Absolutely Nothing (CAT 5)

[kelty.niles]

If |x|×y+ 9 > 0, and x and y are integers, is x < 6?

(1) y is negative

(2) |y| < 1


I'm having trouble with the solution to part 1 of this problem. It reads:

(1) INSUFFICIENT: We know that |x|×y > -9 and that y is a negative integer. Suppose y = -1. Then |x|×(-1) > -9, which means |x| < 9 (since dividing by a negative number reverses the direction of the inequality). Thus x could be less than 6 (for example, x could equal 2), but does not have to be less than 6 (for example, x could equal 7).

I understand that you can simplify to |x|×(-1) > -9, but when you divide out the -1, I'm left with |x|x<9, not |x| < 9. What happens to the extra X?

Thank you

[debmalya.dutta]

Are you sure that the second x is not the multiplication sign x but the variable x ??? :)

[tim]

Typographically, that's a multiplication sign. i'm assuming you copied and pasted it from the CAT exam, so yeah that's not an x..