Integrated Reasoning( MultiSource Reasoning)

I'm happy to help with this.

For the first one, the prompt says:
Facebook is offering 180,000,000 shares of Class A common stock and selling stockholders are offering 241,233,615 shares of Class A common stock. Closing of the offering is expected to occur on May 22, 2012, subject to customary closing conditions.
In addition, Facebook and the selling stockholders have granted the underwriters a 30-day option to purchase up to 63,185,042 additional shares of Class A common stock to cover over-allotments, if any.

So FB, the company itself, will sell 180,000,000 shares, and folks who already have FB shares (presumably investors and other insiders) will sell 241,233,615 shares.

The question asks:
The number of selling inside stockholders exceeds the number of new public investors on the day of the IPO.

Well, here's what we do know --- the number of shares sold by those selling inside stockholders (241,233,615) is less than the total number of shares offered for sale to new investors (180,000,000 + 241,233,615). More importantly, the question is not about the number of shares but about the number of actual people. Well, those 241,233,615 share sold by inside stockholders --- how many people owned those? We don't know, but typically those are owned by big money investors --- it may be that one individual could have plunked down some sizeable investment and wound up with, say 50,000,000 shares all by herself. There tend to be a small number of investors, each owning a gigantic number of shares. Now, thinking about the feeding frenzy when FB IPO'ed. Everyone's Aunt Jenny wanted to own a handful of shares. The number of new public investors was enormous, much much larger than the presumed number of big investors. Therefore, this statement is blatantly false. There's no way that there are more investors & insiders than general public investors, the great unwashed masses, all of whom want a piece of FB. Statement #1 is false.

The second question ask:
If the compounded annual growth rate (CAGR) is defined as

[(ending value)/(beginning value)]^(1/n) - 1

where n is number of years, then the CAGR between October 2007 and September 2009 is in excess of 100%.

An intimidating looking question, but not actually too bad. We look at the second card "User Growth", and we see

Ending Value (September 2009) = 300

Starting Value (October 2007) = 50

Yes, those numbers are really in millions, but for a percent change, we don't need to have all the extra zeros --- we can just treat them as 300 and 50.

The time period technically is 23 months, or 1 and 11/12 of a year, but for simplicity, I am going to approximate that as 2 years, n = 2. Plugging in, we get:

CAGR = (300/50)^(1/2) - 1

Well, that ratio inside parentheses --- 300/50 = 30/5 = 6, so we have

CAGR = (300/50)^(1/2) - 1 = (6)^(1/2) - 1

Now, here, we could use the calculator, but I think it's much more efficient to approximate. When we take something to the 1/2 power, we are taking the square-root of it. The square root of twelve --- we don't need the exact value --- since 4 < 6 < 9, we know 2 < sqrt(6) < 3 --- it's a number between 2 and 3. When we subtract one, we will get a number between 1 and 2 for the value of the CAGR.

A CAGR = 1 would be 100% annual growth
A CAGR = 2 would be 200% annual growth
Here, we have a CAGR between 1 and 2, so it's more than 100% annual growth and less than 200% annual growth.

So, now, we can answer the question --- yes, absolutely, the CAGR between October 2007 and September 2009 is in excess of 100%. So, yes, the statement is true.

Does all this make sense?

Here's a video lesson you may find helpful:
https://gmat.magoosh.com/lessons/644-int ... -reasoning

Here's an IR eBook you may find helpful:
https://magoosh.com/gmat/2012/gmat-integ ... ing-ebook/

Let me know if you have any further questions.

Mike