Is the positive integer j divisible by a greater number of : GMAT Data Sufficiency (DS)
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# Is the positive integer j divisible by a greater number of

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Is the positive integer j divisible by a greater number of [#permalink]

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03 Feb 2008, 13:51
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Is the positive integer j divisible by a greater number of different prime numbers than the positive integer k?

(1) j is divisible by 30.
(2) k = 1000
[Reveal] Spoiler: OA
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04 Feb 2008, 17:54
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prasannar wrote:
C

J & K are unknowns

for knowing the multiples of a number, we need to know the number or the multiple of the number

now using both the statements we can figure out that J is multiple of 30 so all the primes that divide 30 also divide J and K is given to be 1000, we can figure out the # of the primes that divide 1000 and then find the relationship that both are required.

I dont understand how C is the answer.

Question is that if the total number of prime factors that J has is more than K.

From St.1 -- Since j is divisible by 30 it is divisible by 2*3*5*n. n can potentially be a prime number or a product of several prime numbers. So total number of factors of j can be anywhere between 4 or infinity. For example n can be equal to 7*11*13*17*19*23*29*31*......... so it is indeterministic what the total number of prime factors j has and if it is less than k.

From St. 2 -- We know that k=1000. But we still dont know what j is. All we know is that j 2*3*5*n. n can be a product of just 2 prime numbers or several infinite prime numbers and hence we cannot establish if total number of prime factors of j is less than 1000 or greater than 1000.

E in my opinion.

What is the OA ?
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04 Feb 2008, 22:59
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neelesh wrote:
prasannar wrote:
C

J & K are unknowns

for knowing the multiples of a number, we need to know the number or the multiple of the number

now using both the statements we can figure out that J is multiple of 30 so all the primes that divide 30 also divide J and K is given to be 1000, we can figure out the # of the primes that divide 1000 and then find the relationship that both are required.

I dont understand how C is the answer.

Question is that if the total number of prime factors that J has is more than K.

From St.1 -- Since j is divisible by 30 it is divisible by 2*3*5*n. n can potentially be a prime number or a product of several prime numbers. So total number of factors of j can be anywhere between 4 or infinity. For example n can be equal to 7*11*13*17*19*23*29*31*......... so it is indeterministic what the total number of prime factors j has and if it is less than k.

From St. 2 -- We know that k=1000. But we still dont know what j is. All we know is that j 2*3*5*n. n can be a product of just 2 prime numbers or several infinite prime numbers and hence we cannot establish if total number of prime factors of j is less than 1000 or greater than 1000.

E in my opinion.

What is the OA ?

st 1 ==> j is a multiple of 30. lets take j = 30 - so 3 prime divisors (2, 3 & 5). Note that any multiple of 30 will have atleast these 3 divisors.
st 2 ==> k = 1000. only divisors are 2 and 5

regardless of the actual value of j, it has more divisors than k. so the answer is (C)
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05 Feb 2008, 18:54
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jimmyjamesdonkey wrote:
Is the positive integer j divisible by a greater number of different prime numbers than the positive integer k?

1) j is divisible by 30.
2) k = 1000

does J have a greater number of DIFFERENT primes than k?

together lets take the worst case scenario for j. j=30. Primes of 30 are 2,3,5

2: primes of 1000 are 2,5... and thats it.

So we sufficed our worst case scenario here. J will always have more primes than k, even if its only 30.

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08 Feb 2008, 02:03
jimmyjamesdonkey wrote:
Is the positive integer j divisible by a greater number of different prime numbers than the positive integer k?

1) j is divisible by 30.
2) k = 1000

1) different prime numbers are 2, 3 and 5. Insuffisient as it needs to be compared to the number of prime factors of K
2) the only different prime factors are 5 and 2. Alone insufficient because we'd have to know how many factor J has.

Together sufficient as K has 3 factors vs. J's 2 factors

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Re: Is the positive integer j divisible by a greater number of [#permalink]

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27 Jan 2012, 03:56
can any one give me a proper explanation for this question, for some reasons i donot find the sentence construction of this problem correct ?
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Re: Is the positive integer j divisible by a greater number of [#permalink]

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27 Jan 2012, 04:08
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pbull78 wrote:
can any one give me a proper explanation for this question, for some reasons i donot find the sentence construction of this problem correct ?

Is the positive integer j divisible by a greater number of different prime numbers than the positive integer k?

Question basically asks: is the # of distinct prime factors of j more than the # of distinct prime factors of k?

(1) j is divisible by 30 --> j=30*n=(2*3*5)*n --> j has at least three distinct prime factors 2, 3, and 5. Not sufficient as no info about k.

(2) k = 1000 --> k=1,000=2^3*5^3 --> k has exactly two distinct prime factors 2 and 5. Not sufficient as no info about j.

(1)+(2) The # of distinct prime factors of j, which is at least 3, is more than the # of distinct prime factors of k, which is exactly 2. Sufficient.

Hope it's clear.
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Re: Is the positive integer j divisible by a greater number of [#permalink]

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22 Oct 2013, 18:34
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Re: Is the positive integer j divisible by a greater number of [#permalink]

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25 Nov 2014, 03:55
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26 Nov 2015, 08:40
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19 Dec 2016, 16:46
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Re: Is the positive integer j divisible by a greater number of   [#permalink] 19 Dec 2016, 16:46
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