in the EIV Manhattan book (p.94), it says that we cannot multiply or divide an inequality by a variable unless we know the sign of the variable.
If x/y<1, is x<y?
according to the EIV book, this question cannot be solved because if Y is positive, then yes x<y. However, if Y is negative, then X>Y (we flip the sign). as we don't know the sign of Y, we cannot know the answer.
This totally makes sense for me.
On the other hand, if we look at the OG edition 12 - DS - p.303 - Q#44
Robots X, Y & Z each assemble components at their respective constant rates. If Rx is the ratio of Robot X's constant rate to Robot Z's constant rate and Ry is the ratio of Robot Y's constant rate to Robot Z's constant rate, is Robot Z's constant rate the greatest of the three?
1) Rx < Ry
2) Rx < 1
so the answer is C
1) tells us the X < Y
2) Here is what doesn't make sense for me. According to the explanation, since Ry <1 then Y< Z. this is because Ry = y/z < 1, so Y < Z. we don't know the sign of Z, so how can we know that it is Y < Z, not Y > Z???
the explanation assumes that Z is positive...why??