Question

three friends have a set of 6 algebraic cards as shown below. Each card has an algebraic expressions written on it. here,X is a positive integer.

first card: 2x-3

second card: 3x-2

third card: 3(X+4)

forth card: 4x+1

fifth card: 4(3x+1)

sixty card: 2x+1

Rohan picks a card whose value is always Even.meera picks a card which is always a multiple of 3.sid picks a card which is a factor of 4x²-1

Q1. how many cards are picked by Rohan?

Q2. how many cards are picked by Meera?

Q3. how many cards are not picked by any one of the three friends?

I have already posted this question two time and I also have less point so please give right answer.​

Answer 1

Given :-

first card: 2x-3

second card: 3x-2

third card: 3(X+4)

forth card: 4x+1

fifth card: 4(3x+1)

sixty card: 2x+1

Rohan picks a card whose value is always Even.meera picks a card which is always a multiple of 3.sid picks a card which is a factor of 4x²-1

Solution :-

first card: 2x-3

• at x = 2 => 2 * 2 - 3 = 1 = odd number
• at x = 5 => 2 * 5 - 1 = 9 = odd number .
• Always odd .

second card: 3x-2

• at x = 2 => 3 * 2 - 2 = 4 = even number
• at x = 7 => 3 * 7 - 2 = 19 = odd number
• odd and even both .

third card: 3(X+4)

• at x = 4 => 3(4 + 4) = 24 = even number
• at x = 1 => 3(1 + 4) = 15 = odd number
• Always a multiple of 3 .

forth card: 4x+1

• at x = 3 => 4*3 + 1 = 13 = odd number
• at x = 2 => 4*2 + 1 = 9 = odd number
• Always odd .

fifth card: 4(3x+1)

• at x = 3 => 4(3*3 + 1) = 40 = even number
• at x = 2 => 4(3*2 + 1) = 28 = even number
• Always even .

sixty card: 2x+1

• 4x² - 1 = (2x)² - (1)² = (2x + 1)(2x - 1)
• Factor of 4x² - 1 .

so,

→ Total cards picked by rohan = only even = 4(3x + 1) = Only 1 .

→ Total cards picked by meera = Always a multiple of 3 = 3(x + 4) = Only 1 .

→ Total cards picked by sid = Factor of 4x² - 1 = (2x + 1) = only 1 .

then,

→ Total cards not picked by any one of the three friends = 6 - 3 = 3 cards .

Learn more :-

Let a, b and c be non-zero real numbers satisfying (a³)/(b³ + c³) + (b³)/(c³ + a³) + (c³)/(a³ + b³)

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if a²+ab+b²=25

b²+bc+c²=49

c²+ca+a²=64

Then, find the value of

(a+b+c)² - 100 = __

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