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# Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5610
GMAT 1: 800 Q59 V59
GPA: 3.82
Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is [#permalink]

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04 Sep 2017, 02:05
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Difficulty:

5% (low)

Question Stats:

88% (00:29) correct 13% (00:20) wrong based on 56 sessions

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Is a positive integer x divisible by 12?

1) x is divisible by 8
2) x is divisible by 6

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 27 Dec 2016 Posts: 231 Concentration: Marketing, Social Entrepreneurship GPA: 3.65 WE: Marketing (Education) Re: Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is [#permalink] ### Show Tags 04 Sep 2017, 09:46 MathRevolution wrote: Is a positive integer x divisible by 12? 1) x is divisible by 8 2) x is divisible by 6 Q : Is X divisible by $$12 (2^2*3)$$? #1. X is divisible by 8 - X can be 24 -> divisible by 12. - X can be 32 -> NOT divisible by 12. NOT SUFFICIENT. #2. X is divisible by 6 - X can be 12 -> divisible by 12. - X can be 18 -> NOT divisible by 12. NOT SUFFICIENT. Combine #1 & #2 - X must divisible by LCM of 8&6 = 24. - Since 24 is multiple of 12, so X must divisible by 12. SUFFICIENT. _________________ There's an app for that - Steve Jobs. BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 2846 Location: India GPA: 3.12 Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is [#permalink] ### Show Tags 04 Sep 2017, 10:09 Is a positive integer x divisible by $$12(2^2 * 3)$$? From the information given in Statement 1 If x is divisible by $$8(2^3)$$, 8 is not divisble by 12 but 24 is (Insufficient) From the information given in Statement 2 If x is divisible by $$6(2*3)$$, 8 is not divisble by 6 but 24 is (Insufficient) However, on combining the information available in both the statements, it is the clear the positive number x is definitely divisible by 12 as it is a multiple of $$24(2^3 * 3)$$ (Option C) _________________ You've got what it takes, but it will take everything you've got Intern Joined: 10 Jul 2017 Posts: 30 Re: Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is [#permalink] ### Show Tags 04 Sep 2017, 10:55 My answer is C. We need both statements together to have a definite answer. X is a positive int. Means x greater than 0 and is an interger. 12= 2*2*3. Statement 1- x is divisible by 8. This implies that x has a minimum of 2*2*2. But it does not say anything about the factor 3. So, not sufficient. Statement 2- x is divisible by 6. That is x has a minimum of 2*3. This does not say anything about the another 2. Thus, not sufficient. Now statement 1 + 2- X is factor of 8 and 6. Thus, x has minimum of 2^4 and 3 as factors. This sufficiently proves that x is divisible by 12, and gives us a definite answer. Hence, answer is C. Sent from my iPhone using GMAT Club Forum Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5610 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is [#permalink] ### Show Tags 06 Sep 2017, 01:28 =>1) Since 8 is not a multiple of 12, this is not sufficient. 2) Since 6 is not a multiple of 12, this is not sufficient. 1) & 2) Since lcm(8,6) = 24 is a multiple of 12, these are sufficient. Ans: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: Is a positive integer x divisible by 12 1) x is divisible by 8 2) x is   [#permalink] 06 Sep 2017, 01:28
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