Question

Three friends have a set of 6 algebraic cards 2x-3,3x-2,3(x+4),2x-1,4(3x+1),2x+1.Each card has algebraic expression written on it. Here, x is a positive integer. Rohan picks a card whose value is always even. Meera picks a card which is always a multiple of 3. Sid picks two cards such that product of values on both the cards is 4x^2-1 .Which cards are picked by Rohan? ​

Answer 1

SOLUTION

GIVEN

Three friends have a set of 6 algebraic cards 2x-3 , 3x-2 , 3(x+4) , 2x-1 , 4(3x+1) , 2x+1

Each card has algebraic expression written on it.

Here, x is a positive integer.

Rohan picks a card whose value is always even.

Meera picks a card which is always a multiple of 3.

Sid picks two cards such that product of values on both the cards is (4x²- 1)

TO DETERMINE

The cards are picked by Rohan

EVALUATION

Here it is given that

Three friends have a set of 6 algebraic cards 2x-3 , 3x-2 , 3(x+4) , 2x-1 , 4(3x+1) , 2x+1

Each card has algebraic expression written on it.

Here, x is a positive integer.

Rohan picks a card whose value is always even.

For explanation we take x = 3

For x = 3 :

2x - 3 = 3 which is odd

3x - 2 = 7 which is odd

3(x+4) = 21 which is odd

2x-1 = 5 which is odd

4(3x+1) = 40 which is even

2x+1 = 7 which is odd

So the algebraic expression which is always even is 4(3x + 1)

Hence the card Rohan picks is

$\sf{4(3x + 1)}$

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