Question

Here are five number cards.

2 5 7 8 9

One of the cards is removed and the mean average of the remaining four number cards is 6.

Which card was removed?
You must show your working.

Note: please make sure your final answer says card...

Answer 1

Card 7

Explanation:

This is a really roundabout explanation, but I wanted to have a bit of fun.

So if we reverse the steps needed to find the mean average (sum / cards = average), we find that the value of the cards needs to add to 24 (4 cards x 6 average = 24 sum)

From there we can determine that the CARD REMOVED IS ODD. Because there are 3 odd numbers and 2 even numbers, we know that in order to get an even number, we need to remove an odd, because odd + odd ALWAYS equals even.

Now, since we know a even number card was NOT removed we can add the two even cards together, resulting in (2+8) 10. Now with 14 remaining, we need to figure out which 2 odd numbers add together to make 14.

5+7 = 12

7+9 = 16

5+9 = 14

So we now know that the cards needed are 2, 8, 5, and 9, which singles out CARD 7