Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 1612:00 PM EDT
-11:59 PM EDT
You’re first to know: Save $200 on GMAT prep starting tomorrow, 4/13. Get 6 official practice tests and study with real questions. Be ready to save!
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
13 Sep 2022, 07:38
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (01:54) correct
41%
(02:04)
wrong
based on 443
sessions
History
Date
Time
Result
Not Attempted Yet
If p is a positive integer and p^3 is divisible by 576, the largest positive integer that must divide P is...
(A) 2
(B) 4
(C) 6
(D) 12
(E) 24
(A) 2
(B) 4
(C) 6
(D) 12
(E) 24
The correct answer here is D) 12.
I have a doubt that if I consider P = 24 then P^3 will be 24*24*24 then it will be divisible by 576 and the greatest integer which will divide P will be 24, how am I wrong?
I have a doubt that if I consider P = 24 then P^3 will be 24*24*24 then it will be divisible by 576 and the greatest integer which will divide P will be 24, how am I wrong?
13 Sep 2022, 08:15
Kudos
Bookmarks
yashrajrathi20
Notice this: since p is an integer then prime factorization of p^3 will be something like this:
- \(p^3 = a^{(some \ multiple \ of \ 3)}*b^{(some \ multiple \ of \ 3)}*c^{(some \ multiple \ of \ 3)}*...\), where a, b, and c are primes of p.
For example, p^3 could be:
- \(p^3=2^9*3^6*11^{333}\). (Notice that the powers of primes are all multiples of 3.)
While, p^3 cannot be for example:
- \( p^3=2^4*5^6\). In this case \(p=50\sqrt{2}\), which is NOT an integer.
Next, we are told that p^3 is divisible by 576;
\(p^3 = 576*k\), for some positive integer k;
\(p^3 = 2^6*3^2*k\);
As discussed above, k must complete the powers of 2 and 3 to some multiple of 3. The power of 2 is already a multiple of 3, so k must complete 3^2 to a multiple of 3. Thus, the LEAST value of k is 3.
So, the LEAST value of p^3 is \(p^3 = 2^6*3^2*3=2^6*3^3\). This in turn gives the LEAST value of p as \(p =\sqrt[3]{2^6*3^3} =2^2*3=12\).
Of course, k could be more that 3. For example, k could be 3^7*17^99 (notice that in this case k also completes primes of p^3 to some multiples of 3) but the LEAST value of k is 3, and thus the least value of p is 12..
Now, the question asks: what is the largest positive integer that MUST divide p?" Since the least value of p is 12, then we can guarantee that p MUST be divisible by 12! p COULD be divisible by infinitely many larger numbers but that's not what the question asks!
Answer: D.
General Discussion
13 Sep 2022, 09:08
Kudos
Bookmarks
Bunuel thanks for the reply, you mentioned that the least value of P is 24 in your answer. The question is the largest positive integer that must divide P, so shouldn't that be 24? then the answer would be E, right? I think its just a typing mistake haha.
