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# What is the highest common factor of three positive integers X, Y, and

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What is the highest common factor of three positive integers X, Y, and  [#permalink]

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Updated on: 20 Jul 2019, 04:58
What is the highest common factor of three positive integers X, Y, and Z?

(1) X = 32, Y = 81
(2) Y = 81, Z = 121

condition 1,
(1) X = 32, Y = 81

only 2 variables are known so HCF cannot be found insufficient no .. dont overlook. they are prime nos , so hcf is 1. so sufficient

condition 2
(2) Y = 81, Z = 121

only two variables are given, so HCF cannot be found insufficient..dont overlook. they are prime nos , so hcf is 1. so sufficient

ans is D..
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Originally posted by ccheryn on 19 Jul 2019, 10:06.
Last edited by ccheryn on 20 Jul 2019, 04:58, edited 2 times in total.
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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 10:10
1
What is the highest common factor of three positive integers X, Y, and Z?

(1) X = 32, Y = 81

We don't have Z but HCF of X & Y is 1. So, whatever the value of Z may be, it's ll remain 1 for X, Y & Z.
Sufficient.

(2) Y = 81, Z = 121

We don't have X but HCF of Y & Z is 1. So, whatever the value of X may be, it's ll remain 1 for X, Y & Z.
Sufficient.

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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 11:34
1
What is the highest common factor of three positive integers X, Y, and Z?

The greatest common factor, or Highest common, is the greatest factor that divides two numbers. To find the GCF of two or more numbers: List the prime factors of each number. Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1

(1) X = 32, Y = 81
X =2^5
Y=3^4

X and Y has no common factor other than 1,
Highest common factor will be 1
Sufficient

(2) Y = 81, Z = 121
X and Y has no common factor other than 1,
Highest common factor will be 1
Sufficient

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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 12:23
What is the highest common factor of three positive integers X, Y, and Z?

To know the highest common factor of three positive integers X, Y, and Z, we need to know the value of each X, Y, and Z.

(1) X = 32, Y = 81
This statement only provides the value of X and Y. Value of Z is not know. HCF cannot be found.
Insufficient.

(2) Y = 81, Z = 121
This statement only provides the value of Y and Z. Value of X is not know. HCF cannot be found.
Insufficient.

Considering both statements, we have X = 32, Y = 81 and Z = 121. All three values are know. HCF can be found.
Hence, Both statements are together sufficient.

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What is the highest common factor of three positive integers X, Y, and  [#permalink]

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Updated on: 19 Jul 2019, 23:30
1
What is the highest common factor of three positive integers X, Y, and Z?

(1) X = 32, Y = 81

The factors of 32 are: 1, 2, 4, 8, 16, 32
The factors of 81 are: 1, 3, 9, 27, 81
Then the highest common factor is 1.
We don't given Z here, even if Z has common factor with X and Y, anyway all of them will have highest common factor as 1.
Sufficient

(2) Y = 81, Z = 121

The factors of 81 are: 1, 3, 9, 27, 81
The factors of 121 are: 1, 11, 121
Then the highest common factor is 1.
We don't given X here, even if X has common factor with X and Y, anyway all of them will have highest common factor as 1.
Sufficient

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Originally posted by GKomoku on 19 Jul 2019, 12:24.
Last edited by GKomoku on 19 Jul 2019, 23:30, edited 1 time in total.
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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 12:34
1
(1) X = 32, Y = 81; $$X=2^{5}, Y=3^{4}$$,Clearly, x and y are co-prime to each other, hence their HCF is 1. Whatever be the third number, HCF of 3 numbers is going to be 1, since there won't be a common factor apart from 1. -Sufficient
(2) Y = 81, Z = 121, $$Y=3^{4}, Z=11^{2}$$, Y and Z are co-prime -> Their HCF=1. Just like (1) ->Sufficient

Ans:D
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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 12:38
1
Quote:
What is the highest common factor of three positive integers X, Y, and Z?

(1) X = 32, Y = 81
(2) Y = 81, Z = 121

This is a trap question for option C.
HCF(X,Y,Z) = ?
statement 1:
X = 32 = $$2^5$$
Y= 81= $$9^2$$
Hence both are co-prime so HCF has to be 1. if HCF(X,Y)= 1 then HCF(X,Y,Z)= 1
therefore SUFF.
statement 2:
Y= 81= $$9^2$$
Z= 121= $$11^2$$
Hence both are co-prime so HCF has to be 1. if HCF(Y,Z)= 1 then HCF(X,Y,Z)= 1
therefore SUFF.
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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 12:56
1
What is the highest common factor of three positive integers X, Y, and Z?

(1) X = 32, Y = 81
(2) Y = 81, Z = 121

The usual idea in GMAT is to split information about 3 variables in 2 statements.
However, this question is not a usual one, because from each piece of given information we can extract the answer.

X=32=2^5
Y=81=3^4

The only common factor of these integers is 1. And any other third positive integer will have only one factor in common with these previous two. And this factor is 1.

The same idea may be seen in the second statement:

Y=81=3^4
Z=121=11^2

No common factor except 1. Any other positive integer will have the only common factor with 3^4 and 11^2. And this factor is 1.

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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 13:55
1
What is the highest common factor of three positive integers $$x, y,$$ and $$z$$?

ST1. $$x = 32, y = 81$$. From this statement we know only about what x and y are equal to. Is this ST enough to find the highest common factor for all integers x, y, and z? Yes. We know that the lowest common factor is 1 and 1 is the common factor of all numbers. Since $$x=2^5$$ and $$y=3^4$$ are co-prime numbers, their highest common factor will be 1. As 1 is by no means a factor of y, whatever y may be, then the highest common factor for x, y, and z is $$1$$.
Sufficient

ST2. $$y = 81, z = 121$$. As it was in the ST1, we again have co-prime numbers $$y = 3^4$$ and $$z = 11^2$$. Hence, whatever x is, the highest common factor for x, y, and z is again 1.
Sufficient

Hence D
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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 14:35

Question is asking what is the highest common factor of three positive integers X, Y, and Z?
Therefore we need to know the values of X, Y, and Z

St.1 - X = 32, Y = 81. 2^5=32, 3^4=81, but we have no information about Z so Insufficient.

St.2 - Y = 81, Z = 121. 3^4=81, 11^2=121, but we have no information about X so Insufficient.

St. 1 &2 - X= 32, Y=81, Z=121.Now we can calculate the Highest common factor of three positive integers X, Y, and Z and it is 1 since X, Y, and Z do not share any common term. Sufficient

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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 15:33
What is the highest common factor of three positive integers X, Y, and Z?
So HCF of X,Y and Z =?

(1) X = 32, Y = 81
No information on Z as this will influence the value of the HCF
(not sufficient)

(2) Y = 81, Z = 121
No information X (not sufficient)

(1+2) X=32 ,Y=81 , z=121
.: X= 2^5 ,Y = 3^4 , z= 11^2
.: HFC =1 (Sufficient)

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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 18:25
1
What is the highest common factor of three positive integers X, Y, and Z?

(1) X = 32, Y = 81
X = 32 = 2^5
Y = 81 = 3^4
There is nothing common in between x and y other than 1 so we can say that there will be nothing more than common between all three numbers than 1.
Sufficient.

(2) Y = 81, Z = 121
Y = 81 = 3^4
Z = 121 = 11^2
There is nothing common in between y and z than 1. So we can say that for any value of x highest common factor will be 1.
Sufficient.

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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 19:45
1
a) X=2^5, Y=3^4

Whatever the number Z will be , HCF of X,Y,Z is 1.

a) z=11^2, Y=3^4

Whatever the number X will be , HCF of X,Y,Z is 1.

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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 20:08
1
(1) X = 32, Y = 81

Since 2 of the 3 values (X, Y, Z) have no common factors. All the 3 will NEVER have a common factor
--> HCF (X, Y, Z) = 1

Sufficient

(2) Y = 81, Z = 121

Since 2 of the 3 values (X, Y, Z) have no common factors. All the 3 will NEVER have a common factor
--> HCF (X, Y, Z) = 1

Sufficient

IMO Option D

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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 20:35
What is the highest common factor of three positive integers X, Y, and Z?

(1) X = 32, Y = 81
(2) Y = 81, Z = 121

It cannot be A, because from (1) you don't know any value for Z.

It cannot be B, because from (2) you don't know any value for X.

Taken together, you have all 3 values and know the common factor.
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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 20:36
In order to know the answer, we need to know what is X, Y and Z

(1) gives you only X and Y, and we don't know anything about Z, so (1) is insufficient

(2) gives you Y and Z, but we don't know anything about X, so (2) insufficient.

combined (1) and (2), know we know what is X, Y and Z, so now we can solve the question.

Choose C
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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 20:41
What is the highest common factor of three positive integers X, Y, and Z?

(1) X = 32, Y = 81
(2) Y = 81, Z = 121

To determine the highest common factor of three integers, we would need all the 3 integers.
Hence Statements alone are not sufficient.

Combining both the statements we get 1 as the common factor.

Option C.
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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 20:48
1
(1) x = 32 = 2^5
y = 81 = 3^4

Since z is positive integer, and the highest common factor of x & y is 1, the highest common factor of x,y & z is also 1.
Sufficient

(2) y = 81 = 3^4
z = 121 = 11^2

Since x is positive integer, and the highest common factor of y & z is 1, the highest common factor of x,y & z is also 1.
Sufficient

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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 21:04
What is the highest common factor of three positive integers X, Y, and Z?

To start with we need to know exact values of X, Y, and Z to determine their highest common factor

(1) X = 32, Y = 81
X = $$2^5$$ , Y = $$3^4$$
Value of Z is not provided , hence not sufficient

(2) Y = 81, Z = 121
Y = $$3^4$$ , Z = $$11^2$$
Value of X is not provided , hence not sufficient

Combined 1 & 2 - X, Y, Z are powers of prime numbers. they will not have any factors in common except 1. so 1 is the highest common factor. sufficient.

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Re: What is the highest common factor of three positive integers X, Y, and  [#permalink]

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19 Jul 2019, 21:16
1
Info given X, Y, Z are a postive integer.

HCF -- the highest common number among the given set of number
In the current scenario, HCF will be the highest positive integer among X,y and Z

A - 1 is common among X and Y so anyone number we add the HCF will remain 1

B - same reasoning as A

Re: What is the highest common factor of three positive integers X, Y, and   [#permalink] 19 Jul 2019, 21:16

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