BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Puzzling GCD

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 208
Joined: Sun Sep 28, 2008 12:30 pm
Thanked: 22 times

Puzzling GCD

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 ?
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

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
Top
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
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 435
Joined: Mon Mar 15, 2010 6:15 am
Thanked: 32 times
Followed by:1 members

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
Top
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 am
Thanked: 137 times
Followed by:5 members

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
Top
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
Top
Post new topic Post Reply
• Page 1 of 1