DrDre Posted June 10, 2014 Share Posted June 10, 2014 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 , Quote Link to comment Share on other sites More sharing options...

Brent Hanneson Posted June 10, 2014 Share Posted June 10, 2014 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 Answer(s): C, D and E Cheers, Brent Quote Link to comment Share on other sites More sharing options...

DrDre Posted June 11, 2014 Author Share Posted June 11, 2014 Thanks Brent. I got it now. :) Cheers! Quote Link to comment Share on other sites More sharing options...

optimus141 Posted December 28, 2015 Share Posted December 28, 2015 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)? Please, can you clarify? Thanks a lot Quote Link to comment Share on other sites More sharing options...

Brent Hanneson Posted December 28, 2015 Share Posted December 28, 2015 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 Answer(s): C, D and E Cheers, Brent Quote Link to comment Share on other sites More sharing options...

Brent Hanneson Posted December 28, 2015 Share Posted December 28, 2015 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)? Please, can you clarify? Thanks a lot You're absolutely correct - nice catch! I have reposted my answer above. Cheers, Brent Quote Link to comment Share on other sites More sharing options...

karanmehta Posted February 19, 2016 Share Posted February 19, 2016 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 Answer(s): C, D and E 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 Quote Link to comment Share on other sites More sharing options...

Jason Osajima Posted March 8, 2016 Share Posted March 8, 2016 Hey! Just did a quick write-up for this problem. Let me know if you have any questions about it. Quote Link to comment Share on other sites More sharing options...

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