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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, 17:58
3
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

36% (01:09) correct 64% (01:22) wrong based on 74 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, 16:29.
Last edited by philipssonicare on 19 Dec 2018, 17:58, 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, 17:48
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, 17:57
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, 09:29
1
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, 16:02
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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answer.jpg [ 27.04 KiB | Viewed 390 times ]

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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, 18:37
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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If p, q are different prime numbers greater than 2, which of the follo &nbs [#permalink] 07 Jan 2019, 18:37
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If p, q are different prime numbers greater than 2, which of the follo

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