huda wrote:
The numbers {a,b,c} are three positive integers. If \(\frac{(a×b×c)}{14}\) equals an integer and \(\frac{(b×c)}{4}\) equals an integer, what is the smallest possible integer value of a?
A. \(1\)
B. \(2\)
C. \(4\)
D. \(7\)
E. \(14\)
Notice that 28 is divisible by both 14 and 4.
So, if b equals 28, then abc/14 and bc/4 are both integers, REGARDLESS of the values of the other two variables.
For example, if a = 1, b = 28 and c = 1, then abc/14 and bc/4 both simplify to be integers.
Since variable a must be a POSITIVE INTEGER, the smallest possible value of a = 1
Answer: A
Cheers,
Brent