Question

Three friends have a set of 6 algebraic cards as shown below. Each card has algebraic expressions
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.
Question 1:
Which cards are picked by Rohan?
5
Question 2:
Which cards are picked by Meera?
Question3 :
Which cards are picked by Sid?
Question 4:
How did you come to the conclusion about the card picked by Sid?
Question 5:
How many cards are not picked by any one of the three friends?

Answer 1

Answer:

Given:

Rohan chooses a card with an even value.

Meera chooses a card that is always a multiple of three.

Sid chooses a card with a factor of 4x2-14x.

Solution:

1) Rohan selects an even-numbered card:

Card number 5 with the expression 4(3x + 1) is the only one that meets the given condition.

Rohit always chooses a card with an even number, so the expression will return an even number for any value of x.

So Rohan chooses one card.

2) Meera chooses a card that is always a multiple of 3: Only card number 3 with the expression 3(x + 4) will satisfy the given condition.

Meera chooses a card that is a multiple of three, and only expression 3 meets that requirement.

As a result, Meera will only select one card.

3) Sid picks a card which is a factor of  4x²-14x

We will find the factors of  4x²-14x

4x²-14x = 2x(2x - 7)

2x and 2x - 7 are the factors of  4x²-14x.

Therefore, card number 5 with expression 4(3x + 1) will be a multiple of 2x and a factor of  4x²-14x. Rohan and Sid will choose the same card and 4 cards will not be picked by any of the three friends.

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