Tom and his friends got bored of the game they were playing. They decided to change the rules of the game in which only numbered cards (non-face cards) can be drawn. The score of each player is the product of the numbers on the cards drawn. The scores are written on a sheet of paper after each game. Tom drew the cards as shown in the figure.

Figure: Cards drawn by Tom

Harry was the person writing the scores of all the players, he wrote Tom’s score as 8^x instead of writing it as the product of the numbers on the cards. What is x? (Enter an integral value)

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Solution

According to the new rules of the game, Tom’s score is 8 $\times 8 \times 8 \times 8 = 8^{4}$ . This is given as $8^{x}$ . Since bases are equal, their exponents can be equated. So, $x = 4$ .

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Similar questions

Goutham, Vignesh, Pavan, Herman and Kushagra went to play arena to play Laser Tag. After the game was over they got score cards which showed the scores of each of them individually as shown. Whose score is the highest?

Goutham, Vignesh, Pavan, Herman and Kushagra went to arena to play Laser Tag. After the game was over they got score cards which showed the scores of each of them individually as shown below. Whose scored highest?

$\begin{matrix} Herman & Vignesh & Pavan & Goutham & Kushagra 98674 & 98759 & 98908 & 98910 & 98798 \end{matrix}$

Jiya	Priya	Rahul	Rohan	Kushal
98664	98675	98782	98911	97229

Q. Two players play the following game :

A

writes

3, 5, 6

on three different cards;

B

writes

8, 9, 10

on three different cards. Both draw randomly two cards from their collections. Then

A

computes the product of two numbers he/she has drawn, and

B

computes the sum of two numbers he/she has drawn. The player getting the larger number wins. What is the probability that

A

wins?

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According to the new rules of the game, Tom’s score is 8×8×8×8=84. This is given as 8x. Since bases are equal, their exponents can be equated. So, x=4.

According to the new rules of the game, Tom’s score is 8 $\times 8 \times 8 \times 8 = 8^{4}$ . This is given as $8^{x}$ . Since bases are equal, their exponents can be equated. So, $x = 4$ .