Math Problem Statement

Directions for questions 6 to 10:

Answer the questions on the basis of the information given below.

Four persons P, Q, R and S are playing a game of blindly picking the cards from a box. This box contains five cards, each of a different colour among Red, Green, Blue, Yellow and White, and these five cards fetch 1, 2, 3, 4 and 5 points respectively. The game is being played in four rounds. In each round, each person randomly takes out one card from the box and places it back into the box. Based on the colour of the card, they have been given points as mentioned above.

Further it is known that,

i. Each card was picked by at least one person and each card was picked a different number

ii. None of P, Q and R picked the same card in any two rounds and the maximum points

scored by any of P, Q and R in all the four rounds put together are 12 iii. Among the four rounds, the maximum points were scored in round Ill and P picked the white

card in round Ill.

iv. In each of rounds I, Ill and IV no two players picked the same card.

v. The points scored by P and that by Q in all the four rounds put together are equal. vi. The green card was picked more times than the white card. The sum of the points scored by

P in round I and that scored by S in round IV is 5.

vii. One of the five cards contributed a score of 20 to the total points scored in all the four

rounds put together.

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Logical Reasoning
Combinatorics

Formulas

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Theorems

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Suitable Grade Level

Grades 10-12