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

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Manager
Joined: 15 Feb 2018
Posts: 176
If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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Updated on: 19 Dec 2018, 17:58
3
00:00

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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Joined: 07 Dec 2014
Posts: 1152
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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
D
Manager
Joined: 15 Feb 2018
Posts: 176
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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19 Dec 2018, 17:57
gracie

Apologies, there was a typo. Option D is $$p^2q$$, not $$p^2$$
Intern
Joined: 26 Nov 2018
Posts: 6
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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 ?
Manager
Joined: 15 Feb 2018
Posts: 176
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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?
Attachments

answer.jpg [ 27.04 KiB | Viewed 390 times ]

Intern
Joined: 05 Dec 2017
Posts: 4
If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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.
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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