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After two numbers are removed from the list
9, 13, 15, 17, 19, 23, 31, 49
the average and the median each increase by 2. What is the product of the two numbers that were removed?

SmartMathMan  Dec 9, 2017
edited by SmartMathMan  Dec 9, 2017
edited by SmartMathMan  Dec 10, 2017
edited by SmartMathMan  Dec 10, 2017
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4+0 Answers

 #1
avatar+80874 
+1

Increase by  what  ????

 

cool cool cool

CPhill  Dec 9, 2017
 #2
avatar+308 
+1

sorry increased by two i re wrote it.

SmartMathMan  Dec 10, 2017
 #3
avatar+80874 
+2

Average before removal   = ( 9 + 13+ 15+ 17+19+ 23 + 31+ 49)  / 8  = 22

Median before removal =  (17 + 19) / 2  =  18

 

Avg  after removal  =   24

Median after removal  = 20

 

19 must have been one of the numbers removed because  (17 + 23) / 2  = 20

 

So.....if the new average is 24......the sum of the numbers must be 24 * 6  = 144

 

So....the sum of the 7 numbers after 19 is removed is  157....so......13 must be the other number removed to have a sum of 144

 

Proof

9,15,17,23,31,49

Average = 24

Median  = 20

 

So...the product of the removed numbers is    19 * 13   =  247

 

 

cool cool cool

CPhill  Dec 10, 2017
 #4
avatar
+1

9, 13, 15, 17, 19, 23, 31, 49

Mean =22, Median= 18

Remove 19 and 13 and you have:

mean(average) =24 and Median =20

19 x 13 =247

Guest Dec 10, 2017

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