Given that (a + b) > (c + d), is a > c? (1) a < (c + d) (2) b < d

My brain is not a linear optimizer, so sometimes it is hard for me to just pick apart the question stem and solve using algebra.
I don't know who it was, but I really appreciated learning that just using algebra to solve inequalities can work in many problems.
Obviously, sometimes intuition is more powerful, but for this question, this approach helped me. These questions feel like a game to me now.


We are given that \((a + b) > (c + d)\)

(1) \(a < (c + d)\)

This means that

\((a + b) > (c + d) > a \)

OR

\(c + d - b < a < (c + d)\)

From here, there is no way to isolate a and c. So, I'd be highly suspicious.
Furthermore, we don't know what d is. Having \(d\) would help.

(2) \(b < d\)

Using the same line of thinking. I can just plug in the inequalities.
I can either isolate \(b\)

\(c + d - a < b < d\) ====== > \(c + d - a < d\)

OR I can isolate d

\(b < d < a + b - c\) ====== > \(b < a + b - c\)

Either one simplifies down to our target, so 2 is sufficient alone.

\(c < a\)

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.