Baten80 wrote:
If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?
A. 4
B. 5
C. 6
D. 7
E. 8
A
lotof integer properties questions can be answered by
testing values. So, let's do that here.
KEY: x is an integerSo, if x =
1, then y = 3(
1) + 2 =
5. Since 5 is a divisor of
5, we can ELIMINATE B
If x =
2, then y = 3(
2) + 2 =
8. Since 4 and 8 are both divisors of
8, we can ELIMINATE A and E
If x =
3, then y = 3(
3) + 2 =
11. Doesn't help us
If x =
4, then y = 3(
4) + 2 =
14. Since 7 is a divisor of
14, we can ELIMINATE D
By the process of elimination, the correct answer is
CCONVENIONAL APPROACH: Since 3x represents a multiple of 3 for all integer values of x, it must then be the case that (
3x + 2) represents a value that’s
2 greater than some multiple of 3.
Since
y = 3x + 2, we now know that y is
2 greater than some multiple of 3, which means y is NOT a multiple of 3.
In other words,
3 is NOT a divisor of y.
Key divisibility Rule: 6 is a divisor of y if and only if 3 and 2 are both divisors of y. Since
3 is NOT a divisor of y, 6 cannot be a divisor of y.
Answer: C