p_{1}*p_{2}\), where \(p_{1}\) & \(p_{2}\) are two different prime nos.

therefore no of factors \(= (1+1)*(1+1) = 4\). Sufficient

Statement 2: directly provides the value of r, hence we can definitely calculate number of factors (either Yes or NO). Hence Sufficient

Although not required but just FYI \(r=6=2*3\). Hence no of factors \(= (1+1)*(1+1) =4\)

Option D



Hi ,

I suppose the answer should be B.
In option A it is given that it is the product of 2 different prime numbers but that prime numbers can itself have some powers .example 2^3 . 3^5 then in this case the number of factors are (3+1)(5+1) that is a total of 24.Hence this option is not sufficient.

Experts please clarify if my understanding is correct.

Regards,
Sandeep


hi Sandeep,

2^3 = 8, which is not a prime number. The question states that R is the product of two prime numbers. If we have two prime numbers put to the Nth power, we are changing the question. I think you may have over thought this.

I hope this helps!

My opinion is D
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Re: If r is a positive integer, does r have exactly four distinct positive   [#permalink] 27 Sep 2017, 12:10
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