Hey metamorphasif,
If I can chime in, one thing caught my eye about this post - your title "Rules, Tips, and Tricks" is something I like to caution students about. The GMAT isn't a test of reciting back rules nor is it a test that lends itself to being defeated simply by "tricks". There are definitely some things you need to know and some tricks that will save you time, but for those interested in a high score it's typically the logic behind the rules and the tricks that's going to help you the most.
For example, one of the tougher problems in the Official Guide tests divisibility and remainders in a way that most people haven't seen:
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?
Now, what's tricky here isn't the math itself...you learned remainders and division in grade school. But the difficulty comes from the fact that they're asking you to blend concepts - typically you'd either take a remainder or calculate the entire decimal-based result...you're rarely ever in a position to do both, but without a way to calculate the numbers to the left of the decimal point.
Here is where "rules" and "tricks" may stall you (and the GMAT designs question specifically to do so). Long division requires that you have all the information to divide. But if you really understand what you're doing with the remainder when you divide, you can solve this one pretty efficiently...the key is in the knowledge of the logic that makes the math work.
Take, for example, 11/4. You could express it as:
2, remainder 3
or 2.75
How do you get the 2.75? You take the remainder, 3, and divide back by the divisor, 4. The decimal is created by dividing the remainder back over the divisor.
So in the given question, if we know that the decimal is .12, then that must be the result of 9, the remainder, divided by y.
So: 9/y = .12
9 = .12y
900 = 12y
300 = 4y
75 = y
My point here is this - when you study for the GMAT, hold yourself accountable not just for rules and tricks, but rather try to also think about the logic behind why they work. Rules/tricks are often situation-specific and may help you on the questions written directly for them. Flexible knowledge allows you to do a lot more, and that's what the GMAT is looking for.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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