could be; that tells you there may be more than one possible value for
b
a
. You’re told the ratio of 2a to b is 8 times the ratio of b to a. That’s awkward to keep track of in English—it’s a little easier to write fractions. The ratio of 2a:b equals 8(
b
a
). So, 2(
a
b
) = 8(
b
a
) , or
2a
b
=
8b
a
. Cross multiply to get 2a2 = 8b2 or a2 = 4b2. Multiply each side of the equation by
1
4a2
:
a2
4a2
=
4b2
4a2
. This is the same as
1
4
=
b2
a2
. Take the square root of both sides of the equation: ±
1
2
=
b
a
. The ratio of b to a is
1
2
or −
1
2
. So, (B) and (D) are the answers. This problem is also a great candidate for Back solving, although since this question could have more than one correct answer, you would need to test all answer choices to see which ones work out.