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Greatest common factor

Expert replies
by jfranco23 » Fri Mar 13, 2009 4:53 pm
What is the greatest common factor of the positive integers j and k?

1. k=j+1
2. jk is divisible by 5
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Source: — Data Sufficiency |

by cramya » Fri Mar 13, 2009 5:40 pm
Stmt II

j=5 k=5 (j and k can be equal no where its given it cant be)

gcf = 5

j=2 k=5

gcf=1

INSUFF


Stmt I

k = j+1

Either k is odd j is even or j is odd k is even which means only 1 can be the greatest common factor

SUFF

Choose A
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by Ian Stewart » Fri Mar 13, 2009 6:01 pm
cramya wrote: Stmt I

k = j+1

Either k is odd j is even or j is odd k is even which means only 1 can be the greatest common factor

SUFF
It's not that one of the numbers is even and one odd that makes the GCD equal to 1 here -- after all, 12 is even, and 15 is odd, but their GCD is not 1 -- it's the fact that the numbers are consecutive. The GCD of consecutive integers x and x+1 is always equal to 1, since if d is a divisor of x, then x+d will be the closest multiple of d which is larger than x, so d couldn't be a divisor of x+1 unless d=1.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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by cramya » Fri Mar 13, 2009 6:14 pm
Thanks Ian!
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