instruction:
You are given a math word problem and you are supposed to make use of mathematical concepts like probability, combinatorics, linear equations, sequences/series, or simple operators like addition, subtraction, division, or multiplication to answer the given question. Choose the best option from the 5 given options and report that option.
question:
Question: Two pipes A&B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.

 Option A: 8 min

 Option B: 3 min

 Option C: 21 min

 Option D: 23 min

 Option E: 24 min
answer:
Option A


question:
Question: P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?

 Option A: 11 days

 Option B: 16 days

 Option C: 13 days

 Option D: 15 days

 Option E: 19 days
answer:
Option B


question:
Question: Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.
What is the average score for all the three classes, taken together?

 Option A: 81

 Option B: 81.5

 Option C: 82

 Option D: 84.5

 Option E: None of these
answer:

Option B