If x is a positive integer greater than 1

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jjjinapinch: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Mon Jul 24, 2017 8:16 amFollowed by: 1 member

by jjjinapinch » Wed Aug 02, 2017 10:55 am

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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

Official Guide question
Answer: A

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Source: Beat The GMAT — Data Sufficiency | Wed Aug 02, 2017 10:55 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Aug 02, 2017 11:21 am

jjjinapinch 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

Official Guide question
Answer: A

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

Answer = A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8144; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Dec 08, 2017 7:15 am

jjjinapinch 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

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

Statement One Alone:

2x is a common factor of 18 and 24.

Let's determine all of the common factors of 18 and 24:

1, 2, 3, and 6.

Since x must be an integer greater than 1, 2x will be an even integer greater than 2. Therefore the only common factor from the above list that can equal 2x is 6. Thus, x = 3. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:
x is a factor of 6.

The factors of 6 are 1, 2, 3, and 6. Since x > 1, x could equal 2, 3 or 6. Since we do not know the exact value of x, statement two is not sufficient to answer the question.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
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SampathKp: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Nov 13, 2019 9:42 pm

by SampathKp » Wed Dec 18, 2019 8:21 am

jjjinapinch 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

Official Guide question
Answer: A

For (1) 6 is the only common factor of 18 and 24. 2x = 6 , then x = 3. This is sufficient to answer the question.

For (2), 1, 2 , 3 are factors of 6. so we dont have sufficient information to get unique value of X.

So Answer is A , Statement (1) alone is sufficient and (2) is not sufficient to answer the question.

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