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Difficulty:
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Question Stats:
63% (00:50) correct
37%
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wrong
based on 438
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What is the greatest common factor of positive integers x and y?
(1) x and y share only one common factor.
(2) x and y are unique prime numbers.
Below is my solution. Struggling to understand the official answer. Can someone please help?
(1) x and y share only one common factor.
(2) x and y are unique prime numbers.
Below is my solution. Struggling to understand the official answer. Can someone please help?
Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.
Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.
Hence, I went for B, which is not the case.
Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.
Hence, I went for B, which is not the case.
31 Dec 2013, 03:55
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enigma123
What is the greatest common factor of positive integers x and y?
(1) x and y share only one common factor.
(2) x and y are unique prime numbers.
Below is my solution. Struggling to understand the official answer. Can someone please help?
(1) x and y share only one common factor.
(2) x and y are unique prime numbers.
Below is my solution. Struggling to understand the official answer. Can someone please help?
Considering statement 1 : If X = 6 and Y = 9 then X = 2*3 and Y = 3 *3 and the GCF is 3 which is the common factor shared by both X and Y and of X = 4 and Y = 12 then X = 2^2 and Y = 2^2 * 3. Therefore the GCF is 4. Therefore this statement should be insufficient.
Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.
Hence, I went for B, which is not the case.
Considering statement 2 : If X = 2 and Y = 3, the GCF is 1 as this is the common factor shared by both.
Hence, I went for B, which is not the case.
What is the greatest common factor of positive integers x and y?
(1) x and y share only one common factor --> every integer has 1 as a factor, thus since x and y share only one common factor it must be 1. Sufficient.
(2) x and y are unique prime numbers. Two different primes can have only 1 as common factor. Sufficient.
Answer: D.
Hope it's clear.
General Discussion
unceldolan
Joined: 21 Oct 2013
Last visit: 03 Jun 2015
Posts: 151
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Given Kudos: 19
Location: Germany
Schools: Owen '17 (A$) Sauder '17 (A$) Schulich '17 (WD) Anderson FEMBA '17 (S) McDonough '17 (A) Desautels '17 (S)
GMAT 1: 660 Q45 V36
GPA: 3.51
Schools: Owen '17 (A$) Sauder '17 (A$) Schulich '17 (WD) Anderson FEMBA '17 (S) McDonough '17 (A) Desautels '17 (S)
GMAT 1: 660 Q45 V36
Posts: 151
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18 Feb 2014, 04:33
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Let's start with (2). A prime number is only divisible by 1 and itself. Hence the factors of a prime number are only 1 and itself. Now if you have two DIFFERENT unique prime numbers, the factor is 1.
Statement (1). At first I started as you, thought about types of numbers sharing common divisors/factors. Then I remembered that every number is also divisible by 1 and itself. Hence, the numbers mustn't share another factor than one. Hence the GCD would again be 1. Thus D is the correct answer.
Statement (1). At first I started as you, thought about types of numbers sharing common divisors/factors. Then I remembered that every number is also divisible by 1 and itself. Hence, the numbers mustn't share another factor than one. Hence the GCD would again be 1. Thus D is the correct answer.
