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If n is a positive integer, what is the greatest common factor
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01 Aug 2018, 19:50
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If n is a positive integer, what is the greatest common factor of n and 64? (1) No two different factors of n sum to a prime number. (2) The greatest common factor of n and 2,310 is 165.
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If n is a positive integer, what is the greatest common factor
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01 Aug 2018, 19:59
If n is a positive integer, what is the greatest common factor of n and 64?Notice that 64 = 2^6. So, the GCF of n and 2^6 is either 1 or some power of 2 (from 2 to 2^6). (1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient. (2) The greatest common factor of n and 2,310 is 165. So, the GCF of n and some even number is NOT even. This implies that 2 is NOT a factor of n. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient. Answer: D. Hope it's clear.
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Re: If n is a positive integer, what is the greatest common factor
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22 Sep 2018, 11:03
Hi BunuelI often struggle with such questions. What topic should I revisit to get better on such questions?



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Re: If n is a positive integer, what is the greatest common factor
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23 Sep 2018, 01:39



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If n is a positive integer, what is the greatest common factor
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23 Sep 2018, 11:12
Bunuel wrote: If n is a positive integer, what is the greatest common factor of n and 64?
Notice that 64 = 2^6. So, the GCF of n and 2^6 is either 1 or some power of 2 (from 2 to 2^6).
(1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.
(2) The greatest common factor of n and 2,310 is 165. So, the GCF of n and some even number is NOT even. This implies that 2 is NOT a factor of n. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.
Answer: D.
Hope it's clear. Hi Bunuel what if the n is in the form of 2^p where none of the two factors of 2^p will add to a prime number. but we do not know what is the value of P so we certainly can not determine GCF .So statement 1 is not sufficient.



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Re: If n is a positive integer, what is the greatest common factor
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23 Sep 2018, 19:47
LoneSurvivor wrote: Bunuel wrote: If n is a positive integer, what is the greatest common factor of n and 64?
Notice that 64 = 2^6. So, the GCF of n and 2^6 is either 1 or some power of 2 (from 2 to 2^6).
(1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.
(2) The greatest common factor of n and 2,310 is 165. So, the GCF of n and some even number is NOT even. This implies that 2 is NOT a factor of n. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.
Answer: D.
Hope it's clear. Hi Bunuel what if the n is in the form of 2^p where none of the two factors of 2^p will add to a prime number. but we do not know what is the value of P so we certainly can not determine GCF .So statement 1 is not sufficient. 2^p is 2, 4, 8, ... For any of these values you can pick 1 and 2 as factors, which gives the sum of 3, which is a prime.
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: If n is a positive integer, what is the greatest common factor
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24 Sep 2018, 04:11
Dear Bunuel, Can you elaborate more about the line (1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number.



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Re: If n is a positive integer, what is the greatest common factor
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24 Sep 2018, 04:16




Re: If n is a positive integer, what is the greatest common factor &nbs
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24 Sep 2018, 04:16






