Stuart, having noticed the superb quality of your insights on other posts, I'm crossing my fingers and hoping that you might tack a crack at the following question from one of my official GMAT CATs (the software from the testmakers). I think it highlights a fundamental question about inequalities that may help other students more broadly:
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. I can easily pick numbers and prove why that is so. The thing that has me baffled is why a straightforward algebraic approach doesn't work (see my next paragraph). But, I always thought you could add inequalities as long as the ineq symbol was pointed in the same direction. In my practice thus far, that's the approach I've taken and it's always worked.
So, when I saw this question, I quickly wrote the question as "Is x<20", statement 1 as "x+y < 20" statement 2 as "y< 20." Then, after quickly eliminating S1 & S2, I 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. Where did I go wrong? 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. Where am I going astray here? Many thanks.
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. I can easily pick numbers and prove why that is so. The thing that has me baffled is why a straightforward algebraic approach doesn't work (see my next paragraph). But, I always thought you could add inequalities as long as the ineq symbol was pointed in the same direction. In my practice thus far, that's the approach I've taken and it's always worked.
So, when I saw this question, I quickly wrote the question as "Is x<20", statement 1 as "x+y < 20" statement 2 as "y< 20." Then, after quickly eliminating S1 & S2, I 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. Where did I go wrong? 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. Where am I going astray here? Many thanks.
