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:
If the positive integer y is divisible by 3, 8, and 12, then which of
[#permalink]
Show Tags
04 Sep 2014, 09:26
PareshGmat wrote:
neeti1813 wrote:
If the positive integer y is divisible by 3, 8, and 12, then which of the following must y be divisible by?
I. 24 II. 36 III. 48
A. I only B. II only C. I and II only D. II and III only E. I, II, and III
Answer = A
LCM of 3, 8, 12 = 24
Answer = 24
It seems this problem is already present in the forums where Bunuel has explained difference between must & could used
I always search for the problems on GMAT club & then post my query. Sorry but I couldn't find anything similar to this & as Kaplan gave such a huge explanation I got a bit confused.
Oh ! Must & Could I will find it.
Thanks !!
Here is the detailed explanation:
Let’s look at the prime factors of 3, 8 and 12.
The prime factorization of 3 is 3.
Let's find the prime factorization of 8. We have 8 = 2 × 4 = 2 × 2 × 2.
Let's find the prime factorization of 12. We have 12 = 2 × 6 = 2 × 2 × 3.
Thus,
A multiple of 3, 8, and 12 must have at least three factors of 2 and one factor of 3, or 2 x 2 x 2 x 3.
Let's write the prime factorizations of 24, 36, and 48.
This is a Roman Numeral question, so let’s start with the numeral that appears most in the answer choices or Statement I. Since 24 has 3 factors of 2 and one factor of 3, y is a multiple of 24. So the correct answer will contain Statement I. We can eliminate choices (B) and (D) which do not contain Statement I.
Since 36 contains two factors of 3, but not three factors of 2, the correct answer will not contain II. We can eliminate choices (C) and (E) which contain Statement II. We have eliminated the 4 incorrect answer choices, so we know that choice (A) must be correct. Although we’ve eliminated all the wrong answer choices, we can that show that Statement III is incorrect. Since 48 contains four factors of 2, while y must contain at least three factors of 2, y does not have to be a multiple of 48, because y could contain exactly three factors of 2. The correct answer will not contain Statement III. Answer Choice (A) is correct.
Re: If the positive integer y is divisible by 3, 8, and 12, then which of
[#permalink]
Show Tags
04 Sep 2014, 22:01
neeti1813 wrote:
If the positive integer y is divisible by 3, 8, and 12, then which of the following must y be divisible by?
I. 24 II. 36 III. 48
A. I only B. II only C. I and II only D. II and III only E. I, II, and III
The official solution is overly complicated for no reason.
y needs to be divisible by 3, 8 and 12. This means that it must be the LCM of 3, 8 and 12 or a multiple of the LCM. The LCM is the smallest number which is divisible by all 3 numbers.
LCM of 3, 8 and 12 will be 3*8 = 24
Now y must be either 24 or a multiple of 24. In any case it will always be divisible by 24. Will it be divisible by 36 necessarily? No. Say if y is 24, it will not be divisible by 36. Will it be divisible by 48 necessarily? No. Say if y is 24, it will not be divisible by 48.
Answer (A)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT self-study has never been more personalized or more fun. Try ORION Free!
Re: If the positive integer y is divisible by 3, 8, and 12, then which of
[#permalink]
Show Tags
09 Feb 2018, 11:09
neeti1813 wrote:
If the positive integer y is divisible by 3, 8, and 12, then which of the following must y be divisible by?
I. 24 II. 36 III. 48
A. I only B. II only C. I and II only D. II and III only E. I, II, and III
The LCM of 3, 8, and 12 is 24. So y must be 24 or a multiple of of 24. Let’s test each answer choice.
We see that Roman numeral I is correct; if y = 24, then y/24 = 24/24 = 1.
Roman numeral II is not a multiple of 24, so it is not correct.
You might think that Roman numeral III, the value 48, should be correct, but it isn’t. If y were equal to 24, then y is NOT divisible by 48, because y/48 = 24/48 does not yield an integer as the answer.
The only answer that MUST be correct is y = 24.
Answer: A
_________________
Jeffery Miller Head of GMAT Instruction
GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions
close
72% (01:13) correct 
