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If p, q are different prime numbers greater than 2, which of the follo

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If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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New post Updated on: 19 Dec 2018, 18:58
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A
B
C
D
E

Difficulty:

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Question Stats:

40% (01:47) correct 60% (01:37) wrong based on 123 sessions

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If p, q are different prime numbers greater than 2, which of the following can have at most 3 different factors?

A) \(2p+q\)
B) \(p+q\)
C) \(pq\)
D) \(p^2q\)
E) \(p^q\)

Originally posted by philipssonicare on 19 Dec 2018, 17:29.
Last edited by philipssonicare on 19 Dec 2018, 18:58, edited 1 time in total.
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Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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New post 19 Dec 2018, 18:48
philipssonicare wrote:
If p, q are different prime numbers greater than 2, which of the following can have at most 3 different factors?

A) \(2p+q\)
B) \(p+q\)
C) \(pq\)
D) \(p^2\)
E) \(p^q\)


p^2 can only have p, p^2, and 1 as factors
e.g., 3, 9, 1; 7, 49, 1; 11, 121, 1
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Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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New post 19 Dec 2018, 18:57
gracie

Apologies, there was a typo. Option D is \(p^2q\), not \(p^2\)
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Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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New post 25 Dec 2018, 10:29
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philipssonicare wrote:
gracie

Apologies, there was a typo. Option D is \(p^2q\), not \(p^2\)


Can you please explain the solution to this problem ?
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Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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New post 25 Dec 2018, 17:02
1
ilepton

I have attached the answer from math revolution. I feel it is wrong/I misunderstand though.
2P+Q, if p=5 and q=11
2·5+11=21, 3^1·7^1=(1+1)(1+1)=4. Can’t be A?
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If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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New post 07 Jan 2019, 19:37
1
As p and q are primes greater than 2, both are odd.

Quote:
A) 2p+q


Quote:
B) p+q

odd1 + odd2 = even
p+q is an even greater than 2, so at least it will have 4 factors: 1, 2, (...), (p+q)
Try p=3 and q=5
p+q=8, Factors: 1, 2, 4, 8

Quote:
C) pq

At least 4 Factors: 1, p, q, pq

Quote:
D) (p^2)*q

5 factors: 1, p, p^2, pq, q, (p^2)*q

Quote:
E) p^q

Remember that p and q are prime numbers greater than 2, so p^q > p^2
At least 5 factor (similar to D): : 1, p, p^2, p^q

So the only possible answer is A.
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Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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New post 26 Jan 2019, 11:08
philipssonicare wrote:
If p, q are different prime numbers greater than 2, which of the following can have at most 3 different factors?

A) \(2p+q\)
B) \(p+q\)
C) \(pq\)
D) \(p^2q\)
E) \(p^q\)


Hello!

Can we always assume that the statements will work for any different prime numbers?

Kind regards!
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Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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New post 26 Jan 2019, 11:34
philipssonicare wrote:
If p, q are different prime numbers greater than 2, which of the following can have at most 3 different factors?

A) \(2p+q\)
B) \(p+q\)
C) \(pq\)
D) \(p^2q\)
E) \(p^q\)


At most 3 means they can be 3 or less than 3 as well

p = 3, q = 5, in all the cases

A) \(2p+q\)
11 => 11^1 => 2 factors ( while calculating powers we add 1 to the power)

B) \(p+q\)
8 => 2^3 => 4 factors

C) \(pq\)
15 => 3 * 5 => 4 factors

D) \(p^2q\)
45 => 3 * 5 * 3 => 6 factors

E) \(p^q\)
3^5 will again be more than 3 factors

A
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If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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New post 26 Jan 2019, 11:42
1
jfranciscocuencag wrote:
philipssonicare wrote:
If p, q are different prime numbers greater than 2, which of the following can have at most 3 different factors?

A) \(2p+q\)
B) \(p+q\)
C) \(pq\)
D) \(p^2q\)
E) \(p^q\)


Hello!

Can we always assume that the statements will work for any different prime numbers?

Kind regards!


Would like to share my 2 cents on this,

Not necessary,we will have to search for that particular pair which will satisfy the question.

For option A

If you take another pair such as 7,11 => 25 => 3 factors, this will hold good

But when you take 7,13 => 27 => 4 factors, this will fail

Nevertheless the approach mentioned might not be the easiest one to solve this question, Brute force does take time, to get to the answer.
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Quote which i can relate to.
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If p, q are different prime numbers greater than 2, which of the follo   [#permalink] 26 Jan 2019, 11:42
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