Transcript Add 8x to 2x and then subtract 5 from the sum.

Add 8x to 2x and then subtract 5 from the sum. If x is a positive integer, the
result must be an integer multiple of
a) 2
Difficulty: Medium
b) 5
c) 8
d) 10
e) 15
HINT
It may be helpful to write out mathematically the expression that is given in words
in the question. Then see which of the answers must be a factor of the number
represented by the expression in x.
B: 5
Explanation
The mathematical expression given in the question is 8x + 2x – 5, which is equivalent
to 10x – 5. The expression 10x – 5 can be factored as 5(2x – 1). For every positive
integer x, 5(2x – 1) must be a multiple of 5. If x = 1, then 5(2x – 1) = 5, which is not an
integer multiple of 2, 8, 10, or 15. Therefore, the correct answer is 5.