what is 7 times 9?
....
....
Come on! what's keeping you?

If you can't answer that question INSTANTLY, and without thinking, then you are not going to get a high score in the GMAT Math section.

You see, in order to become someone who can solve a difficult Math problem, you have to be able to speak the language that the problem is written in. While I am the first person to stand up and say that you improve your intellectual reasoning not through rote learning, but through problem solving and frameworks, I will also stand up and say "You can't even begin understanding frameworks until you rote-learn the basics".

Now, if you answered the question without thinking, and happened to know how to express (x-y)*(x+y) in a nice short expression, then you need read no further. but if you had to think a bit, and write something down, then you and I really need to talk

Anyway, what are those basics we need to have at "the tip of our tongue"? Believe it or not, it's the stuff of primary / elementary education - the "times tables" - and the basic manipulation of symbols drilled into us in secondary / junior high school. The stuff it is "assumed" you have mastered before even attempting to study the GMAT.

Every math problem can be approached in a series of three layers - Visualisation, Cognitive and Numerical.

While the Art of GMAT Math is at its most subtle in the Visualisation (where you identify the pieces of the puzzle, those given and those missing) and Cognitive (where you identify the necessary relationships between the visualised components to complete the picture - essentially "solving" the problem) layers, the meat and potatoes of GMAT Math problem solution lies in the Numerical Layer, where you take the high level brain work, and turn it into a real solution.

It might be less glamorous than knowing tricks and tips, knowing how to turn (3/21)*72 - 42/9 into a number and cross-checking against the answers given (and it can be a hell of a lot more frustrating, when your answer doesn't even appear in the list!). But it's what gets you over the finish line.

Equally, while the allure of being able to solve an apparently complex stated problem in just a few steps using a nice little shortcut is appetizing, you won't be able to use this shortcut if you have even the slightest trouble convincing yourself that (x + y)/y = x/y + 1.

If you find that you have problems in replicating solutions that the trainer went through in class, ask yourself the following questions :

• Am I able to follow every quantum leap the trainer makes when moving from one line of the solution to the next?



• If not, is it because (s)he is doing "mental math" that is faster than I am able to follow?



• Does this mean the trainer is speaking too quickly, or maybe I need to brush up on my basics before trying to solve the most difficult problems?

Bottom line (and this is not just figurative, the bottom line of your calculations is in fact the solution you seek!), you need to be fluent in the fundamentals before moving forward.

You simply CANNOT transcend the first stage of mathematical problem solving (namely the memorisation of the ground rules) in order to get to the more satisfying and productive problem solving techniques.

Many people, from our experience, manage to get through school somehow avoiding the mastery of the fundamentals of maths. This is in part due an ironic ability to memorise and rote learn "standard problems" and their solutions to get past the pass rate line, but also because their education in general, and the career paths that follow, are based on a wide variety of intellectual disciplines. People with a passion for literature and a serious disinterest in numbers, can easily convince themselves that math is irrelevant, and get by somehow. Then, later in life, in a GMAT class surrounded by 5 IT engineers spitting out the first ten powers of the number 3 from memory, they feel very left behind indeed.

There's only one solution : you have to go back to those basics, and master them this time round.

7 x 9 is 63. 12 x 11 is 132. 7 goes into 56 8 times. x plus y all to be squared is x squared plus 2 xy plus y squared. And it's like singing your favourite song, the words just come naturally.

Once you've gotten the basics shored up, then you can throw yourself with gusto into the bookshelf problem, the cunning use of radial isoceles triangles within a circle, and working out whether you have enough information to determine John's tax requirements for a year when the average monthly wage was X amount.

So - crack open the intro texts on adding fractions, remind yourself that 7 squared is 49 and remember the biggest math genius in your class would get equally lost if she couldn't say "12 + 89 equals 101" with supreme confidence.

Go for it.