So these are two very different (but equally awesome) GMAT skills to have in your back pocket.
Approximation is valuable for Integrated Reasoning and for certain Number Properties questions (especially those involving roots or fractions). It's not a MANDATORY skill you need for the GMAT, but it's nice to know you can round numbers off and "ballpark" sometimes, usually on the easier-to-medium level Number Prop questions.
Plugging In (also known as Backsolving) is a MAJOR asset in many Problem Solving questions, especially helpful in difficult Word Problems. When we "plug in," we essentially avoid doing algebra by testing out the 5 answer choices AS IF THEY ARE CORRECT, and seeing if we arrive at the original numbers given in the question-stem. If we do, then we must have landed on the correct answer choice! If an answer choice does NOT make sense with the givens from question-stem, it is obviously incorrect and can be eliminated.
Here's two great pages to see it explained:
https://www.800score.com/content/gre/guidec5b3.html
https://magoosh.com/gmat/2013/backsolving-on-gmat-math/
Backsolving teaches us to BE FLEXIBLE and USE THE ANSWER CHOICES. Here's a tough question we can solve by playing with the answer choices:
If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is divisible by 4, all of the following could be the value of j - k EXCEPT:
A) 43
B) 33
C) 21
D) 13
E) 5
--
(j - 2) / 4
(k - 5) / 4
Let's say j = 6 and k = 9. The difference will be a multiple of 3. ELIMINATE B and C.
Now let's keep k = 9 and just keep adding 4 to j, seeing how the difference changes.
If j = 14 and k = 9, the difference is 5. ELIMINATE E.
If j = 22 and k = 9, the difference is 13. ELIMINATE D.
The answer is (A).
