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What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 21:31
What is the highest common factor of three positive integers X, Y, and Z? (1) X = 32, Y = 81 (2) Y = 81, Z = 121 Sol: HCF is the greatest common factor for all the numbers. Considering statement (1) alone:X = 32 = 2^5 Y = 81 = 3^4 As the two numbers only have 1 as the common factor, the HCF of the three numbers X, Y, and Z is 1. SUFFICIENTConsidering statement (2) alone:Y = 81 = 3^4 Z = 121 = 11^2 As the two numbers only have 1 as the common factor, the HCF of the three numbers X, Y, and Z is 1. SUFFICIENTThe answer is (D).
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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 21:45
A tricky question. At first glance answer is C, but it is a trap answer Let's prime factorize to find GCF: Statement 1. X=\(2^5\), Y=\(3^4\) The only factor they share is 1. No matter what number is Z, GCF will have to be 1 because only 1 is common between X and Y. A is Sufficient Statement 2. Y=\(3^4\), Z=\(11^1\). Again, Y and Z share only 1 as their common factor. Whatever number is X, it will not affect GCF of X, Y, and Z because only 1 is common between Y and Z. Sufficient Answer is D



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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 21:52
What is the highest common factor of three positive integers X, Y, and Z? (1) X = 32, Y = 81 \(X = 2^5 y = 3^4.\) Hence common factor of X and Y is 1. Given that Z is a positive integer, 1 will be common between X, Y and Z and no other factor can be common between X, Y and Z. Hence, it is sufficient. (2) Y = 81, Z = 121 \(Y = 3^4 z = 11^2.\) Here common factor between Y and Z is 1. Given that X is a positive integer, 1 will be common between X, Y and Z and no other factor can be common between X, Y and Z. Hence, it is sufficient. Option D.
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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 22:03
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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 22:06
The answer should be D. As each statement alone is sufficient.
In both the statements the 2 nos given are coprime (prime to each other). So the highest common factor between the two of them is 1. Whatever the third no be in both the cases, the HCF of 3 numbers has to be 1 as the HCF of the given 2 number is 1.
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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 22:13
We need to find GCD of 3 positive integers
(1) X = 32, Y = 81...> GCD of X and Y is:
X= 2*2*2*2*2 Y= 3*3*3*3
Greatest Common factor =1 Now, GCD of all three numbers will always be 1 irrespective of 3rd number. So, this is sufficient
(2) Y = 81, Z = 121
Y= 3*3*3*3 Z= 11*11
Greatest common factor =1
With same reasoning, this equation is also sufficient.
Therefore, Answer is D



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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 22:24
Considering (1) X = 32, Y = 81 Since 32=2^5*1 and 81= 3^4*1 Since X and Y have only 1 as the common factor we don't need Z to decide HCF of X,Y,Z. I will be 1. Hence sufficient (2) Y = 81, Z = 121 81=3^4*1 and 121=11^2*1 So as in Statement (1) 1 will be be only common factor and hence the HCF of X,Y,Z. Hence sufficient D is correct choice IMO.
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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 22:26
What is the highest common factor of three positive integers X, Y, and Z? (1) X = 32, Y = 81 (2) Y = 81, Z = 121 #1 x=2^5 and y=3 ^4 z value not know insufficient #2 y=3^4 and z=11^2 x value not know insufficient from 1 & 2 x=2^5,y=3^4 and z=11^2 HCF of x,y,z sufficient IMO C
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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 22:59
HCF of three given numbers can be find out by 1) calculating HCF of any two numbers. and then 2) calculating HCF of the other two numbers with the HCF obtained in step 1. consider x=3,y=6,z=12 A=HCF(x,y)=3 B=HCF(y,z)=6 HCF(A,B)=3 Hence option C
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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 23:21
What is the highest common factor of three positive integers X, Y, and Z?
So we need all the three values to answer the question
(1) X = 32, Y = 81  insuff (2) Y = 81, Z = 121  insuff
Combined we get all the values, therefore sufficient. Answer is D



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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 23:47
What is the highest common factor of three positive integers X, Y, and Z?
(1) X = 32, Y = 81 (2) Y = 81, Z = 121
St. 1 : X=32, Y=81 , no info for Z but since X= 32 can be written as 2^5 & Y=81 can be written as 3^4 and both do not share any common factor, whatever be the value for Z the highest common factor for all three variable would be 1 Hence Sufficient
St. 2 : Y=81 and Z= 121, no info for X but since Y=81 can be written as 3^4 & Z= 121 can be written as 11^2 and and both do not share any common factor, whatever be the value for X the highest common factor for all three variable would be 1 Hence Sufficient
Answer= D



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Re: What is the highest common factor of three positive integers X, Y, and
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19 Jul 2019, 23:54
What is the HCF of three positive integers X,Y, and Z?
1. X=32, Y=81 Factors of X=32 {1, 2, 4, 8, 16, and 32} Factors of Y=81 {1, 3, 9, 27, and 81} It can be seen that the only common factor between 32 and 81 is 1. And we know every positive integer has 1 as factor. Irrespective of the value of Z, the only factor it will have in common with 32 and 81 will still be 1. Hence Statement 1 on its own sufficient.
2. Y=81, Z=121 Factors of Y=81 {1, 3, 9, 27, and 81} Factors of Z=121 {1, 11, and 121} HCF of Y and Z is 1. We know X is a positive integer which will have 1 as part of its factors. We can therefore determine that the HCF of X, Y, and Z is 1. Hence Statement 2 is also sufficient on its own.
The answer is D.



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Re: What is the highest common factor of three positive integers X, Y, and
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20 Jul 2019, 00:07
What is the highest common factor of three positive integers X, Y, and Z?
(1) X = 32, Y = 81 (2) Y = 81, Z = 121
Stmts 1 and 2 by themselves are clearly not sufficient because they only provide values for 2 of the 3 integers.
The two statements together we have, X=32, Y=81 and Z=121 with prime factorization of X = 2^5, Y=3^4 and Z=11^2 and sufficient to say the highest common factor will be 1.
Correct answer C



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Re: What is the highest common factor of three positive integers X, Y, and
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20 Jul 2019, 00:10
Given,
X, Y, Z are positive integers.
To find,
Highest Common Factor of the 3 positive integers X, Y, Z.
Let us check the options now,
Option 1: X = 32, Y = 81
X = 2^5 Y = 3^4
=> Their HCF is 1.
Hence the HCF of X, Y, Z will be 1.
Option 1 is sufficient.
Option 2: Y = 81, Z = 121
Y = 3^4 Z = 11^2
=> Their HCF is 1.
Hence the HCF of X, Y, Z will be 1.
Option 2 is sufficient.
Answer: D



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Re: What is the highest common factor of three positive integers X, Y, and
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20 Jul 2019, 00:28
What is the highest common factor of three positive integers X, Y, and Z?
(1) X = 32, Y = 81 X = 2^5 & Y = 3^4. Here, HCF of X and Y is "1". It does not matter what value 'Z' have, HCF for X, Y & Z will also be "1".
So, first can answer the question independently.
(2) Y = 81, Z = 121 Y = 3^4 & Z = 11^2. Here, HCF of Y and Z is "1". It does not matter what value 'X' have, HCF for X, Y & Z will also be "1".
So, second can answer the question independently.
ANSWER: D



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Re: What is the highest common factor of three positive integers X, Y, and
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20 Jul 2019, 00:28
What is the highest common factor of three positive integers X, Y, and Z?
(1) X = 32, Y = 81, common factor is 1 only. X=2^5 and Y=3^4. Z can have both 2 and 3 but a HCF between three numbers is 1. (2) Y = 81, Z = 121, common factor is 1 only. Y=3^4 and Z=11^2, X can have both 3 and 11, but a HCF between three numbers is 1. Answer D



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Re: What is the highest common factor of three positive integers X, Y, and
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20 Jul 2019, 00:36
highest common factor of three positive integers X, Y, and Z?
STATEMENT (1) X = 32, Y = 81 X = \(2^5\) Y = \(3^4\) x and y are co primes they have no factor in common except 1
any positive integer value of Z will not have a common factor with (X,Y and Z) except 1 suppose Z =6 Z have a common factor with X and Y (individually) but X,Y and z combined doesnt have any common factor except 1
so X ,y and Z have highest common factor 1 SO SUFFICIENT
STATEMENT (2) Y = 81, Z = 121 Y and Z are co prime they have common factor 1 any positive integer value of X will not have a common factor with (X,Y and Z) except 1 so X,Y and Z highest common factor = 1 SUFFICIENT
D is the answer



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What is the highest common factor of three positive integers X, Y, and
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Updated on: 20 Jul 2019, 17:16
Question: What is the highest common factor of three positive integers X, Y, and Z?(1) X = 32, Y = 81\[\text{Prime Factor Calculation of 32}\\ \begin{pmatrix*} &&32&& \\ &\swarrow&&\searrow&\\ 2&&\downarrow&&2\\ &&8&&\\ &\swarrow&&\searrow&\\ 2^2&&&&2\\ &&&& \end{pmatrix*} \rightarrow \text{Prime Factors of 32 are } 2,2,2,2,2 = 2^5\\ \text{ } \\ \text{ } \\ \text{Prime Factor Calculation of 81}\\ \begin{pmatrix*} &&81&& \\ &\swarrow&&\searrow&\\ 3&&\downarrow&&3\\ &&9&&\\ &\swarrow&&\searrow&\\ 3&&&&3\\ &&&& \end{pmatrix*} \rightarrow \text{Prime Factors of 81 are } 3,3,3,3 = 3^4\\ \text{ } \\ \text{No prime factors are shared between the number 32 and 81. Therefore the only shared factor is 1. } \\ \] (2) Y = 81, Z = 121\[\text{Prime Factor Calculation of 81}\\ \begin{pmatrix*} &&81&& \\ &\swarrow&&\searrow&\\ 3&&\downarrow&&3\\ &&9&&\\ &\swarrow&&\searrow&\\ 3&&&&3\\ &&&& \end{pmatrix*} \rightarrow \text{Prime Factors of 81 are } 3,3,3,3 = 3^4\\ \text{ } \\ \text{ } \\ \text{Prime Factor Calculation of 121}\\ \begin{pmatrix*} &&121&& \\ &\swarrow&&\searrow&\\ 11&&&&11\\ &&&& \end{pmatrix*} \rightarrow \text{Prime Factors of 121 are } 11,11 = 11^2\\ \text{ } \\ \text{No prime factors are shared between the number 121 and 81. Therefore the only shared factor is 1. } \\ \] Correct Answer: D \(\implies\) The greatest common factor of ALL three integers is 1.
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Re: What is the highest common factor of three positive integers X, Y, and
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20 Jul 2019, 03:12
(i) x = 32 > 2^5, y = 91 > 3^4, the common factor of x & y is 1, and for any value (odd or even) of z, 1 is one factor. So, the common factor of x, y, and z is 1, which happens to be the highest common factor, sufficient Example: if z = 2, then we have 2^5, 3^4, and 2^1, the highest common factor is 1. if z = 12 = 2^2*3, then we have 2^5, 3^4, and 2^2*3, the highest common factor is 1
(ii) y = 91 > 3^4, z = 121 > 11^2, 1 is the common factor of y and z. So, for any value of x, 1 is one common factor, and highest common factor of x, y, and z is 1, sufficient
Answer is D



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Re: What is the highest common factor of three positive integers X, Y, and
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20 Jul 2019, 03:22
Statement 1: \(X = 32 = 2^5\) \(Y = 81 = 3^4\) As there are no common factors between X and Y other than 1, HCF of X and Y = 1 Hence, even if Z has a common factor (other than 1) with either X or Y or both, the HCF of X, Y and Z will be 1. Sufficient.
Statement 2: \(Y = 81 = 3^4\) \(Z = 121 = 11^2\) As there are no common factors between Y and Z other than 1, HCF of Y and Z = 1. Hence, even if X has a common factor (other than 1) with either Y or Z or both, the HCF of X, Y and Z will be 1. Sufficient.
Option (D)




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