Lower Elementary:
Question: The 25th of a month falls on Tuesday. On what day of the week would the 7th fall during that same month?
Answer: Friday
Solution: Students can use a calendar. Students can also use the strategy that 7 days before the 25th is the 18th and that will also be a Tuesday. 7 days before that is the 11th which is also a Tuesday. The 10th is a Monday, the 9th is a Sunday, the 8th a Saturday, and finally, the 7th falls on a Friday.
Upper Elementary:
Question: A teacher is dividing 46 pieces of candy into 7 bags labeled 1 to 7. She puts the candy, one at a time, into the bags. The first piece goes into bag 1, the second into bag 2, the third into bag 3, and so on. She repeats this pattern until all 46 pieces are placed into the bags. Into which bag is the 39th piece of candy placed?
Answer: Bag 4
Solution: Every 7th piece of candy goes into bag 7, that means the 14th, 21th, 28th, and 35th piece of candy goes into bag 7. That means the 36th piece of candy goes into bag 1, 37th into bag 2, and the 38th goes into bag 3, and the 39th goes in bag 4.
Middle School:
Question: Using the clues below, to find the number.
1. I am a six digit number.
2. The sum of my digits is 29.
3. Each digit is a different number.
4. I am an odd number and divisible by 5.
5. The digit in the tens place is the largest.
6. The digit in the hundreds place is the smallest.
7. There is only one even digit, the rest are odd.
8. I am less than 400,000.
9. The digit before the comma is a 7.
Answer: 347,195
Solution:
• Read through all of the clues.
• Starting with the first clue, the number is a six digit number.
___ ___ ___ , ___ ___ ___
• Look through the clues to start filling in the blanks.
• Clue 3 tells us each digit is a different number. So, there will be no repeats.
• Clue 4 lets us know that the ones digit is a 5 because it’s odd and divisible by 5.
• Clue 9 lets us know the thousands digit is 7.
___ ___ 7 , ___ ___ 5
• Clue 5 says the tens place is the largest digit. Our choices for that digit is 8 or 9 because 7 was already used. Clue 7 tells us there is only one even digit and the rest our odd. If the tens place is 8 then there are only 2 available numbers to fill 3 blanks. So, the tens place must be 9.
___ ___ 7 , ___ 95
• Clue 2 tells us that the sum of all the digits is 29. Adding the digits already used and subtracting that from 29 leaves us with 8. So the sum of the final three digits must be 8. Let’s look at the remaining digits:
0, 1, 2, 3, 4, 6, 8
The only three number combination with one even number that adds up to 8 is 3, 4, and 1.
• Clue 6 says the smallest digit is in the tens place. This number is 1.
___ ___ 7 , 195
• Clue 8 tells us that number is less than 400,000. That means that 3 is in the hundred thousands place which means 4 is in the tens thousands place.
347,195
Algebra and Up:
Question: A hybrid car traveled 60 miles and averaged 45 miles per gallon of gasoline. A normal car traveled 25 miles for each gallon of gasoline it used. How many miles did the normal car traveled when it used the same amount of gasoline as the hybrid car used to travel 60 miles?
Answer: 33â…“ miles
Solution: We start by finding how many gallons of gasoline the hybrid car used to go 60 miles.
60 ÷ 45 = 1â…“ gallons
Because the normal car goes 25 mile per gallon of gasoline it will go 40 miles on 1â…“ gallons.
25(1) + 25(â…“) = 25 + 8â…“ = 33â…“ miles
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