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 Your Progress
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
The world's most "Complete" GMAT "Math" course! Easy-to-use solutions for anyone regardless of math skills (100 hours of video lessons (28 topics with 490 sub-topics, 1,500 practice questions)
Are you struggling to achieve your target GMAT score? Most students struggle to cross GMAT 700 because they lack a strategic plan of action. Attend this Free Strategy Webinar, which will empower you to create a well-defined study plan to score 760+.
To score Q50 on GMAT Quant, you would need a strategic plan of action which takes your strengths and weakness into consideration. Attend this workshop to attempt a supervised quant quiz and gain insights that can help you save 35+ hours in preparation.
Is the positive integer n a multiple of 24 ?
[#permalink]
26 Feb 2014, 01:33
3
Expert Reply
29
Bookmarks
siddhans wrote:
If in the same question we were to replace 'multiple' by 'divisible' what the difference??? What exactly happens when something is a multiple of something or when something is a divisbile of something ?
There is no difference between saying that 12 is a multiple of 4 and that 12 is divisible by 4.
As for the question. Is the positive integer n a multiple of 24?
(1) n is a multiple of 4. Not sufficient. (2) n is a multiple of 6. Not sufficient.
(1)+(2) n is a multiple of both 4 and 6 which means that it's a multiple of least common multiple of 4 and 6, which is 12. So, even taken together statements are not sufficient, since n can be for example 12 as well as 24. Not sufficient.
Answer: E.
Generally if a positive integer n is a multiple of positive integer a and positive integer b, then n is a multiple of LCM(a,b).
Yes, you are right. I ignored the fact that the 2 in the prime factor of 6 may be the same 2 from the prime factor of 2's in the factors of 12. Thus, n definitely has only two 2's and one 3 as factor, which is 12. thanks.
Yes, you are right. I ignored the fact that the 2 in the prime factor of 6 may be the same 2 from the prime factor of 2's in the factors of 12. Thus, n definitely has only two 2's and one 3 as factor, which is 12. thanks.
fluke please make clear in your way such as:
Prime factors of 24: 2^3*3 (1) 4: 2^2; Not sufficient. (2) 6: 2*3; Not sufficient.
Combining both; minimum factors of n= 2^2*2*3 = 2^3*3 = all factors of 24. Sufficient. _________________
Yes, you are right. I ignored the fact that the 2 in the prime factor of 6 may be the same 2 from the prime factor of 2's in the factors of 12. Thus, n definitely has only two 2's and one 3 as factor, which is 12. thanks.
fluke please make clear in your way such as:
Prime factors of 24: 2^3*3 (1) 4: 2^2; Not sufficient. (2) 6: 2*3; Not sufficient.
Combining both; minimum factors of n= 2^2*2*3 = 2^3*3 = all factors of 24. Sufficient.
If in the same question we were to replace 'multiple' by 'divisible' what the difference??? What exactly happens when something is a multiple of something or when something is a divisbile of something ?
Is the positive integer n a multiple of 24 ?
[#permalink]
25 Apr 2020, 06:51
Top Contributor
Expert Reply
1
Bookmarks
Bunuel wrote:
Is the positive integer n a multiple of 24 ?
(1) n is a multiple of 4. (2) n is a multiple of 6.
Target question:Is the positive integer n a multiple of 24 ? This is a good candidate for rephrasing the target question. -----ASIDE--------------------- A lot of integer property questions can be solved using prime factorization. For questions involving divisibility, divisors, factors and multiples, we can say: If N is a multiple of k, then k is "hiding" within the prime factorization of N
Consider these examples: 24 is a multiple of 3 because 24 = (2)(2)(2)(3) Likewise, 70 is a multiple of 5 because 70 = (2)(5)(7) And 112 is a multiple of 8 because 112 = (2)(2)(2)(2)(7) And 630 is a multiple of 15 because 630 = (2)(3)(3)(5)(7) -----ONTO THE QUESTION!---------------------
Since 24 = (2)(2)(2)(3), we can rephrase the target question as follows... REPHRASED target question:Are three 2's and one 3 hiding in the prime factorization of n?
Aside: the video below has tips on rephrasing the target question
Statement 1: n is a multiple of 4. 4 = (2)(2), so statement 1 is telling us that there are two 2's hiding in the prime factorization of n. Of course, there COULD be additional 2's (and 3's for that matter) hiding in the prime factorization of n. Given this, there's no way we can answer the target question with certainty. If you're not convinced, consider these two possible cases: Case a: n = 12 (which is a multiple of 4). In this case, the answer to the target question is NO, n is not divisible by 24 Case b: n = 48 (which is a multiple of 4). In this case, the answer to the target question is YES, n is divisible by 24 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is a multiple of 6 6 = (2)(3), so statement 2 is telling us that there is one 2 and one 3 hiding in the prime factorization of n. Of course, there COULD be additional 2's and 3's for that matter hiding in the prime factorization of n. Given this, there's no way we can answer the target question with certainty. Consider these two possible cases: Case a: n = 12 (which is a multiple of 6). In this case, the answer to the target question is NO, n is not divisible by 24 Case b: n = 48 (which is a multiple of 6). In this case, the answer to the target question is YES, n is divisible by 24 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED. In other words, Case a: n = 12 (which is a multiple of 4 and 6). In this case, the answer to the target question is NO, n is not divisible by 24 Case b: n = 48 (which is a multiple of 4 and 6). In this case, the answer to the target question is YES, n is divisible by 24 Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
20 - 50% Discount codes on GMAT Club Tests, Magoosh, Veritas Prep, Math Revolution, Kaplan, Manhattan Prep, Applicant Lab, and others! All Black Friday Deals
A Tribute to Daagh
It is with a heavy heart and deep regret that I share the news that one of the most humble and helpful members of GMAT Club, daagh, has left this world; passed away in October 2020. A Tribute to Daagh