Puzzling GCD

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neoreaves: Master | Next Rank: 500 Posts; Posts: 208; Joined: Sun Sep 28, 2008 12:30 pm; Thanked: 22 times

by neoreaves » Sun Apr 25, 2010 2:21 am

If x and y are positive integers such that x = 8y +12. What is the greatest common divisor of x and y ?

1) x = 12u, where u is an integer.
2) y = 12z, where z is an integer.

OA = B

Ok my question is why is this the OA when in 2) i narrowed it down to x = 96(z+1) and y = 12z ....here we can have 12 as the factor ..but it is not the GCD ...what if z = 8 ...then 12x8 =96 will be the GCD ...No ?

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Source: Beat The GMAT — Data Sufficiency | Sun Apr 25, 2010 2:21 am

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

by thephoenix » Sun Apr 25, 2010 4:38 am

Ok my question is why is this the OA when in 2) i narrowed it down to x = 96(z+1) and y = 12z ....here we can have 12 as the factor ..but it is not the GCD ...what if z = 8 ...then 12x8 =96 will be the GCD ...No ?

small error
x=12(8z+1) and y=12z
hence gcd=12

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ansumania: Master | Next Rank: 500 Posts; Posts: 301; Joined: Sun Mar 21, 2010 3:18 pm; Thanked: 4 times

by ansumania » Sun Apr 25, 2010 5:58 pm

hi,

pl. explain why "1" can't be used to find the GCD.

regards,

Ansumania

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eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member; Thanked: 32 times

by eaakbari » Thu Apr 29, 2010 11:17 pm

thephoenix wrote:
Ok my question is why is this the OA when in 2) i narrowed it down to x = 96(z+1) and y = 12z ....here we can have 12 as the factor ..but it is not the GCD ...what if z = 8 ...then 12x8 =96 will be the GCD ...No ?
small error
x=12(8z+1) and y=12z
hence gcd=12

Can you explain in detail?

Whether you think you can or can't, you're right.
- Henry Ford

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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 » Thu Apr 29, 2010 11:58 pm

q stem : x=8y+12 (x and y are int)
q: GCD of x and y

s1)if u=3 then x=36 and y=3 gcd=3
if u=5 then x=60 and y=6 and gcd is 6 ; hence we are getting diff values so insuff

s2) if z=1 then y=12 and x=12*9 and gcd is 12
if z=2 then y=24 and x=12*17 and gcd is 12
if z=10 then y=12*10 and x=12*81 and gcd is 12 so gcd is same always so suff

Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working

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hardnstrong: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun Apr 04, 2010 9:53 am

by hardnstrong » Fri Apr 30, 2010 2:03 am

It dosent look like a 2 min problem
If we put in all the values to check which condition satisfies, it takes long time
it there a shorter way

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