GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Jan 2019, 19:52

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### \$450 Tuition Credit & Official CAT Packs FREE

January 15, 2019

January 15, 2019

10:00 PM PST

11:00 PM PST

EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth \$100 with the 3 Month Pack (\$299)
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.

# For a positive integer p, the index-3 of p is defined as the greatest

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52108
For a positive integer p, the index-3 of p is defined as the greatest  [#permalink]

### Show Tags

21 Sep 2018, 00:32
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:52) correct 40% (02:24) wrong based on 40 sessions

### HideShow timer Statistics

For a positive integer p, the index-3 of p is defined as the greatest integer n such that 3^n is factor of p. For example, the index-3 of 54 is 3 as 3 is the greatest exponent of 3 and is a factor of 54. If q and r are positive integers, is the index-3 of q greater than the index-3 of r ?

(1) q − r > 0
(2) q/r is a multiple of 3

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 867
Re: For a positive integer p, the index-3 of p is defined as the greatest  [#permalink]

### Show Tags

21 Sep 2018, 01:07
1
Bunuel wrote:
For a positive integer p, the index-3 of p is defined as the greatest integer n such that 3^n is factor of p. For example, the index-3 of 54 is 3 as 3 is the greatest exponent of 3 and is a factor of 54. If q and r are positive integers, is the index-3 of q greater than the index-3 of r ?

(1) q − r > 0
(2) q/r is a multiple of 3

To know if the index-3 of q is greater than the index-3 of p, we need to know if the prime factorization of q has a larger power of 3 than the prime factorization of p/
We'll look for statements that give us this information, a Logical approach.

(1) This tells us nothing about the prime factorization of p and q.
Insufficient.

(2) Since q/r is an integer, then all the factors of r are factors of q, and since q/r is a multiple of 3, q has at least one 3 in its prime factorization in addition to all those that r have. This is exactly what we need! (as it means that the 3-index of q is larger than that of r)
Sufficient.

_________________
Re: For a positive integer p, the index-3 of p is defined as the greatest &nbs [#permalink] 21 Sep 2018, 01:07
Display posts from previous: Sort by