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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## does x = 2? ##### This topic has 1 expert reply and 3 member replies ## does x = 2? If the integer x is greater than 1, does x = 2? 1) x is evenly divisible by exactly two positive integers. 2) The sum of any two distinct positive factors of x is odd. OA IS B My doubt is in stmtn 1 ; what does "evenly divisible mean" ? should the quotient be an even number ? take for example if x =2 ; then 1 evenly divides i.e. 1 *2 = 2 (quotient = 2) then 2 oddly divides itself i.e 2 * 1 = 2 (quotient = 1) is this the reason why A is not sufficient ? ### GMAT/MBA Expert GMAT Instructor Joined 02 Apr 2010 Posted: 3835 messages Followed by: 522 members Upvotes: 1854 GMAT Score: 770 pappueshwar wrote: If the integer x is greater than 1, does x = 2? 1) x is evenly divisible by exactly two positive integers. 2) The sum of any two distinct positive factors of x is odd. OA IS B My doubt is in stmtn 1 ; what does "evenly divisible mean" ? should the quotient be an even number ? take for example if x =2 ; then 1 evenly divides i.e. 1 *2 = 2 (quotient = 2) then 2 oddly divides itself i.e 2 * 1 = 2 (quotient = 1) is this the reason why A is not sufficient ? (1) x is evenly divisible by exactly two positive integers implies x can be any prime (because a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself), say, 2, 3, 5, 7, and so on. NO definite answer; NOT sufficient. (2) The sum of any two distinct positive factors of x is odd. If x = odd, then 1 will be one of the factors of x and 1 + x = even, which means x cannot be odd. If x = even and x > 2, then since x is even so 2 will be one of its factors. So, 2 + x = even, which means x cannot be more than 2, implies x = 2, as 2 has 2 factors, 1 and 2. Also, 2 + 1 = 3 (odd); SUFFICIENT. The correct answer is B. _________________ Anurag Mairal, Ph.D., MBA GMAT Expert, Admissions and Career Guidance Gurome, Inc. 1-800-566-4043 (USA) Join Our Facebook Groups GMAT with Gurome https://www.facebook.com/groups/272466352793633/ Admissions with Gurome https://www.facebook.com/groups/461459690536574/ Career Advising with Gurome https://www.facebook.com/groups/360435787349781/ Legendary Member Joined 09 Nov 2010 Posted: 934 messages Followed by: 14 members Upvotes: 63 Test Date: N.A Target GMAT Score: 750 Sir OA for this question cannot be B. 2) The sum of any two distinct positive factors of x is odd. The sum of any two distinct positive factors of x is odd. If x = odd, then 1 will be one of the factors of x and 1 + x = even, which means x cannot be odd. If x = even and x > 2, then since x is even so 2 will be one of its factors. So, 2 + x = even, which means x cannot be more than 2, implies x = 2, as 2 has 2 factors, 1 and 2. Also, 2 + 1 = 3 (odd); SUFFICIENT. The statement 2 clearly states that any two distinct factors of x is odd. Let us say that the number is 6. The factors are 1, 2, 3, 6. Now let us say we take any two integers greater than 1, lets say 3 and 2. Now 3 + 2 is also odd ie 5. So x is 6 here and not 2. According to me the answer should be C and not B. Kindly see if my explanation is correct... _________________ IT IS TIME TO BEAT THE GMAT LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!! Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button. Master | Next Rank: 500 Posts Joined 01 Oct 2010 Posted: 234 messages Followed by: 4 members Upvotes: 5 Target GMAT Score: 680 if 6 is the number then the factors are 1,2,3,6 the summation of these factors is : 1+2 = 3 (odd) 2+3 = 5 (odd) 1+6= 7 (odd) 2+6 = 8 (even) hence 6 cannot be the number . the question stem says the sum of any two distinct factors is ODD number it happen only for the number 2. the factors of 2 are 1 & 2 and their summation is 1 +2 = 3 (odd) hence resolved. hope my explanation makes sense... thanks Legendary Member Joined 09 Nov 2010 Posted: 934 messages Followed by: 14 members Upvotes: 63 Test Date: N.A Target GMAT Score: 750 Hey thanx!!! Pappueshwar, I was making a silly mistake,,, This is where the DS actually traps us.. It tries to trap us in its usual format only, forget the concepts and so many formulae. I think I got the answer...B... _________________ IT IS TIME TO BEAT THE GMAT LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... 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