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

edited by SmartMathMan Dec 10, 2017

edited by SmartMathMan Dec 10, 2017

#3**+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

CPhill Dec 10, 2017