What's the Sum? Trivia Quiz

Answer: Sigma

The upper case sigma is the notation for summation or addition operation. The lower case sigma is used to denote the standard deviation of a set of data in statistics.

Answer: 9

No matter what number you pick, the final answer would be 9.

Let's look at a few examples. Let say you pick number 2. 2 x 9 = 18. 1 + 8 = 9.

If you pick 5, 5 x 9 = 45. 4 + 5 = 9.

And if you pick 9, 9 x 9 = 81. 8 + 1 = 9.

The multiples of 9 are 18, 27, 36, 45, 54, 63, 72 and 81. No matter what multiple you arrive at, the sum of its individual digit is 9.

Answer: 767676767

Let's look at the number 767676767. The sum of the individual digits is 59, which is not divisible by 3.

Now, the second number, 123321333. The sum of the individual digits is 21, which is divisible by 3. So the number 12332133 itself can also be divisible by 3.

Also, the sums of the individual digits of 696222333 and 998877663 are 36 and 63 respectively. 36 / 3 = 12. Besides, 63 / 3 = 21. Therefore, both 696222333 and 998877663 are divisible by 3.

Answer: 7

Pi (3.142..), e (2.718...) and Phi (1.618...) are all irrational numbers. Their sum is 7.478..., which is close to 7.

Answer: 550

In other words, the question is asking for the sum of 10 + 20 + 30 +...+ 80 + 90 + 100 = 10 + 100 + 20 + 90 + 30 + 80 + ... = (10 + 100) + (20 + 90) + (30 + 80) + ... = 110 + 110 + 110 + ... = 5(110) = 550

Answer: 500500

By applying the same technique, 1 + 2 + ... + 999 + 1000 = 1 + 1000 + 2 + 999 + 3 + 998 + ... = (1 + 1000) + (2 + 999) + (3 + 998) + ... = (1001) + (1001) + (1001) + ... = 500 (1001) = 500500

Keep in mind that there are all together 1000 / 2 = 500 pairs of doublet here. The sum of each doublet is 1001. So 500 x 1001 = 500500

Answer: 10100

Notice that there are all together 100 terms in our summation of the first 100 even numbers. Also, there are 100 terms in the summation of the first 100 odd numbers.

2 + 4 + ... + 198 + 200 = (1 + 1) + (3 + 1) + ... + (197 + 1) + (199 + 1) = (1 + 3 + ... + 197 + 199) + (1 + 1 + ... + 1 + 1) = 10000 + 100 (1) = 10000 + 50 = 10100

The trick here is that we can make use of the first equation given in the question. Observe that 2 is one more than 1, 4 is one more than 3 and so on. After some rearranging and algebraic manipulation, we only need to evaluate the sum of 10000 and 100, which gives us the answer of 10100.

Answer: No

1 + 2 - 3 + 4 ... -97 + 98 - 99 + 100 = 1 + (2 - 3) + (4 - 5) ... + (96 - 97) + (98 - 99) + 100 = 1+ (-1) + (-1) ... + (-1) + (-1) + 100 = 1 + 49 (-1) + 100 = 1 - 49 + 100 = 52

On the other hand, 1 - 2 + 3 - 4 ... + 97 - 98 + 99 - 100 = (1 - 2) + (3 - 4) ... + (97 - 98) + (99 - 100) = (-1) + (-1) ... + (-1) + (-1) = 50 (-1) = -50

So the answer is no. We can solve this problem by a simpler approach, namely by breaking down the summation into several smaller parts. By observing the pattern, we will found out that there are many repeating -1's. We can group them together and use the multiplication operation which is much simpler compared to the tedious repetitive addition operation.

Answer: 0.99

Instead of adding up 1/2 + 1/6 + 1/12 + ... + 1/9702 + 1/9900 one by one, we can use the formula 1/[(n)(n+1)] = 1/n - 1/(n+1) to simplify our calculation.

1/(1x2) + 1/(2x3) + 1/(3x4) + ... + 1/(98x99) + 1/(99x100) = [1/1 - 1/2] + [1/2 - 1/3] + [1/3 - 1/4] + ... + [1/98 - 1/99] + [1/99 - 1/100] = 1/1 - 1/100 = 99/100 = 0.99

Notice that -1/2 and +1/2 cancel up each others, so do -1/3 and -1/3, and the other pairs. These are called additive inverses. The sum of any additive inverse with its pair will yield zero as the answer.

Answer: 25

A pentagon has 5 sides and also 5 diagonals. So, A = D = 5. The first few odd numbers are 1, 3, 5, 7... So, B = 5. The first few Fibonacci numbers are 1, 1, 2, 3, 5... Hence, C = 5. The first few prime numbers are 2, 3, 5, 7, 11...Therefore, E = 5.

A + B + C + D + E = 5 + 5 + 5 + 5 + 5 = 5 x 5 = 25