Combining Inequalities: Add em up!

[rkafc81]

Hi all - in the MGMAT book for Equations, Inequalities and VICS, there is a bit about adding up inequalities... However, can someone explain why you can actually add up inequalities such as the ones in the question below? How do you know that in this case, you can't do this --> a + d < c + b?


here is the example:

Is a + 2b < c + 2d?

(1) a < c
(2) d > b


And the answer:


For this problem, we can add the inequalities together to make them match the question.
First, we need to line up the inequalities so that they are all facing the same direction:
a < c
b < d

Then we can take the sum of the two inequalities to prove the result. We will need to add
the second inequality TWICE:
a < c
+ b< d
a+ b < c+ d
+ b< d
a+2b < c+ 2d
If you use both statements, you can answer the question. Therefore the answer is (C).



thanks!

[jnelson0612]

Hi there,
You are allowed to add inequality as long as the sign is pointing the same way for the inequalities you are adding together. Your example adds inequalities in which signs are facing opposite ways, and this is not allowed.

Sub in some numbers for a, b, c, and d, and see why this works (and doesn't work in the instance you suggested).

[M521]

Can someone explain why "You will need to add the second inequality twice" ? p. 95 Manhattan GMAT Algebra

[tim]

How else are you going to get 2b and 2d?

[RonPurewal]

Yep. ALWAYS keep the goal of the problem in mind.

Basically, just remember what you're trying to build.
Imagine you're building a piece of furniture. Super mundane task, of course—but think about the constant goal-oriented focus that's involved.
At no point do you ever forget what you're trying to build, and at no point are you ever clueless about how the current piece fits into the overall item.

Here, the only difference is that you're trying to "build" a mathematical expression rather than a piece of furniture; the thought process is exactly the same. The whole time, you should be exquisitely aware that you're "building" something that has "2b" and "2d" in it.