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Given that p and q are positive, prime numbers greater than

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Given that p and q are positive, prime numbers greater than [#permalink] New post   10 Nov 2012, 05:17
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Given that p and q are positive, prime numbers greater than 3, what is the product of 2p and 4q?

(1) The Least Common Multiple (LCM) of 2p and 4q is 140

(2) The Greatest Common Divisor (GCD) of 2p and 4q is 2.
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Bunuel
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Re: Given that p and q are positive, prime numbers greater than [#permalink] New post   10 Nov 2012, 05:24
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Given that p and q are positive, prime numbers greater than 3, what is the product of 2p and 4q?

(1) The Least Common Multiple (LCM) of 2p and 4q is 140 --> 140=2^2*5*7. Since we know that p and q are prime numbers greater than 3 and factors of 140, then p=5 and q=7 or vise-versa (p=q=5 or p=q=7 is not possible because in this case LCM won't be 140, it would be less). Sufficient.

(2) The Greatest Common Divisor (GCD) of 2p and 4q is 2. This statement just implies that \(p\neq{q}\), thus any two different primes greater than 3 will satisfy this condition. Not sufficient.

Answer: A.

Hope it's clear.
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Re: Given that p and q are positive, prime numbers greater than [#permalink] New post   01 Jun 2017, 15:46
I got to A the same way Bunuel explained.
we have 2p & 4q
since p and q are primes and definitely not even, pq will be 35 (140 / 2 = 70, and we have one more factor of 2 = 35)
since the question indirectly asks for pq - we can answer the question.

I can see why some guys would pick C - the product of two numbers is the product of LCM and GCF of these two numbers.
unfortunately, it is not the case, and B itself is not sufficient either.
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Re: Given that p and q are positive, prime numbers greater than [#permalink] New post   01 Jun 2017, 16:19
Ok. I am really confused on this. If the first statement is not true, how can it be sufficient to answer the question. If the LCM is <140, then that proves this statement is false. Would any answer you arrive at using a false statement be false?
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Re: Given that p and q are positive, prime numbers greater than [#permalink] New post   01 Jun 2017, 17:44
mcm2112 wrote:
Ok. I am really confused on this. If the first statement is not true, how can it be sufficient to answer the question. If the LCM is <140, then that proves this statement is false. Would any answer you arrive at using a false statement be false?


Statements are always true
First statement says lcm is 140
Not that it is less than 140

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Re: Given that p and q are positive, prime numbers greater than [#permalink] New post   01 Jun 2017, 23:51
mcm2112 wrote:
Ok. I am really confused on this. If the first statement is not true, how can it be sufficient to answer the question. If the LCM is <140, then that proves this statement is false. Would any answer you arrive at using a false statement be false?


Hi

When we consider a statement in DS questions, we have to take that statement to be completely true, and then try to arrive at an answer to the given question using the data of this statement.

So in case of first statement, we have to assume that LCM of 2p and 4q is 140 only, and then evaluate whether the required answer (product of 2p and 4q) can be found using this data.
If we can get a unique value for the required product, then we have found our answer and we conclude that the statement is sufficient,
But if we do not have a unique value, then the answer has not been found and we conclude that the statement is not sufficient.
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Re: Given that p and q are positive, prime numbers greater than [#permalink] New post   02 Jun 2017, 13:48
Apologies. I got it after correctly reading how mvictor explained the question.
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Re: Given that p and q are positive, prime numbers greater than [#permalink] New post   13 Jun 2017, 15:58
can someone clarify the statement 2.
thanks
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Re: Given that p and q are positive, prime numbers greater than [#permalink] New post   14 Jun 2017, 05:50
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akulsoni100 wrote:
can someone clarify the statement 2.
thanks


We know that p and q are primes greater than 3, so they are some odd primes.

(2) says: the Greatest Common Divisor (GCD) of 2p and 4q is 2. Now, since both p and q are primes greater than 3, then this will be true for any distinct p and q, for example, the GCD of 2*5 and 2*7 is 2. This is because primes do not share any common factor but 1.

The only case this won't be true is when p = q. For example, if p = q = 5, then GCD of 2*5 and 2*5 will be 10, not 2. So, this statement just implies that p≠q, thus any two different primes greater than 3 will satisfy this condition. Not sufficient.

Hope it's clear.
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Re: Given that p and q are positive, prime numbers greater than [#permalink] New post   04 Jan 2024, 14:13
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Re: Given that p and q are positive, prime numbers greater than [#permalink]
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