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looking at (2) I would say that with the current frasing this statement is sufficient. I would agree with your answer if (2) said "...every distinct prime factor..."

When the GMAT refers to prime factors, should I assume that it is referring only to distinct ones (eg 8 has three prime factors, 2, 2, and 2, but only one distinct prime factor)?

looking at (2) I would say that with the current frasing this statement is sufficient. I would agree with your answer if (2) said "...every distinct prime factor..."

When the GMAT refers to prime factors, should I assume that it is referring only to distinct ones (eg 8 has three prime factors, 2, 2, and 2, but only one distinct prime factor)?

Welcome to the forum Marco83.

For the question. (2) states: "Every prime factor of B is also a prime factor of A." Which exactly means distinct prime factors, how else it could be? In your example: we can say that every prime factor of 8 is a factor of 30, as 8 has only one prime, which is 2 and 2 IS a factor of 30.

Let's suppose prime factorization of B is: \(B=x^p*y^q*z^r\) from the statement we know that A's prime factors must be x, y, and z. But we don't know the powers of x, y, z in A or B. So in the fraction \(\frac{A}{B}\) B may or may not be reduced. If the power of either of prime is higher in B we'll get the fraction.

Also note that we are told that B's primes are A's primes too, but not vise versa, though this doesn't affect the conclusion here.

Hope it helps. Please tell if it needs further clarification.
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If B=x^p*y^q*z^r, the prime factors of B are x x x . . . (p times) y y y . . (q times) z z z . . (r times)

While the distinct prime factors are simply x, y, and z.

If the second clue was frased as "...the DISTINCT prime factors...", I would agree with you that by having different exponents on each distinct prime factor A/B could result in a fraction, but since the clue is frased as "...the prime factors..." to me this means that A=x^p1*x^q1*z^r1*other primes, where p1>=p, q1>=q, and r1>=r. This leads to A/B=x^(p1-p)*y^(q1-q)*z^(r1-r)*other primes, which is indeed an integer.

If B=x^p*y^q*z^r, the prime factors of B are x x x . . . (p times) y y y . . (q times) z z z . . (r times)

While the distinct prime factors are simply x, y, and z.

If the second clue was frased as "...the DISTINCT prime factors...", I would agree with you that by having different exponents on each distinct prime factor A/B could result in a fraction, but since the clue is frased as "...the prime factors..." to me this means that A=x^p1*x^q1*z^r1*other primes, where p1>=p, q1>=q, and r1>=r. This leads to A/B=x^(p1-p)*y^(q1-q)*z^(r1-r)*other primes, which is indeed an integer.

What do you think?

When we have \(B=x^p*y^q*z^r\) we can say that prime factors of B are x, y, and z, which is the same as distinct prime factors of B. When you say that primes are x, p times it still means that the prime is only x, as x in any power higher than 1 is not the prime any more.
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How the two statements, A and B are different? What I understood from the options are - only the values of the factors for B are same as A and not the quantity.

Could you please explain. I chose E. The way you interpreted for option B, I interpreted for option A as well. Hence found the data to be insufficient.

How the two statements, A and B are different? What I understood from the options are - only the values of the factors for B are same as A and not the quantity.

Could you please explain. I chose E. The way you interpreted for option B, I interpreted for option A as well. Hence found the data to be insufficient.

Thanks.

Statement (1) says: every factor of B is also a factor of A, as B is a factor of B itself, then it means that B is a factor of A. So in fraction A/B, B will just be reduced and we get an integer.

I chose for D. Considering that both are sufficient but as you have mentioned the powers of prime factor in the denominator can be greater than numerator which results a fraction... Got it...

1) Each factor of S is also a factor of R ==> R is a multiple of S Sufficient

2) Every prime factor of S is also a prime factor of R ==> Insuff. R & S might have prime factors : 2,3 ... but when R/S Example: 4 * 9/81*4 is not an integer

1) Each factor of S is also a factor of R ==> R is a multiple of S Sufficient

2) Every prime factor of S is also a prime factor of R ==> Insuff. R & S might have prime factors : 2,3 ... but when R/S Example: 4 * 9/81*4 is not an integer

1. Obvious rule for division. Suff. 2. If r = 2x3x7 and s=2x3x7, good. If r = 2x3x7 and s=2x3x7x7, not good. Insuff.

A.
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DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

Re: If r and s are positive integers, is r/s an integer? [#permalink]

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Re: If r and s are positive integers, is r/s an integer? [#permalink]

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