That wasn't a nightmare interview; she is clearly unqualified for an analytical role. She should get a job in advertising instead.
“Google places four ads per e-mail opened in Gmail. Advertisers get to pick their click-through rates, which can be as little as $0.05...Say each G-mail user opens seven new e-mails a day. They would see 28 ads. If they click on ¼ of those ads, then only seven ads are clicked."
Gmail probably has something like 150 million users, so her figure of 7 ads clicked per user at a minimum of 5 cents a click would result in 52.5 million dollars a day. At some point she should have realized the void between her new analysis and her original $70,000 guess. The whole point of the question is to examine your analytical and estimation skills. The fact that she didn't notice that she was moving towards and answer 750 times the size of the her last one says a lot.
But overall, it was probably a good thing for her not to go there. Sounds like Google has a particular mindset (one that reminds me, anecdotally, of stories of Microsoft 15-20 years ago), and she wouldn't fit there. I'm not at all convinced that means she couldn't be effective at marketing somewhere else, though.
For my own part, never having bought Google ads, nor having displayed them, I would rather estimate no more than 1% of people would click on them no more than once per day. That's probably because I'm cynical about ads, use AdBlock, would rather rely on search and recommendation for finding products, and so do my peers. I don't have a good pool of knowledge for answering this question in a way that would be accurate, no matter what my estimation skills are.
Then again you could figure Google makes about $5 billion a year in profit, say a tenth of that comes from gmail, and the profit margin is 10%, suggesting ~$15m a day in earnings (not profits) which is off by a factor of 500 from the above. That sounds a lot more likely.
"In the second quarter alone, Google has managed to reel almost $1.5 billion in earnings."
"If you do the mathematics here, Google is making upwards of $4 million daily"
Except they mistakenly used the quarterly earnings in place of annual earnings. So it would be in the range of 4x that.
Yes, indeed. Someone who has a slightest clue about the whole stuff just can't say 1/4 of users will click an ad in Gmail. I am sorry for her, but that is just so off...
That's even worse: she assumed that 4 ads would be presented per e-mail, so the CTR would be 100% per e-mail.
That's beyond absurd.
First easy thing to do which isn't describe. Tell the person to sit down with a pen and paper. And then talk about the why and how. That was the demeaning part. Antoi-collaborative, very scary.
Even at Google, a job is not a vacation. Wanting to hire people who react well under pressure is completely valid.
The mistake, which is not at all unique to Google, is to think that "high pressure interrogation at a job interview" is usefully similar to the kind of pressure that might occur on the job. For some jobs it will be. For many others, it's completely different.
Compare these scenarios: "QA just found a huge, unexpected performance problem in this server application and no one knows what's causing it. The application goes live in 48 hours and you and your team have until then to make it handle ten thousand times as many users as it does now." vs. "You just landed after a 10-hour flight and will be meeting a major potential customer in 30 minutes. TSA blew up your laptop because it looked suspicious and the airline sent your luggage to Albuquerque so instead of a carefully-prepared presentation all you have are a couple index cards with vague notes about the product. If you don't make a sale, your company will be bankrupt in a week."
Google is not going to be bankrupt in a week. If your interviewer is really smart, do the Seth Godin thing: freelance the person for a few weeks, or offer them a real life case they are currently working on to see what that person is actually going to do.
One of the ways I figured out I would make a horrible teacher was I worked as a teacher. I really believed and worked very hard as a teacher. Ultimately, I needed a more collaborative environment, and I was stressed out because I met some really smart kids who were flunking half of exams on purpose when I confronted them about it. They would not work with me to fix these skills in third grade, particularly when there were background issues going on, and I was not the primary teacher. I found it not appropriate for me. I found that really high pressure, and not appropriate for me. Meanwhile, I know I will stay up all night on my own unpaid looking for affordance of different websites and how they can be applied for different business reasons. There you go? That seems to be appropriate for me. I just wish I knew more people in that field, and I wish I had the time to learn to code (after first round BA critiques....)
Interviewers need to sit down and know what is the pressures of the job, Half that interview would not have helped her at all. Furthermore, It is can I work with that person on the job, and help me and her reach a goal under pressure. That's a reasonable expectation. Very reasonable.
The second point of your comment is legit - this sort of time/pressure constraint isn't really representative of the workplace as a whole. Nobody should have someone hanging over them making sure you do your math right in under one minute - you certainly don't at Google. The interviewer probably should've tried to make the candidate feel a bit more at-ease.
But the sort of quick estimation skill necessary for these interview questions is really important. There've been countless meetings when someone (often me) has proposed a solution and I've done some quick mental math calculations only to find out that it just won't work. It's really valuable to get those calculations done in a minute so that you can brainstorm new ideas, rather than waiting until after the meeting when you probably just won't do the math at all.
And this is something that I really wish schools taught more of. Being able to get a quick, mostly-right-but-slightly-wrong answer, and being able to tell what ways your answer is wrong, is probably more important than being able to come up with exact answers or parrot back the formulas you supposedly memorize.
I would want to work out that problem with someone. For that math problem right:
lets ignore the 20 people problem (aka 20%) right now and pretend that all the people who visisted clicked. for every 100 people who visit, they now get 1 dollar (it was ten cents) before). in order to get $20 if a hundred people visited for every dollar, you would need
20,000 people.
One problem, they need to click. and only 20 people click per 100 people. so in order to really make that money, you would have to multiply again by 20. I would take the 2s out and start counting 0s because I would get confused at this point.
400,000 people. I think. I may have screwed up the 0s. But If I didn't have a chance to slow down and write down the problem I think I would have screwed that up badly. I'm not sitting around and doing those math problems all the time...
If I was at a job interview and was asked these sort of puzzles, I wouldn't feel under pressure. Instead I'd think "Cool, I like solving puzzles! And I'm good at it too so this is a chance to make a good impression." Maybe Google are looking for potential employees with that attitude?