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If x is a positive integer greater than 1, what is the value of x? : Data Sufficiency (DS)
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If x is a positive integer greater than 1, what is the value of x? [#permalink]
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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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]
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]
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


Hence - Answer is 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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Attachment:
File comment: Solution
DS Solution.JPG
DS Solution.JPG [ 1.57 MiB | Viewed 55139 times ]
A. see attached.
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Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
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]
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

Answer: 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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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



X is greater than or equal to 2

1) The common factors of 18 and 24 are: 2, and 3
The option says 2x is factor of 18 and 24
only 3 satisfies the condition. So x = 3
Option 1 is sufficient.

2) This gives 2, 3, and 6; several options. Insufficient.

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


Bunuel,

Statement 1 says 2x is a common factor of 18 and 24.

Can we then say that x is a common factor of 9 and 12?

9 and 12 share 3 as a common factor; x must be 3.
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Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
Expert Reply
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

Solution:

Question Stem Analysis:

We need to determine the value of x given that x is a positive integer greater than 1.

Statement One Alone:

The common factors of 18 and 24 are 1, 2, 3, 6. Setting 2x equal to 1, 2, 3 and 6, we have x equal to 0.5, 1, 1.5 and 3, respectively. Since we are given that x is a positive integer greater than 1, we see that the only possible value for x is 3. Statement one alone is sufficient.

Statement Two Alone:

The factors of 6 are 1, 2, 3 and 6. Since x is a positive integer greater than 1, x could be 2, 3, or 6. Since we have more than one possible value for x, statement two alone is not sufficient.

Answer: 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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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

'

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


Bunuel,

Statement 1 says 2x is a common factor of 18 and 24.

Can we then say that x is a common factor of 9 and 12?

9 and 12 share 3 as a common factor; x must be 3.


Hey Basshead
good logic :-) your approach works if you take into consideration that x is greater then 1.
Otherwise, there is an additional factor "1" for 9 and 12.
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Re: If x is a positive integer greater than 1, what is the value of x? [#permalink]
avigutman

I was able to solve it by identifying factors of 18 and 24 ( 1, 2, 3, 6) and then 2x equal to 1, 2, 3 and 6.
So x could be 0.5, 1, 1.5 and 3, respectively. Given x>1, so x=3

Is there any way to solve it through reasoning?
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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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Sneha2021 wrote:
avigutman

I was able to solve it by identifying factors of 18 and 24 ( 1, 2, 3, 6) and then 2x equal to 1, 2, 3 and 6.
So x could be 0.5, 1, 1.5 and 3, respectively. Given x>1, so x=3

Is there any way to solve it through reasoning?


Certainly, Sneha2021. Reduce statement (1) by a factor of 2 (since the question is about x, not 2x):
If 2x is a common factor of 18 and 24, then x is a common factor of 9 and 12. The only common factor of 9 and 12 (other than 1) is 3.
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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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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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