SIG Quant Research & Quant Systematic Trading OA 题目分享

1小时17个题，正式做OA之前练了两三套就过啦！不过因为有的题目我做完后验算了导致最后差点做不完，还是要提醒大家把控时间！求加米！！！

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 cows.

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:

Exercise	18-22	23-27	28-32	33-37	Total
Run	54	40	42	66	202
Bike	77	68	90	70	305
Swim	28	43	50	52	173
Other	90	78	71	81	320
Total	249	229	253	269	1,000

You meet someone who took the survey and prefers swimming. 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 if the following system is balanced and weighs 160 pounds in total.（图省略）

Question 5
On Facebook, 30% of stories are fake news. Fake news stories have an 80% probability of having

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s the three-digit number BCA rather than the product A*B*C. (图省略)

Question 15
Choose 6 numbers from the first 25 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 3 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(8,4). 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.

整理不易，求加米！！！