Number Prop

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artstudent: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Mar 28, 2011 9:35 pm; Thanked: 4 times

by artstudent » Thu Jul 07, 2011 8:50 pm

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.

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Source: Beat The GMAT — Data Sufficiency | Thu Jul 07, 2011 8:50 pm

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Thu Jul 07, 2011 10:13 pm

Hi,
From(1):
if x= 36, y= 3. GCD of x and y is 3
if x= 60, y= 6. GCD of x and y is 6
So, it depends on the value of u
Not sufficient

From(2):
y = 12z
x = 8(12z) + 12 = 12(8z+1)
8z+1 when divided by z(>1) always gives remainder 1. So, z and 8z+1 do not have any common factors except one. That is z and 8z+1 are relatively prime. So, their GCD is 1
Hence, GCD of 12z and 12(8z+1) is 12.
Sufficient

Hence, B

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Fri Jul 08, 2011 1:59 am

a for x=36= 8*3+12, hence 36,3 have 3 as max divisor.
for x=60= 8*6+12, hence 60,6 have 6 as max divisor. Not sufficient.

b x= 12(8z+1). will always have 12 as the common factor.
also z and 8z+1 are for z=1,8z+1=9, for z=2, 8z+1=17. hence max divisor = 1 always.
Hence B it is.

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