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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If p, q are different prime numbers greater than 2, which of the follo

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Senior Manager  P
Joined: 15 Feb 2018
Posts: 258
If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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4 00:00

Difficulty:   75% (hard)

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

### HideShow timer Statistics 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.
VP  P
Joined: 07 Dec 2014
Posts: 1210
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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
Senior Manager  P
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Posts: 258
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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gracie

Apologies, there was a typo. Option D is $$p^2q$$, not $$p^2$$
Intern  B
Joined: 26 Nov 2018
Posts: 7
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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 ?
Senior Manager  P
Joined: 15 Feb 2018
Posts: 258
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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 710 times ]

Intern  B
Joined: 05 Dec 2017
Posts: 7
GMAT 1: 570 Q48 V20 If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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.
Senior Manager  S
Joined: 12 Sep 2017
Posts: 298
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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!
VP  G
Joined: 09 Mar 2018
Posts: 1002
Location: India
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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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Quote which i can relate to.
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VP  G
Joined: 09 Mar 2018
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Location: India
If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

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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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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up. If p, q are different prime numbers greater than 2, which of the follo   [#permalink] 26 Jan 2019, 11:42
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