SIG Data Scientist Interview Experience — Seventeen Quantitative and Logic Questions

The online assessment contained 17 questions.

Question 1

You walk into a barn and see ants, cows, and chickens. There are 570 legs in total. The number of ants is twice the number of chickens, and the number of cows is twice the number of ants. Compute the number of ants.

Question 2

You are on an island inhabited by knights, who always tell the truth, and knaves, who always lie. Perlica and Chen say:

• Perlica: We are different types of people.
• Chen: Perlica always lies.

Determine each person's type.

Question 3

One thousand people were asked about their preferred exercise, with these results by age:

You meet someone who took the survey and prefers biking. What is the probability that the person is 23 through 27 years old? Express the answer as a fraction in simplest form.

Question 4

Compute the weight of the green triangle in pounds. The balanced system weighs 160 pounds in total. Express the answer as an integer without units.

Every horizontal bar is balanced. The top bar supports a balanced sub-mobile on the left. On the right it supports one gray octagon followed by another balanced sub-mobile.

The left sub-mobile supports one orange octagon and one pink pentagon on the left, and another balanced bar on the right. That bar supports another balanced bar on the left, and one gray octagon plus one pink pentagon on the right. The next bar supports a balanced bar containing two purple hexagons on the left and one green triangle on the right.

The right sub-mobile supports one gray octagon followed by a balanced bar containing two green triangles on the left, and another balanced bar on the right. That last bar supports one red circle on the left and a balanced bar containing two yellow stars on the right.

Question 5

Factory A makes 40% red widgets and 60% black widgets. Factory B makes 80% red widgets and 20% black widgets. A factory is selected uniformly at random, and then two widgets are sampled uniformly from it. Both widgets are black. Compute the probability that they came from Factory B, as a fraction in simplest form.

Question 6

Roll two fair six-sided dice. If the rolls differ, you receive the higher roll in dollars. If they match, you lose the sum of the two rolls. Compute the expected payoff in dollars. Express it as a decimal rounded to the nearest cent, without a dollar sign, with digits 0 through 4 rounding down and 5 through 9 rounding up.

Question 7

At a bakery, every customer buys exactly one item. Each customer has a 75% chance of buying a croissant and a 25% chance of buying a muffin. Only two muffins remain, and five people are waiting. Compute the probability that the two muffins will be sufficient, meaning nobody wants a muffin after they are gone. Express the answer as a percentage rounded to the nearest whole percent, with digits 0 through 4 rounding down and 5 through 9 rounding up.

Question 8

Astra, Breach, and Cypher have different numbers of cats. They say:

1. Cypher tells Breach: You have an even number of cats.
2. Breach tells Cypher: You have exactly 40% more cats than I do.
3. Breach tells Astra: Your number of cats is the average of mine and Cypher's.
4. Astra tells Breach: My number of cats exceeds yours by at least 3.

Not all statements are true. A speaker always tells the truth when addressing someone with more cats and always lies when addressing someone with fewer cats. How many cats does Breach have?

Question 9

Two friends canoe upstream for 3 hours before realizing that their campsite is downstream. They turn around and paddle downstream for 4 hours. The next day they pack up and canoe 48 miles upstream to their original starting point, arriving at 9:30. The river flows at a constant 3 miles per hour, and the friends always paddle at a constant rate. What time did they leave on the return trip? Express the answer as h:mm.

Question 10

I want to bake 5 cookies for my friend, but I can make only 4 flavors. How many combinations of cookies can I bake?

Question 11

Three rabbits compete in a race. The least athletic rabbit wins with probability 1/13. I choose a rabbit uniformly at random to cheer for, but it does not win. Compute the probability that I chose the least athletic rabbit, as a fraction in simplest form.

Question 12

A spinner has three regions with landing probabilities 1/5, 3/10, and 1/2. Compute the expected number of spins needed to land in two distinct regions. Express the answer as a fraction in simplest form.

Question 13

A gardener is waiting for two favorite flowers to bloom. The purple flower will blossom at a uniformly random point during the next 60 days and remain in bloom for 10 days. Independently, the red flower will blossom at a uniformly random point during the next 60 days and remain in bloom for 20 days. Compute the probability that their bloom periods overlap at some point. Express the answer as a fraction in simplest form.

Question 14

Place a building with 1, 2, 3, or 4 floors in each cell of a grid so that no two buildings in the same row or column have the same number of floors. Numbers outside the grid show how many buildings are visible from that direction, because taller buildings block shorter buildings behind them. Shaded cells make buildings invisible and do not count toward the outside numbers. Find the floor counts in cells A, B, and C. Express the answer as the three-digit number ACB, rather than the product A × B × C.

The grid needed for Question 14 was not visible in the provided screenshot.

Question 15

Choose 6 numbers from the first 35 positive integers. Compute the expected number of consecutive pairs among them. For example, choosing 1, 10, 11, 12, and 20 produces 2 consecutive pairs. Express the answer as a fraction in simplest form.

Question 16

You have 2 tokens in a betting game and want to reach 5 tokens before running out. On every turn, you bet as many tokens as possible, but no more than needed to bring the total to 5. Every bet has a 1/3 probability of winning. Compute the probability of reaching 5 tokens before running out, as a fraction in simplest form.

Question 17

A frog travels from A(0, 0) to B(5, 5). Each step is one unit up or one unit right, and the frog refuses to move three steps in the same direction consecutively. Compute the number of possible paths from A to B.