Hey aakanksha003,
Glad to hear you're making progress! And I definitely admire the way that you're breaking down and analyzing your performance. The more that you can focus in on problem areas for yourself, the more effective your study time will be. So I think you're on the right track.
You know, I think the best way for you to improve on the quant side of things is to use your creativity to your advantage. Don't try to simply learn formulas or let books and forums dictate to you why things are the way they are - experiment a little and construct that knowledge for yourself. There's a pretty distinct difference between "reading" and "learning" and I think a lot of times those who struggle with this stuff don't focus enough on "learning".
So for example, you mentioned that probability is something that's giving you trouble. Personally, I never really understood probability (even though I could get most of the questions right by somehow having memorized the lists of formulas I had seen) until I had to teach it, and the reason for that is that in teaching I needed to build that knowledge for people. I'm reading a great book right now, recommended by Nick who teaches for Veritas in Seattle, called "A Drunkard's Walk: How Randomness Affects Our Lives". And the biggest lesson for me there is that:
1) Probability just is...it's nothing that someone created but rather something that has always existed and that we've learned over time.
2) People tend not to think much deeper than the surface about probability, but once you get to that next layer it's a lot easier and more enjoyable to understand.
So what I mean by using your creativity to discover probability (instead of just reading about probability) is this. Take a coin flip and ask yourself the probability of:
One flip - probability of heads
You know this is 50%...but why? Well, two things can happen - it's either heads or tails, and one of those two (1 out of 2 = 1/2) gets you what you want.
Now tweak that...how could someone make a harder question? Well, what if there were multiple flips:
Two flips - probability of two heads
You may well know that you're supposed to multiply 1/2 * 1/2 here to get 1/4. But why? Think back to what we just did in the first one...we calculated the number of things that could happen (heads or tails, so it was 2) and then determined how many of those would give us what we wanted (one). Now we just need to do that on a larger scale. Here, 4 things can happen:
Heads, Heads (which we like); Heads, Tails; Tails, Tails; Tails, Heads ---> 4 outcomes, only one of which we like, so the answer is 1/4
Mathematically, what did we do? We multiplied the two things that could happen on flip 1 by the 2 things that could happen on flip 2 (because each of the outcomes in step 1 has its own set of flip 2 outcomes, so we're calculating the total number of sequences) to determine the total number of outcomes. Then we calculated the number of those outcomes that would give us what we wanted. 4 outcomes total, one we like, so the answer is 1/4.
Now that we've done that, again get creative - how could they make this harder? There was only one way to get two straight heads, but what if our goal was to have one of each?
Two flips, one heads and one tails
Here, with two flips the total number of outcomes is the same as it was above. But since we don't need one particular sequence, there are multiple outcomes that will help us. Heads-Tails and Tails-Heads are two different sequences, and each satisfies our goal, so there are 2 outcomes that will give us what we want, and the answer is then 2/4 or 1/2.
Now say that there were more flips...say, 4 of them. For now we've been happy to just list out the various sequences, but as the number of sequences becomes larger that's a lot tougher to do. So say we wanted the same outcome - at least one heads and one tails, on 4 flips. How could we do that?
Four flips, at least one heads and one tails
As we've seen above, the most-specific sequences are the easiest to calculate. It's much easier to determine all of one type in a row than it is to calculate the multiple sequences (H-T-H-H, H-T-T-H, etc.) that allow for changes. So here we need to be creative. There are a ton of sequences that will work for us, but how do we count all those up? Well, what if we noticed that there aren't as many sequences that don't work - the only way to NOT get one of each is to get ALL of one or the other. And we know that those are easy to calculate. It's either HHHH or TTTT, and each of those only occurs once, so two of the 16 sequences don't work for us, so 14/16 or 7/8 do.
My biggest goal with this demo is this - you can figure out how to do these things by thinking your way through them in practice, and that's a whole lot more permanent a type of knowledge than just reading them. As a creative thinker, you're probably going to learn a whole lot more from trying to come up with creative solutions (and questions) than you will by having the answers and processes dictated to you.
Keep this in mind, too - this is a QUANTITATIVE REASONING test, not a "math test". They're testing your ability to think your way through these problems and not really your ability to crunch the numbers. So your skill set is perfectly suited to this in many ways...it's just a matter of embracing it and using it. Probability is best learned by teaching it to yourself by asking follow up "what ifs":
-What if they were using dice and not coins?
-What if they asked you to draw cards from a deck and the odds didn't reset each time (so when you draw the ace of spades, that card is no longer in the deck as an option for the second draw)?
The same is true of Data Sufficiency:
-What if they flip the inequality from > to < ?
-What if they limited this to positive numbers?
-What if they didn't say "integer"?
By asking these what-ifs and creating knowledge for yourself you're getting inside the mind of the testmaker and doing pretty much exactly what they're trying to learn about you - you're thinking and using information, not just trying to archive it. The GMAT quant section isn't as weighted against "poets" and creative thinkers as a lot of people think, and in many ways Data Sufficiency itself is the "great equalizer". That requires you to think and not just do, so your creative thinking abilities should actually help you a lot more than you realize.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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