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# Problem

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For the following question, select all the answer

choices that apply.

3.7, 4.1, a, 8.5, 9.2, 2a

The six numbers shown are listed in increasing

order. Which of the following values could be

the range of the six numbers?

Indicate all such values.

A 4.0

B 5.2

C 7.3

D 11.6

E 12.9

F 14.1

Thanks ,

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For the following question, select all the answer

choices that apply.

3.7, 4.1, a, 8.5, 9.2, 2a

The six numbers shown are listed in increasing

order. Which of the following values could be

the range of the six numbers?

Indicate all such values.

A 4.0

B 5.2

C 7.3

D 11.6

E 12.9

F 14.1

Thanks ,

Let's examine the two EXTREME values of a.

Case a: The SMALLEST value of a

If the values are strictly increasing (i.e., no values are equal), them a could be a little bit smaller than 8.5.

So, a could equal 8.499999999999

For all intents and purposes, let's just say that the a COULD equal 8.5

In this case, 2a = 9.2, which means the range = 5.5

Case b: The GREATEST value of a

If the values are strictly increasing (i.e., no values are equal), them a could be a little bit smaller than 4.1.

So, a could equal 4.10000000001

For all intents and purposes, let's just say that the a COULD equal 4.1

In this case, 2a = 17, which means the range = 13.3

Now that we've examined the EXTREME cases, we can see that the range can be between 5.5 and 13.3

Cheers,

Brent

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Thanks Brent. I got it now. :)

Cheers!

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• 1 year later...

Hey Brent, so I do not understand how come the smallest value in the set can be 8.5 and the largest 4.1? Isn't it the other way around?

Also if the 2a is 9.2 how did you get 5.5 (when you subtract 9.2 from the smallest value in a set, which is 3.7, you don't get 5.5)?

Thanks a lot

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For the following question, select all the answer

choices that apply.

3.7, 4.1, a, 8.5, 9.2, 2a

The six numbers shown are listed in increasing

order. Which of the following values could be

the range of the six numbers?

Indicate all such values.

A 4.0

B 5.2

C 7.3

D 11.6

E 12.9

F 14.1

Thanks ,

Let's examine the two EXTREME values of a.

Case a: The GREATEST value of a

If the values are strictly increasing (i.e., no values are equal), them a could be a little bit smaller than 8.5.

So, a could equal 8.499999999999

For all intents and purposes, let's just say that the a COULD equal 8.5

In this case, 2a = (2)(8.5) = 17, which means the range = 17 - 3.7 = 13.3

Case b: The SMALLEST value of a

If the values are strictly increasing (i.e., no values are equal), them 2a could be a little bit bigger than 9.2

So, 2a could equal 9.20000000001

For all intents and purposes, let's just say that the 2a COULD equal 9.2

This mean a = 4.7

This is fine, because we're told that a is greater than 4.1.

If 2a = 9.2, then the range = 9.2 - 3.7 = 5.5

Now that we've examined the EXTREME cases, we can see that the range can be between 5.5 and 13.3

Cheers,

Brent

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Hey Brent, so I do not understand how come the smallest value in the set can be 8.5 and the largest 4.1? Isn't it the other way around?

Also if the 2a is 9.2 how did you get 5.5 (when you subtract 9.2 from the smallest value in a set, which is 3.7, you don't get 5.5)?

Thanks a lot

You're absolutely correct - nice catch!

I have reposted my answer above.

Cheers,

Brent

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• 1 month later...
Let's examine the two EXTREME values of a.

Case a: The GREATEST value of a

If the values are strictly increasing (i.e., no values are equal), them a could be a little bit smaller than 8.5.

So, a could equal 8.499999999999

For all intents and purposes, let's just say that the a COULD equal 8.5

In this case, 2a = (2)(8.5) = 17, which means the range = 17 - 3.7 = 13.3

Case b: The SMALLEST value of a

If the values are strictly increasing (i.e., no values are equal), them 2a could be a little bit bigger than 9.2

So, 2a could equal 9.20000000001

For all intents and purposes, let's just say that the 2a COULD equal 9.2

This mean a = 4.7

This is fine, because we're told that a is greater than 4.1.

If 2a = 9.2, then the range = 9.2 - 3.7 = 5.5

Now that we've examined the EXTREME cases, we can see that the range can be between 5.5 and 13.3

Cheers,

Brent

I think you have got it wrong here

since the number are increasing 4.1 , a , 8.5 this indicate 4.1

8.2

now range would be 8.2 -3.7 = 4.5

to 17 - 3.7 = 13.3

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• 3 weeks later...
Hey! Just did a quick write-up for this problem. Let me know if you have any questions about it.

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