G2 Cassie VTAMPS 13 COMBINATORICS

A) According to the following answers, how many 3-digit number(s) is/are there?
9×9, 47×3, 100÷10, 450÷3, 80+19, 50+51

Answer explanation

Solution: Solving all the given expressions,
9 ×9=81
47 ×3 =141
100 ÷10 =10
450 ÷3 =150
80 +19 =99
50 +51 =101
From the answers, there are 3 3-digit numbers.

E) If we are using 3, 4, 9 and 2 without repetition to form two 2-digit numbers, what is the minimum possible value of their positive difference?

Answer explanation

Solution:
From the given digits, we can use either 2 and 3, or 3 and 4 for the tens digit of the two 2-digit numbers because it gives the minimum possible value of their difference.

If we choose 2 and 3, the possible two 2-digit numbers are 29 and 34, which gives a difference of 5.

If we choose 3 and 4, the possible two 2-digit numbers are 39 and 42, which gives a difference of 3.

Since we need to find the minimum possible value of their difference which is positive, the answer is 3.

E) If we are choosing 2 digits, without repetition, from 1, 0, 5, 6 and 4 to form 2-digit numbers, how many of these 2-digit numbers are even numbers?

Answer explanation

Solution:

From the given, 0, 4, and 6 are the possible units digit that gives an even number.

If we choose 0 for the units digit, there are 4 possible combinations.

If we choose 4 for the units digit, there are 3 possible combinations.

If we choose 6 for the units digit, there are 3 possible combinations.

So, 4 + 3 + 3 = 10.

c) Choose 4 digits, without repetition, from 0, 3, 4, 5, and 9 to form two 2-digit even numbers.
What is the minimum possible value of the difference of these pairs of numbers?

Answer explanation

Solution:

From the given digits, 0 and 4 are the only even digits, so they are both units digit. From the remaining digits 3, 5 and 9, 5 and 3 gives the biggest difference which is 2.

Forming the 2 2-digit even numbers that gives the minimum difference, we have 50 and 34, then 50 – 34 = 16.

B) What is the least 3-digit even number composed of digits 0, 2, 3, 5, or 7?
(Each number can only be used once)

Answer explanation

Solution: The only even numbers from the given digits are 0 and 2. And the least digit that could be used for the hundreds digit is 2. So, choosing the least 3-digit even number, we have 230.

B) Separate 20 as a sum of two positive whole numbers. How many way(s) are there?
(Consider 4+3 and 3+4 as the same method)

Answer explanation

Solution: Finding the 2 largest possible whole numbers that has 20 as their sum, we have 10 and 10.
Then listing all the possible pairs
(10+10, 11+9, 12+8,…), we get 10 pairs.

A) How many 3-digit number(s) are there where the tens digit is a multiple of 5, the hundreds digit is an even number, and the units digit is an odd number?

Answer explanation

Solution: From the given, there are 4 possible numbers for the hundreds digit:
2, 4, 6, 8 (0 isn’t included since we need a 3-digit number).
There are only 2 possible numbers for the tens digit: 0 and 5.
There are 5 possible numbers for the units digit: 1, 3, 5, 7, 9
Multiplying the possible combinations, we have 4 × 2 × 5 = 40.

E) Jessie, Andy and Buzz have some oranges. If Andy gives 19 oranges to Buzz and Buzz gives 7 oranges to Jessie, they will all have the same numbers of oranges.

What is the difference between the number of oranges of Andy and Buzz?

Answer explanation

Solution:

From the given,

Andy – 19 = Buzz + 19 – 7 = Jessie + 7.

This means that

Andy – 19 = Buzz + 19 – 7

Andy – 19 = Buzz + 12.

Since this is an equality, we can add both sides by 19, so

Andy – 19 + 19 = Buzz + 12 + 19

Andy = Buzz + 31

So, there is a difference of 31 oranges between Andy and Buzz.

A) What is the least 3-digit even number you can make using the digits 0, 1, 2, 4, 8, and 9?
(Each number can only be used once)

Answer explanation

Solution: Starting with the hundreds digit, the least number that we can use is 1. Combining the given digits, the least number that we can form is 102, which is also an even number.

A) Choose 6 digits, without repetition, from 1, 2, 3, 4, 5, 6 to form two 3-digit numbers. What is the maximum value of the difference between the two 3-digit numbers?

Answer explanation

Solution:
From the given digits, 6 and 1 can give the biggest difference, which is 5, next is 5 and 2 which has a difference of 3, and last is 4 and 3 which has a difference of 1.

Forming the 2 3-digit numbers that gives the maximum difference, we have 654 and 123, then 654 – 123 = 531.