Ineq Problem: Question for Ron

[ells1986]

Is x less than 20?

Question: Is x less than 20?
(St 1): The sum of x and y is less than 20.
(St 2): y is less than 20.

OA is E. My problem is not seeing why E is correct. Eliminating 1 & eliminating 2 is easy. Also, if you pick numbers, it's relatively straightforward to see why E is correct and C is not. HERE's my question: I always thought you could add inequalities as long as the ineq symbol was pointed in the same direction. RON, one of your comments on another question (the "Is xy<0?" question) confirm this as far as I can tell: is-xy-0-t3253.html

When I saw this question, I quickly wrote statement 1 as x+y < 20 and I wrote statement 2 as y< 20. Then, I just subtracted S2 from S1 and I got x < 0. If x<0, then x is less than 20. So I picked C and moved on, thinking I'd cracked it. Is the fundamental issue that while you can ADD ineqs (as long as ineq symbol pointed in the same way), that you CAN't subtract them? I thought I'd shredded this one quickly and was surprised to see the result. Many thanks.

[RonPurewal]

Is the fundamental issue that while you can ADD ineqs (as long as ineq symbol pointed in the same way), that you CAN't subtract them?

yep. that's it.