What is the sum of the first 10 odd numbers, the first 25 odd numbers and the first 50 odd numbers? You should be able to give me the answer in one (1) minute.

Answers:

• Sum of the first 10 odd numbers = 100
• Sum of the first 25 odd numbers = 625
• Sum of the first 50 odd numbers = 2500

How did you get the correct answer? Did you use a calculator? There is no need for that and if ever you will need a calculator it only needs push on the numeric keypad for you to get the correct answer!

Here’ how: Multiply the quantity of odd numbers you want to find the sum for by itself. Example: If you want to get the sum of the first 5 odd numbers (1, 3, 5, 7, 9) and you do it by adding it yourself then this will be your result:

1 + 3 + 5 + 7 + 9 = 25

Using the shortcut I just gave you, we have 5 odd numbers to add. So the answer should be 5 multiplied by itself:

5 x 5 = 25

Did we not just got the same results? Try it with the first 10 odd numbers (10 x 10 = 100):

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100

Now, can you believe that? It’s even fun and easy!

Ron bought a pack of apples from the supermarket. On his way home he was so hungry that he ate a third of the apples. That night while watching the late night movie he ate half of the remaining apples. At breakfast the following day, Ron got out the pack of apples and found only 2 apples left. His little brother John told him that he got two apples from the pack and had it in his lunch box. So Ron has 4 apples left including the two apples in John’s lunch box. How many apples did Ron have originally in the pack? How many apples did he eat on his way home? How many apples did he eat while watching the late night movie?

How will you answer this brain twister when you do not know the original quantity of apples in the pack? I know how you are going to do it! You will do a manual test-and-trial for sure. But there is a way to find out the answers.

Given:
• A = 4 apples left in the pack in the morning (2 in the pack and 2 in John’s lunch box)
• Z/3 = Ron ate a third of the original number of apples in the pack
• (Z – Z/3)/2 = Ron ate half of the remaining apples while watching the late night movie

Find:
• y = How many apples Ron ate while watching the late night movie
• z = How many apples Ron ate on his way home
• x = How many apples are originally in the pack

How to Get The Answer:
1. Let x be the original number of apples in the bag
2. Ron ate a third of the apples on his way home, so we have z = x/3.
3. At home, Ron ate half of what's left. Let this be y.
4. Solving for y:
   • y = ½ • (x - x/3)
   • Multiplying both sides by 2 we have:      2y = x - x/3
   • Evaluating the right side of the equation we have:      2y = 2x/3
   • Multiplying both sides by 3 we have:      6y = 2x
   • Dividing both sides by 2 we have:      3y = x
   • To isolate y, we divide each side by 3:      y = x/3
5. To get the original number of apples, we add (1) the number of apples consumed and (2) the number of apples left:      
   • Total number of apples consumed:      y + z = 2x/3
   • Total number of apples left in the morning:     4
6. Solving for x:
   • x = 2x/3 + 4
   • Multiplying each side by 3:      3x = 2x + 12
   • To isolate x on the left side of the equation, we subtract 2x from each side. We now have:      x = 12
7. Now that we have x we solve for y:     y = x/3 = 4
8. Solving for z:     z = x/3 = 4

Therefore, there were originally x = 12 apples in the bag. Ron ate z = 4 on his way home and ate another y = 4 while watching movies. His brother ate another 2, which is why there were only 2 apples left in the morning when Ron opened the pack/bag.