Integers

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Sun Nov 29, 2009 2:50 pm

What is the greatest possible common divisor of two different positive integers which are less than 144 ?

143

142

72

71

12

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Source: Beat The GMAT — Problem Solving | Sun Nov 29, 2009 2:50 pm

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sun Nov 29, 2009 8:44 pm

IMO 71

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Sun Nov 29, 2009 10:25 pm

Take a maximum integer which is less than 144. Avoid 143 as it is a prime number.
So, consider 142. 142 has 2 prime factors => 2 and 71.

For a number less than 144 to have a 71 as prime factor, it is the number 71 itself.
So, GCD of 71 and 142 = 71 (Option D)

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ssuarezo: Master | Next Rank: 500 Posts; Posts: 126; Joined: Wed Jun 24, 2009 1:12 pm; Location: Montreal; Thanked: 2 times; GMAT Score:510

by ssuarezo » Mon Nov 30, 2009 8:22 am

Hi:

I always get confused with the untold part. The stem question makes no restrictions about primes.
Question: why can't be 143 (143x1), even if prime, it would be the greatest number (as asked).

Thank you,
Silvia

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Mon Nov 30, 2009 8:46 am

When you have 143 and any other number (say 71), GCD of 143 and 71 will be 1. Because they have only a greatest common factor of 1. 143 has only 2 factors - 1, 143. 143 cannot be a factor for some other integer less than 144.

Remember, we are asked to find the greatest possible common divisor. So, we are ignoring 143 in this problem

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Mon Nov 30, 2009 8:54 am

ssuarezo wrote:Hi:

I always get confused with the untold part. The stem question makes no restrictions about primes.
Question: why can't be 143 (143x1), even if prime, it would be the greatest number (as asked).

Thank you,
Silvia

for 143 and 1 , 143 cant be the greatest common divisor as 143 doesnt divide 1 the GCD in this case will be 1

HTH

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Nov 30, 2009 10:01 am

143 is not prime; it is equal to 11x13.

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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ssuarezo: Master | Next Rank: 500 Posts; Posts: 126; Joined: Wed Jun 24, 2009 1:12 pm; Location: Montreal; Thanked: 2 times; GMAT Score:510

by ssuarezo » Mon Nov 30, 2009 11:05 am

Thank you Ian, Phoenix and Papgust.
True. They asked for the greatest common divisor, not the greatest number, and even if 143 is not prime ( didn't see it!), 11 and 13 are much lower than 71. I have to read carefully.
Thank you,
Silvia.

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