Is a/b < 1/2 ?

[jungwkim]

Is a/b < 1/2 ?
(1) a/(b - 1) < 1/2
(2) (a - 1)/b < 1/2

I don't know how to approach this problem.
I thought statement (1) was sufficient because a/(b-1) is always greater than a/b and if something bigger than a/b is less than 1/2 than a/b is also less than 1/2?
Please help.
The oa is E

[kevinmarmstrong]

The trouble is, if 0 < b < 1, b - 1 < 0

Thus if a > 0, a/b could be greater than 1 even though a/(b - 1) < 0 < 1/2

[mschwrtz]

Nice job Kevin.

Here's an example to make Kevin's point:

If a=1, and b=1/2, then a/(b-1)=-2 (so the values are legal for statement 1), but a/b=2 (so we can generate a "no" as well as the "yes" that the OP was able to come up with).

A friendly amendment to Kevin's note:

If a is negative, then b needn't be between 0 and 1. For instance:

If a=-1, and b=-2, then a/(b-1)=1/3 (so the values are legal for statement 1), but a/b=1/2 (so we can generate a "no" as well as the "yes" that the OP was able to come up with).

A good take-away here is that DS inequality questions about proportions (would you call those disproportion question?) often depend on whether the denominators in the proportion are positive or negative. So we should immediately consider that b might be negative, or that b-1 might be negative.