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 is B
Greatest Common Divisor
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Pl. see here.dlencz 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
OA is B
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For many test-takers, the most efficient approach on test day would be to plug in.dlencz 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
OA is B
Statement 1: x=12u, where u is an integer and x=8y+12.
In other words, x is a multiple of 12.
For x to be a multiple of 12, 8y must be a multiple of 12.
If y=3, then x = 8*3 + 12 = 36.
The GCD of 3 and 36 is 3.
If y=6, then x = 8*6 + 12 = 60.
The GCD of 6 and 60 is 6.
Since the GCD can be different values, INSUFFICIENT.
Statement 2: y=12z, where z is an integer and x=8y+12.
In other words, y is a multiple of 12.
Since we're looking for the GCD, view x in terms of its FACTORS.
If y=12, then x = 8(12) + 12 = 12(8+1) = 12*9.
The GCD of 12 and 12*9 is 12.
If y=24, then x = 8(24) + 12 = 12(8*2 + 1) = 12*17.
The GCD of 24 and 12*17 is 12.
I'm almost convinced: the GCD is 12.
Maybe one more just to be sure:
If y=36, then x = 8(36) + 12 = 12(8*3 + 1) = 12*25.
The GCD of 36 and 12*25 is 12.
SUFFICIENT.
The correct answer is B.
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The solution provided by GMATGuruNY is the simplest solution of this question,I have just completed the question and found that the procedure I am following is same and so is the answer.
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In general if a equation has the form -dlencz 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
OA is B
x = n*y +c
It automatically implies that the HCF of x & y has to be a factor of 'c' resulting in
x' * HCF = y'*HCF +c'*HCF.. here x', y' and c' are quotient when HCF divides x, y and c respectively.
Thus, 12 will become HCF iff y has the form y= 12z.
Hence B alone is sufficient.
A implies that y =12(u-1)/8 = 4*(u-1)/3.. tells nothing.
Hope it helps!!
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Hi Mitch - your above explanation is based on the following logic, I think.GMATGuruNY wrote:For many test-takers, the most efficient approach on test day would be to plug in.dlencz 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
OA is B
Statement 1: x=12u, where u is an integer and x=8y+12.
In other words, x is a multiple of 12.
For x to be a multiple of 12, 8y must be a multiple of 12.
If y=3, then x = 8*3 + 12 = 36.
The GCD of 3 and 36 is 3.
If y=6, then x = 8*6 + 12 = 60.
The GCD of 6 and 60 is 6.
Since the GCD can be different values, INSUFFICIENT.
Statement 2: y=12z, where z is an integer and x=8y+12.
In other words, y is a multiple of 12.
Since we're looking for the GCD, view x in terms of its FACTORS.
If y=12, then x = 8(12) + 12 = 12(8+1) = 12*9.
The GCD of 12 and 12*9 is 12.
If y=24, then x = 8(24) + 12 = 12(8*2 + 1) = 12*17.
The GCD of 24 and 12*17 is 12.
I'm almost convinced: the GCD is 12.
Maybe one more just to be sure:
If y=36, then x = 8(36) + 12 = 12(8*3 + 1) = 12*25.
The GCD of 36 and 12*25 is 12.
SUFFICIENT.
The correct answer is B.
1. multiple of X +/- multiple of X = multiple of X ALWAYS
2. multiple of X +/- multiple of Y = multiple of Unknown ALWAYS
and these two will always hold good!
Correct me please if wrong.
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Target question: What is the greatest common divisor of x and y?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
Given: x = 8y + 12
Statement 1: x = 12u, where u is an integer.
There are several pairs of values that satisfy the given conditions. Here are two:
Case a: x=36 and y=3, in which case the GCD of x and y is 3
Case b: x=60 and y=6, in which case the GCD of x and y is 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y = 12z, where z is an integer.
If y = 12z and x = 8y + 12, then we can replace y with 12z to get:
x = 8(12z) + 12, which means x = 96z + 12, which means x = 12(8z + 1) [if we factor]
So, what is the GCD of 12z and 12(8z + 1)?
Well, we can see that they both share 12 as a common divisor, but what about z and 8z+1?
Well, there's a nice rule that says: The GCD of n and kn+1 is always 1 (if n and k are positive integers)
So, the GCD of z and 8z+1 is 1, which means the GCD of 12z and 12(8z + 1) is 12.
This means that the GCD of x and y is 12
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
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Hi Experts - can you please share your thoughts on my above post ?RBBmba@2014 wrote:Hi Mitch - your above explanation is based on the following logic, I think.GMATGuruNY wrote:For many test-takers, the most efficient approach on test day would be to plug in.dlencz 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
OA is B
Statement 1: x=12u, where u is an integer and x=8y+12.
In other words, x is a multiple of 12.
For x to be a multiple of 12, 8y must be a multiple of 12.
If y=3, then x = 8*3 + 12 = 36.
The GCD of 3 and 36 is 3.
If y=6, then x = 8*6 + 12 = 60.
The GCD of 6 and 60 is 6.
Since the GCD can be different values, INSUFFICIENT.
Statement 2: y=12z, where z is an integer and x=8y+12.
In other words, y is a multiple of 12.
Since we're looking for the GCD, view x in terms of its FACTORS.
If y=12, then x = 8(12) + 12 = 12(8+1) = 12*9.
The GCD of 12 and 12*9 is 12.
If y=24, then x = 8(24) + 12 = 12(8*2 + 1) = 12*17.
The GCD of 24 and 12*17 is 12.
I'm almost convinced: the GCD is 12.
Maybe one more just to be sure:
If y=36, then x = 8(36) + 12 = 12(8*3 + 1) = 12*25.
The GCD of 36 and 12*25 is 12.
SUFFICIENT.
The correct answer is B.
1. multiple of X +/- multiple of X = multiple of X ALWAYS
2. multiple of X +/- multiple of Y = multiple of Unknown ALWAYS
and these two will always hold good!
Correct me please if wrong.
@Mitch - could you please clarify this Sir!
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Rule 1 is correct.RBBmba@2014 wrote:
1. multiple of X +/- multiple of X = multiple of X ALWAYS
2. multiple of X +/- multiple of Y = multiple of Unknown ALWAYS
I would state Rule 2 as follows:
(multiple of X) ± (non-multiple of X) = (non-multiple of X).
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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