yellowho wrote: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.
(1) If x = 12 u, where u is an integer, then the equation in the stem x = 8 y + 12 can be read as
A multiple of 12 = 8 y + 12
or simply, A multiple of 12 = 8 y.
Now the big question-Is y a multiple of 12? Don't know, it may or may not be so. Insufficient
(2) If y = 12 z, where z is an integer, then the equation in the stem x = 8 y + 12 can be read as
x = 8 × A multiple of 12 + 12 = Another multiple of 12.
Now since y is a given multiple of 12 and x is hence proved to be another multiple of 12 and in the present case, x and 8 y are both separable by 12, and the two numbers are also spaced out by 12 digits on the real number line, so [spoiler]
12 is the GCD of x and y.
B[/spoiler]
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
