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.
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Question: Question: When n is divided by 19, the remainder is 7. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 7. Z must be divisible by which of the following numbers?

 Option A: 16

 Option B: 18

 Option C: 20

 Option D: 19

 Option E: 22

Answer: Option D


Question: Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.4. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?

 Option A: 0.49

 Option B: 0.6

 Option C: 0.448

 Option D: 0.5

 Option E: 0.52

Answer: Option C


Question: Question: What is the total number of ways in which Dishu can distribute 9 distinct gifts among his 8 distinct girlfriends such that each of them gets at least one gift?

 Option A: 72 * 8!

 Option B: 144 * 8!

 Option C: 36 * 8!

 Option D: 9!

 Option E: None of these

Answer:
Option C