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29 Jan 2012, 17:24
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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
(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105
Ok - I have got the correct answer B, but it was a guess work on statement 1.
Considering statement 1
n and t can have several values for example n = 25, t = 105. GCF will be 5 but the greatest Prime factor will be 7. However if n and t both equals 5 then GCF will be 5 but greatest prime factor will be 5. Therefore this statement is insufficient. Am I right or wrong?
Considering statement 2
It means that greatest value of n & t is 105 and prime factors of 105 are 1,3,5 and 7. Therefore 7 is the greatest Prime factor. Am I right?
Considering statement 1
n and t can have several values for example n = 25, t = 105. GCF will be 5 but the greatest Prime factor will be 7. However if n and t both equals 5 then GCF will be 5 but greatest prime factor will be 5. Therefore this statement is insufficient. Am I right or wrong?
Considering statement 2
It means that greatest value of n & t is 105 and prime factors of 105 are 1,3,5 and 7. Therefore 7 is the greatest Prime factor. Am I right?
29 Jan 2012, 17:40
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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.
Answer: B.
Hope it's clear.
(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.
Answer: B.
Hope it's clear.
31 Jan 2017, 22:18
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Statement 1: GCF(n,t) = 5
if n=15, t=10, greatest prime factor of nt = 5
if n=21, t=15, greatest prime factor of nt = 7. Hence insufficient.
Statement 2: LCM(n,t) = 105 = 3x5x7
7 is the greatest prime factor for 105.
either n or t or both must contain 7 as a factor. Therefore 7 is the greatest prime factor of nt. Sufficient.
Choose B.
if n=15, t=10, greatest prime factor of nt = 5
if n=21, t=15, greatest prime factor of nt = 7. Hence insufficient.
Statement 2: LCM(n,t) = 105 = 3x5x7
7 is the greatest prime factor for 105.
either n or t or both must contain 7 as a factor. Therefore 7 is the greatest prime factor of nt. Sufficient.
Choose B.
