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# If n and t are positive integers, what is the greatest prime

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If n and t are positive integers, what is the greatest prime [#permalink]

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05 Jul 2008, 21:04
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58% (01:24) correct 42% (00:32) wrong based on 216 sessions

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If n and t are positive integers, what is the greatest prime factor of nt?

(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-and-t-are-positive-integers-what-is-the-greatest-prime-126741.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Feb 2014, 04:34, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: Greatest prime factor GMAT Prep question [#permalink]

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05 Jul 2008, 23:17
neeraj.kaushal wrote:
If n and t are positive integers, what is the greatest prime actor of product nt.

1 The greatest common factor of n and t is 5

2 the least common multiple of n and t is 105

OA TO FOLLOW

B. LCM gives the greatest prime factor of nt i.e. 7
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Re: Greatest prime factor GMAT Prep question [#permalink]

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05 Jul 2008, 23:28
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One rule is to remember for such questions is: GCF * LCM will give you the value the 'nt' (not used in this case though); nt = 525

S1. Does not tell you anything except the the GCF of n is 5
S2. From 105 you get the prime factors, whcih are: 3, 5, and 7

Hence IMO B
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Re: Greatest prime factor GMAT Prep question [#permalink]

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06 Jul 2008, 21:59
SORRY TYPING ERROR , OA is B .
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Re: If n and t are positive integers, what is the greatest prime [#permalink]

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31 Jan 2014, 20:00
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Re: If n and t are positive integers, what is the greatest prime [#permalink]

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01 Feb 2014, 04:35
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If n and t are positive integers, what is the greatest prime factor of nt?

(1) The greatest common factor of n and t is 5 --> if n and t does not have any prime greater than 5 then the greatest prime factor of nt will be 5 (example: n=5 and t=5 or n=10 and t=15) BUT if n and/or t have some primes more than 5 then the greatest prime factor of nt will be more than 5 (example: n=35 and t=5 --> the greatest prime of nt is 7 or n=5 and t=55 --> the greatest prime of nt is 11)

(2) The least common multiple of n and t is 105 --> the least common multiple of two integers contains all common primes of these integers, thus 105 has all the primes which appear in both n and t --> the greatest prime factor of 105 is 7, hence it's the the greatest prime factor of nt (no greater factor can "appear" in nt if it's not in either of them). Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-and-t-are-positive-integers-what-is-the-greatest-prime-126741.html
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Re: If n and t are positive integers, what is the greatest prime   [#permalink] 01 Feb 2014, 04:35
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