The GMAT Pill Study Method

Quant Probability Question – make my head itch!

TheGMATPill — Tue, 13 Jul 2010 23:57:38 +0000

Problem Solving Question:
Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, for each value from 1 to 6, there are two cards in the deck with that value. Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?

(A) 8/33

(B) 62/165

(C) 17/33

(D) 103/165

(E) 25/33

Step 1:
Recognize the keyword “AT LEAST”

This means this is a “1 – probability()” question…this is the default strategy when a question is asking the probability of at least X happening. It translates into 1 – probability(that event NOT happening)

Step 2:
Now you need to find the probability of not getting a pair for each of the 4 cards. Recognize that as you go through each card, the number of available cards from the remaining deck is constantly changing. Originally you have 12 cards, but then after you put down 1 card, u have 11 cards left.

Step 3:
1st card = any card = prob of 1 or 100%
2nd card = any card except the value of first card = 10 out of 11 choices
3rd card = any card except first card and except second card = 8 out of 10 choices
(notice we must exclude the 1st card and the 2nd card–but also the corresponding pairs for each of these cards.
4th card = any card except first/second/third card (and their corresponding pair card) = 6 out of 9 choices

Now multiply these probabilities so you know what the probability of NOT getting any pairs for all 4 iterations.
10/11 * 8/10* 6/9 = 480 / 990

1 – 480/990 = 510/990 = 17/33

Answer choice is C (17/33)

I don’t recommend using the nCr formula here, but if you want to use nCr’s, then:

= 1 – prob(choosing all different cards
= 1 – prob(choosing 4 different cards out of 6) * (possibilities for first card to be of two suits, for second card to be of two suits, for third card to be of two suits, and for fourth card to be of two suits)
= 1 – (6c4 * 2 * 2 * 2 * 2) / (12c4)
= 1 – (15 * 16) / (( 12 * 11 * 10 * 9 )/(4*3*2*1))
= 1 – 240 / 495
= 255/495

= 51/ 99
= 17 / 33

But again, this is not the most efficient way to think through this question. The best way is to count according to the method I discussed first above.
_________________
———————
Zeke Lee
Co-Founder, The GMATPill Study Method
http://www.gmatpill.com
98%ile GMAT in 2 weeks

New GMAT Section in June 2012: Integrated Reasoning

TheGMATPill — Mon, 28 Jun 2010 15:06:26 +0000

So the guys over at GMAC are adding a new section to the GMAT!
It’s called integrated reasoning and is basically a combination of Critical Reasoning + MBA level math. You’ll be asked to interpret charts and data sets. So stats, probability, and data analysis will be tested.

I actually think this is a good thing—it’s a lot more accurate to test these skills for an MBA program than it is to test triangles and circles. Interpreting tables of data is something that MBAs/management consultants/investment bankers do a lot–so why NOT test this skill in the GMAT?

I feel testing probability and statistics in the context of theory is pointless. The new integrated reasoning section will be testing these same concepts in a much more relevant context.

Just take a look at the video below. Notice there are data sets categorizing data in terms of country, % change, Rank, etc, in the context of airport data.

More info from the GMAC folks directly.
What does the GMAT prep market look like?

What does the GMAT Prep Market Look Like?

TheGMATPill — Fri, 25 Jun 2010 19:44:46 +0000

So I finally took the time to do some research on the GMAT Prep Marketplace. In management consulting, this is called “competitive analysis” or “competitor benchmarking.”

What should you take away from this chart?

1) GMAT Pill is significantly the lowest price GMAT Prep product out there. The other closest ones are just components of a bigger package (usually around $1,400 range) or they are Online products. “Online?” Funny, they are just video captures of classroom teachings that occur at specified 2-3 hr time slots (ie 8pm-10pm). Our “On-Demand” product is much more flexible. You study at your own pace, 24/7, skip around, take your own bathroom breaks, etc.

2) GMAT Pill has the fewest hours of instruction. Does MORE hours of instruction necessarily equate to better prep material and better score? Absolutely not. While we have the fewest hours of instruction material, the quality of the material and the focus on thought process is what impacts your score the most. We don’t want to waste your time studying. You need to study FAST and EFFICIENTLY with a good thought process.

As you can see, there are several large players out there charging ~$1,500 range. When I look at where GMATPill is priced ($327) I am just blown away. Why are we priced so low when we can raise the price to where competitors are pricing?

I guess the simple answer for now is that price needs to be sacrificed in order to gain visibility. If I were to delve further into details, our cost structure is significantly less since we don’t need physical teaching space, we don’t need to hire teachers and train them which costs a LOT. There is only ONE teacher so the costs are much less.

Is the product quality different? Yes, definitely, the testimonials speak for themselves. In addition to the teaching (it’s “faster and more efficient”), it is also more accessible with on-demand video which is a huge plus since most test takers are busy professionals. This is way better than what our competitors call “Online” because those are just video tapes of the classroom. Classes are scheduled at certain times, you don’t jump around efficiently with the video. If you go to the bathroom you can’t pause the video. A lot of time wasted, doing well on the GMAT is about being efficiently smart.

Our On-Demand videos let you focus your time to get effective studying done. If you have a lunch hour at work, you can fit this in. If you start studying then need to go watch the World Cup or go to the bathroom, you can still do that. In the end, it’s your thought process that we aim to nurture. Think like a top GMAT Test Taker and you will become one.

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