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Is the positive integer x divisible by each integer from 2 through 6 ? [#permalink]
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14 May 2016, 03:14
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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
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Re: Is the positive integer x divisible by each integer from 2 through 6 ? [#permalink]
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14 May 2016, 03:36
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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 5x=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 210x = n, where n is a positive integer divisible by each integer from 2 through 910x = 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
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Is the positive integer x divisible by each integer from 2 through 6 ? [#permalink]
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14 May 2016, 03:47
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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. Answer: A.
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Is the positive integer x divisible by each integer from 2 through 6 ? [#permalink]
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07 Jul 2016, 12:16
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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.
A is the answer.



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Re: Is the positive integer x divisible by each integer from 2 through 6 ? [#permalink]
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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.
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Is the positive integer x divisible by each integer from 2 through 6 ? [#permalink]
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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 5x=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 210x = n, where n is a positive integer divisible by each integer from 2 through 910x = 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!



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Re: Is the positive integer x divisible by each integer from 2 through 6 ? [#permalink]
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23 Jul 2016, 20:17
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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 5x=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 210x = n, where n is a positive integer divisible by each integer from 2 through 910x = 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. Hope it helps



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Re: Is the positive integer x divisible by each integer from 2 through 6 ? [#permalink]
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