Pencils Down in 3, 2, 1... Trivia Quiz

Answer: 738,516,294

Since you are multiplying the number by 2, the answer must be divisible by 2. For this to happen, the digit in the 'ones' place (the "last" digit of the number) must be even (0, 2, 4, 6, or 8). Therefore we can eliminate the potential answers that end in 1, 7, and 9. By the process of elimination, we are left with the only choice that ends in an even number.

Answer: For any number that is divisible by 3, the sum of the individual digits of that number must be divisible by 3

While it's possible the sum of the digits could equal 3, or be greater than 3, this is the only statement that is ALWAYS true. The sum of the digits can never be less than 3, so that statement is always false.
As an example, you can look at the number 99. If you add the digits together, you get 9 + 9 = 18. You may recognize that 18 is divisible by 3, but you could add up those digits as well to get 1 + 8 = 9. Hopefully at this point you know 9 is divisible by 3, and therefore you know that 99 is also divisible by 3.

Answer: 123,456,789

It's actually pretty easy to figure out if a number is divisible by 5. Like the number 2, you only need to look at the digit in the 'ones' place at the end of the number. However, for a number to be divisible by 5, the 'ones' place has only two options, 0 or 5. Since three of these numbers end in 0 or 5, they can be eliminated as choices, leaving the correct answer of 123,456,789.

Answer: Write the number down and add a "0" to the end of it

Any number that is divisible by 10 will end in a 0. Instead of performing the multiplication, just go ahead and add a "0" to the given number. For example, if the problem is 7 x 10, you can add a "0" to 7 and get an answer of 70. On a larger scale, this principle works for any multiple of 10, such as 100, 1,000, 1,000,000, etc. All you have to do is count the "0's" at the end of the multiple of 10 and add them to the end of the original number.

Answer: 2 and 3

Since 2 and 3 are prime factors of 6, you can figure out if a number is divisible by 6 if it is divisible by both 2 and 3. It is not enough for the number to meet the conditions of only 2 or only 3. For example, 8 is divisible by 2, but it is not divisible by 3 or 6. Likewise, 9 is divisible by 3, but it is not divisible by 2 or 6. Since 12 is divisible by both 2 and 3, it is also divisible by 6.

Answer: Multiplying an odd number by an odd number

The only way to get an odd number via multiplication is to multiply two odd numbers. If any of the numbers are even, the final product will also be even. This is consistent with the rules of multiplying by 2, since multiplying a number by 2 will always give an even answer.

This will hold true regardless of how many odd numbers are multiplied with an even number. Knowing this may allow you to eliminate impossible choices in the quiz, increasing the chance you will guess correctly if you are forced to randomly pick an option.

Answer: 15 x 20 = 300

The correct answer is 304, so an estimate of 300 is the closest option. When estimating, it's a good rule to keep the numbers as close to the real numbers as possible to ensure a reasonable approximation. By making the numbers easier to multiply together, you can save a lot of time and hopefully eliminate some bad answers.

At that point, you can guess an answer that is close to your estimate, and then come back and work out the correct answer if you finish the quiz early.

Answer: 101

Using the process of elimination, you can arrive at the answer of 101. Since the number 115 ends in a 5, we know it's divisible by 5 and therefore not prime. Since 92 ends in a 2, we know it's divisible by 2. The number 117 may be tricky to handle at first, but it's actually divisible by 3. If we add the digits together, we get 1 + 1 + 7 = 9, which is divisible by 3. Since we can use the multiplication short cuts to eliminate three of the choices, 101 must be prime.

Answer: 147

This one could be pretty difficult if you don't spot the trick. Hopefully though, you decided to check if any of the numbers are divisible by 3. If you did, you realized that 1 + 4 + 7 = 12. Knowing that 12 is divisible by 3, you can then determine that 147 is composite. Unlike other number like 2 or 5, you cannot just look at the digit in the one's place to determine if a number is divisible by 3.

However, it's a good idea to always check for divisibility by 3 just in case it saves you a lot of work checking other numbers.

Answer: 720

We are looking for a number that is divisible by 2, 3, 4, 5, and 6. If we can eliminate choices, we can easily find the correct answer. The number 715 is not divisible by 2, since it does not end in a 0, 2, 4, 6, or 8. 721 is not divisible by 5, since it does not end in a 0 or 5. From here, we can check the final two numbers to see if they are divisible by 3.

The sum of the digits of 730 = 7 + 3 + 0 = 10, which is not divisible by 3. The sum of the digits of 720 = 7 + 2 + 0 = 9, which is divisible by 3, so 720 is the correct answer.