lheiannie07 wrote:What is the greatest common factor of x and y ?
(1) x and y are both divisible by 4
(2) x - y = 4
Statement 1: x and y are both divisible by 4
Case 1: x=4, y=4
Here, the GCF of x and y is 4.
Case 2: x=8, y=8
Here, the GCF of x and y is 8.
Since the GCF can be different values, INSUFFICIENT.
Statement 2: x = y+4
Case 1: y=1, x=5
Here, the GCF of x and y is 1.
Case 2: y=2, x=6
Here, the GCF of x and y is 2.
Since the GCF can be different values, INSUFFICIENT.
Statements combined:
Case 1: y=4, x=8
Case 2: y=8, x=12
Case 3: y=12, x=16
Case 4: y=16, x=20
In every case, the GCF of x and y is 4.
SUFFICIENT.
The correct answer is
C.
Rule:
For any two consecutive multiples of k, the GCF is k.'
To illustrate:
The GCF of 3 and 6 -- two consecutive multiples of 3 -- is 3.
The GCF of 15 and 20 -- two consecutive multiples of 5 -- is 5.
The GCF of 90 and 99 -- two consecutive multiples of 9 -- is 9.
Here, the statements combined imply that x and y are two consecutive multiples of 4, with the result that the GCF of x and y must be 4.
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