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In a certain lottery drawing, two balls are selected at

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by M7MBA » Sun Feb 11, 2018 3:46 am
In a certain lottery drawing, two balls are selected at random from a container with 100 balls, numbered from 1 to 100, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner?

(A) $9.85 x 10^6
(B) $9.90 x 10^6
(C) $1.00 x 10^7
(D) $1.05 x 10^7
(E) $9.90 x 10^7

The OA is the option B.

How can I determine the which one is the correct answer without knowing the balls selected? Experts, can you give me some help, please?

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by [email protected] » Sun Feb 11, 2018 11:40 am
Hi M7MBA,

We're told that in a certain lottery drawing, two balls are selected at random from a container with 100 balls, numbered from 1 to 100, inclusive and the winner of the lottery is awarded a cash prize in the amount of $1,000 times the PRODUCT of the numbers on the two selected balls. We're asked which of the following is a POSSIBLE amount of the cash prize given to the winner.

Since there are so many possible totals, we can't reasonably calculate them all - so we should use the answer choices to help us 'narrow' down what the two numbers could be. Notice that two of the answer choices start with 9.9.... so let's see what happens if make the two numbers 1 and 99.

IF... the numbers are 1 and 99, then the prize would be (1)(99)($1,000) = $99,000
In Scientific Notation, that would be 9.9 x 10^4
This result looks similar to a couple of the possibilities, but it's too small. Let's see how much BIGGER we can make it.

IF... the numbers are 100 and 99, then the prize would be (100)(99)($1,000) = $9,900,000
In Scientific Notation, that would be 9.9 x 10^6
That is an exact match for Answer B, so that MUST be the answer.

Final Answer: B

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by Scott@TargetTestPrep » Sun Jun 23, 2019 6:23 pm
M7MBA wrote:In a certain lottery drawing, two balls are selected at random from a container with 100 balls, numbered from 1 to 100, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner?

(A) $9.85 x 10^6
(B) $9.90 x 10^6
(C) $1.00 x 10^7
(D) $1.05 x 10^7
(E) $9.90 x 10^7
The smallest possible prize is:

1,000 x 1 x 2 = 2,000

The largest possible prize is:

1,000 x 100 x 99 = 99 x 100,000 = 99 x 10^5 = 9.9 x 10^6

Answer: B

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