Photo: kengz

We’ve been publishing some of Google’s old (now banned) interview questions this week.The first set: 15 Google Interview Questions That Made Geniuses Feel Dumb

Here are the answers to the second set.

### If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?

The trick here is that .95 is the probability for 1 or more cars, not the probability of seeing just one car.
The prob. of NO cars in 30 minutes is 0.05, so the prob of no cars in 10 minutes is the cube root of that, so the prob of seeing a car in 10 minutes is one minus *that*, or ~63%

Job: Product Manager

### You are at a party with a friend and 10 people are present including you and the friend…

Your friend makes you a wager that for every person you find that has the same birthday as you, you get \$1; for every person he finds that does not have the same birthday as you, he gets \$2. would you accept the wager?

Answer: Ignoring seasonal upticks in births, there's about 1/365 probability that any other person has the same birthday as you and 364/365 chance that any other random person does not. Do not take this bet.

Job: Product Manager

### If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands? (The answer to this is not zero!)

7.5 degrees

Every minute on the clock represents 6 degrees (360 degrees/60 minutes)

Every hour, the hour hand moves from one number to the next (in this case, it is moving from 3 to 4) which represents 30 degrees.

Since it is exactly 1/4 past the hour, the hour hand is 1/4 of the way into its 30-degree trip or 1/4 or 30 degrees....which is 7.5 degrees.

Job: Product Manager

### What's 2 to the power of 64?

1.84467441 × 1019
This is a pretty easy answer to figure out when you're not sitting in an interview with no calculator around.

Job: Software Engineer

### How long it would take to sort 1 trillion numbers? Come up with a good estimate.

Here's another question without one answer. The idea is to test the interviewee's creativity.

Merge Sort for sorting.

O(1,000,000,000,000 Log 1,000,000,000,000) - Average Case Scenario
O(1,000,000,000,000 Log 1,000,000,000,000) - Worst Case Scenario

I'd guess you can do 1 billion operations per second, thus 3000 seconds.

Job: Software Engineer

### How many resumes does Google receive each year for software engineering?

This is another question that's about testing the job candidate's ability to frame the problem in a simple way and then creatively solve it.

Our answer: A candiate for Quantitative Compensation Analyst should know that Google hired about 3,400 people in 2008. Figure 75%, or 2,550, of those hired were engineers and that, like Harvard, Google only accepted 3% of those who applied. 2,550 is 3% of 85,000.

Job: Quantitative Compensation Analyst

### You are given a list of numbers…

When you reach the end of the list you will come back to the beginning of the list (a circular list). Write the most efficient algorithm to find the minimum # in this list. Find any given # in the list. The numbers in the list are always increasing but you don't know where the circular list begins, ie: 38, 40, 55, 89, 6, 13, 20, 23, 36.

Create temporary pointer and start from the root. (Most of the time circular lists have a front and back pointers.) Check if front is larger or if back is larger. If front is larger then you know you are at the end of the list and at the front of the list. If front is larger then traverse the opposite direction and compare numbers. If there is no root or a pointer pointing to any part of the list then your data is lost in memory.

Job: Quantitative Compensation Analyst