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Math Expert V
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If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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Question Stats: 72% (01:25) correct 28% (01:28) wrong based on 1821 sessions

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If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

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If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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Bunuel wrote:
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

Target question: What is the value of x?

Given: x is a positive integer greater than 1

Statement 1: 2x is a common factor of 18 and 24
Positive factors of 18: 1, 2, 3, 6, 9, 18
Positive factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
COMMON factors of 18 and 24: 1, 2, 3, 6
So, 2x = 1, 2x = 2, 2x = 3 or 2x = 6
This means, x = 0.5, x = 1, x = 1.5 or x = 3
Since we're told that x is a positive integer greater than 1, we can see that x MUST equal 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is a factor of 6
So, x could equal 1, 2, 3, or 6
Since we're told that x is a positive integer greater than 1, we can see that x COULD equal 2, 3, or 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

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Originally posted by BrentGMATPrepNow on 19 Jul 2016, 11:49.
Last edited by BrentGMATPrepNow on 02 Jan 2019, 14:28, edited 1 time in total.
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Re: If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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Bunuel wrote:
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

(1) 2x is a common factor of 18 and 24
Factors of 18= 2*3*3
Factors of 24= 2*2*2*3

Common factor of both 18 and 24= 2*3

2x=6
x=3
Sufficient.

(2) x is a factor of 6
x can be 1, 2, 3 or 6. Not sufficient.

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If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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Bunuel wrote:
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

This is how tried..

1. 2X is a common factor of 18 and 24. Take LCM of 18 and 24 i.e. 72 is the number. Then 2X = 72 => X = 36...Sufficient.

2 x is a factor of 6 - factors of 6 are 1,2,3 and 6 and here we get different X values.. Insufficient..

IMO correct option is A.

OA please...will correct if I missed anything...
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Re: If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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1
If x is a positive integer greater than 1, what is the value of x?

(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

Statement 1 : GCD of 18 and 24 IS 72 . So x is 36..! Hold on , the next common factor is 2x72=144 so X is 72.
This is insufficient.

Statement 2: 6 has many factors which are positive such as 6,12,36 ..etc

Statement 1& Statement 2 : 36 and 72 are factors of 6 .

So we can determine the value of X using the statement 1 and statement 2
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Re: If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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common factors of 18 and 24 are 2, 3, 6
ST1: 2x is factor of 18 and 24 .
we know x >1
thus only one value satisfies this x = 3
sufficient

St 2:
x is factor of 6
factors of 6 greater than 1 = 2, 3
insufficient

Ans :A
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Re: If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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If x is a positive integer greater than 1, what is the value of x?

x>1

(1) 2x is a common factor of 18 and 24

As 2x is a common fator of 18 & 24, lets fiigure out what can take the value of 2x

18 = 1*2*3*3
24 = 1*2*2*2*3

Common factors are: 1*2*3 = = 2*3 - Here 3 replaces x from the equation 2x, so get the value of x = 3 which is > 1

Hence =====> (1) is SUFFICIENT

(2) x is a factor of 6

x is a factor of 6

Which means x can be any of these numbers: 1, 2, 3

As you an clearly see that we can have twp possibilities, =1 and >1 we really cannot answer the question is x > 1.

Hence, =====> (2) is NOT-SUFFICIENT

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Re: If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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1
Attachment:
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A. see attached.
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Re: If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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I'm confused - why can't x = 1.5 in this case? If 3 and 6 are both factors of 18 and 24 in statement 1. And X > 1.

Then can't 2x = 3 (x=1.5) and 2x = 6 (x=3) work?
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Re: If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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elonmusk

The prompt states that X is an (positive) integer.
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If x is a positive integer greater than 1, what is the value of x?  [#permalink]

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(1)18, 24 has positive factors 1,2,3,6
Now 2x cannot be 1 and 3 because x is an integer
Also 2x cannot be 2, because x>1
Therefore, 2x must be 6, x=3
Sufficient

(2) Positive factors of 6 are 1,2,3 and 6
It cannot be 1 because x>1
but x can be either 2 or 3 or 6.
Not sufficient If x is a positive integer greater than 1, what is the value of x?   [#permalink] 04 May 2020, 10:07

# If x is a positive integer greater than 1, what is the value of x?  