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:
Is the positive integer x divisible by each integer from 2 through 6 ?
[#permalink]
Show Tags
14 May 2016, 03:47
12
10
Is the positive integer x divisible by each integer from 2 through 6 ?
The question asks whether x is divisible by the LCM of 2, 3, 4, 5, and 6, which is 60.
(1) x = 10m, where m is a positive integer divisible by each integer from 2 through 5.
m is divisible by the LCM of of 2, 3, 4, and 5, which is 60. Thus x = 10*(multiple of 60). Sufficient.
(2) 10x = n, where n is a positive integer divisible by each integer from 2 through 9.
n is divisible by the LCM of of 2, 3, 4, 5, 6, 7, 8, and 9, which is 2520 (9*7*8*5). Thus 10x = (multiple of 2520) --> x = (multiple of 252). If x = 252, then the answer is NO but if x is say, 252*60, then the answer is YES. Not sufficient.
Re: Is the positive integer x divisible by each integer from 2 through 6 ?
[#permalink]
Show Tags
14 May 2016, 03:36
11
6
pego2008 wrote:
Is the positive integer x divisible by each integer from 2 through 6 ?
1- x = 10m, where m is a positive integer divisible by each integer from 2 through 5
2- 10x = n, where n is a positive integer divisible by each integer from 2 through 9
Thanks in advance
clearly A is suff.... 1- x = 10m, where m is a positive integer divisible by each integer from 2 through 5 x=10m.. and m is a multiple of 2 to 5................ since m is a multiple of 2 and 3 both, it is also div by 6.. hence suff
2-10x = n, where n is a positive integer divisible by each integer from 2 through 9 10x = n...
if n = 2*3*4*5*6*7*8*9... 10x = 2*3*4*5*6*7*8*9... so x = 3*4*6*7*8*9... so x need not be div by 5...NO
Is the positive integer x divisible by each integer from 2 through 6 ?
[#permalink]
Show Tags
07 Jul 2016, 12:16
1
considering the numbers one at a time in order to figure out what x will need, at a minimum, in it's prime factorization:
2: in order for x to be divisible by 2, x needs a 2 in its PF 3: in order for x to be divisible by 3, x needs a 3 in its PF (so now we have 2*3) 4: in order for x to be divisible by 4, x needs another 2 in its PF (so now we have 2*2*3) 5: in order for x to be divisible by 5, x needs a 5 in its PF (so now we have 2*2*3*5) 6: in order for x to be divisible by 6, x needs a 2 and a 3 in its PF (we already have that so our min doesn't change; x still needs, at min, 2*2*3*5 in its PF)
So we need enough info to prove that x has at least 2*2*3*5 in its PF
Statement 1.
x = (10)(m) ---> rewriting m in terms of what we know about its PF --> x=(2*5)(2*3*2*5*whatever else might be in m)
We can see right away that x has at least 2*2*3*5 in its PF. Sufficient.
Statement 2
10x = n ---> x = n/10 --> rewriting m in terms of what we know about its PF, and factoring 10 --> x = (2*2*2*3*3*5*7*whatever else might be in n)/2*5 --> the two and 5 cancel to get ---> x = (2*2*3*3*7*whatever else might be in n)
We don't know if x has 2*2*3*5 in its PF because we don't know for sure that there is a 5; there may or may not be a 5 in the 'whatever else might be in n' part. Insufficient.
Re: Is the positive integer x divisible by each integer from 2 through 6 ?
[#permalink]
Show Tags
08 Jul 2016, 22:04
If we modify the original condition and the question, since x has to be divisible by 2, 3, 4, 5 and 6, the question becomes “is it x a multiple of 60?” In case of con 1), from x=10m, m is divisible by 2, 3, 4 and 5. Hence, x is a multiple of 60. The answer is yes and the condition is sufficient. Thus, the correct answer is A.
- Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________
Is the positive integer x divisible by each integer from 2 through 6 ?
[#permalink]
Show Tags
23 Jul 2016, 13:19
chetan2u wrote:
pego2008 wrote:
Is the positive integer x divisible by each integer from 2 through 6 ?
1- x = 10m, where m is a positive integer divisible by each integer from 2 through 5
2- 10x = n, where n is a positive integer divisible by each integer from 2 through 9
Thanks in advance
clearly A is suff.... 1- x = 10m, where m is a positive integer divisible by each integer from 2 through 5 x=10m.. and m is a multiple of 2 to 5................ since m is a multiple of 2 and 3 both, it is also div by 6.. hence suff
2-10x = n, where n is a positive integer divisible by each integer from 2 through 9 10x = n...
if n = 2*3*4*5*6*7*8*9... 10x = 2*3*4*5*6*7*8*9... so x = 3*4*6*7*8*9... so x need not be div by 5...NO
if n = 2*3*4*5*6*7*8*9*5... ans is YES Insuff
A
Hello, can someone please explain to me why can we add another five in the second statement? It's kind of driving me nuts!
Re: Is the positive integer x divisible by each integer from 2 through 6 ?
[#permalink]
Show Tags
23 Jul 2016, 20:17
1
Avigano wrote:
chetan2u wrote:
pego2008 wrote:
Is the positive integer x divisible by each integer from 2 through 6 ?
1- x = 10m, where m is a positive integer divisible by each integer from 2 through 5
2- 10x = n, where n is a positive integer divisible by each integer from 2 through 9
Thanks in advance
clearly A is suff.... 1- x = 10m, where m is a positive integer divisible by each integer from 2 through 5 x=10m.. and m is a multiple of 2 to 5................ since m is a multiple of 2 and 3 both, it is also div by 6.. hence suff
2-10x = n, where n is a positive integer divisible by each integer from 2 through 9 10x = n...
if n = 2*3*4*5*6*7*8*9... 10x = 2*3*4*5*6*7*8*9... so x = 3*4*6*7*8*9... so x need not be div by 5...NO
if n = 2*3*4*5*6*7*8*9*5... ans is YES Insuff
A
Hello, can someone please explain to me why can we add another five in the second statement? It's kind of driving me nuts!
Hi,
St2: 10x = n --> x = n/10 n can be any integer. If n = 2*3*4*5*6*7*8*9*5, then x is divisible by each integer from 2 through 6 --> Another 5 is added here to show sufficiency. If n = 2*3*4*5*6*7*8*9, then x is not divisible by 5 because n/10 consumes a 2 and 5 --> In this case St2 is not sufficient We can conclude that St2 is not sufficient at all times.
Re: Is the positive integer x divisible by each integer from 2 through 6 ?
[#permalink]
Show Tags
23 Dec 2017, 01:26
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
close
60% (00:49) correct 
