Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 12:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

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

### Show Tags

Updated on: 19 Dec 2018, 18:58
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
Joined: 07 Dec 2014
Posts: 1210
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

### Show Tags

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

### Show Tags

19 Dec 2018, 18:57
gracie

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

### Show Tags

25 Dec 2018, 10:29
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 ?
Senior Manager
Joined: 15 Feb 2018
Posts: 258
Re: If p, q are different prime numbers greater than 2, which of the follo  [#permalink]

### Show Tags

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?
Attachments

answer.jpg [ 27.04 KiB | Viewed 710 times ]

Intern
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]

### Show Tags

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

### Show Tags

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

### Show Tags

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

### Show Tags

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.
_________________
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
Display posts from previous: Sort by