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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?

 Jun 20, 2020
 #1
avatar+781 
+2

The current average is 9+13+15+17+19+23+31+49\8=22. The current median is 9, 13, 15, 17 | 19, 23, 31, 49: 18.

 

The average increases by 2 so the new average after removing two numbers is 24. The median increases by 2 as well so the new median is 20.

After removing 2 numbers, we have 6 left. The remaining 6 numbers must add up to 24*6=144. 

176-144=32 is the sum of the two numbers removed.  The two numbers removed could be 9, 23; 13, 19; or 15,17. Using guess and check, 13 & 19 satisfy this.

Their product is 247.

 Jun 20, 2020
 #2
avatar+220 
0

Thanks SO much!

notsmart2.0  Jun 20, 2020
 #3
avatar+781 
0

You're welcome. :)

gwenspooner85  Jun 20, 2020

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