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1) Sally is thinking of a three digit number and she tells you this. All the digits are different. Arranging the digits in one order creates an odd number divisible by 5 and 3. Arranging the digits in another order makes a number divisible by 2 and 5. Arranging the digits in a third order creates a number which factors as the product of two primes. The number is the biggest one you can make with the three digits. What is the number? |
1. Well, let's start with the last clue:
the number is the biggest one you can make with the 3 digits.
That means they are in numerical order, highest to lowest because if you swap the position of any two, the number is no longer the biggest.
2. If you can make a 3-digit number out of it that is divisible by 5,
then the number must end in either a 5 or a 0.
3. If you can arrange the digits so that it makes an odd number
divisible by 5 and 3 then the last digit in this arrangement must be a 5.
So there is a 5 here!
4. In the above arrangement, to also be divisible by 3,
the second number must be a 1 (making X15), or a 7 (making X75).
5. If there is both a 7 and a 5 in the number,
then the final number must be one of these: 765, 750, or 975.
If there is a 1 and a 5 in the final number, then it can only be 510.
6. Examine these 4 possibilities to come up with the final number = ______________
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2) A recipe for fruit punch says to use 8 ounces of orange juice for every 3 ounces of grape juice.
Nicky made 99 ounces of fruit punch. How many more ounces of orange juice than grape juice
were used? |
1. Out of ____ total parts, the orange juice is 8 of those parts.
2. Similarly, the grape juice is ____ of those parts.
3. Compute the number of ounces of orange juice in 99 ounces and the number of ounces of grape juice in 99 ounces and subtract = _____
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