| Problem |
Hint |
3) What is the sum of all the two-digit numbers neither of whose digits are prime? For example, 42 is not one while 44 is because 4 is not prime. |
1. The prime single digits are 2,3, 5 and 7.
2. So none of the 2-digit numbers whose 10s digit is one of these qualifies.
3. That leaves 2-digit numbers that start with ___________.
4. Any 2-digit number whose second digit is one of the above does not qualify, so that leaves only __ digits available for the units digit.(don't forget zero!).
These are _____________.
The sum of the ones digits for each 10s digit =
__________________.
5. So the numbers are (ordered by the first digit):
(I'll do the first row for you)
- 10s : 10 + 11 + 14 + 16 + 18 + 19 = 1X60 + 28
- 20s : X (2 is prime!)
- 30s : X
- 40s : ______________________________
- 50s : X
- 60s : ______________________________
- 70s : X
- 80s : ______________________________
- 90s : ______________________________
This sum is ______________
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4) A palindromic number is one which is the same read backwards and forwards. For example, 121 and 3443 are palindromic numbers. What is the next palindromic number after 79311397 and how much more is it? |
1. The number 79311397 is in 2 parts 7931 and 1397
2. The next palindromic number will be higher
than this one and the middle 2 digits (the last one of the first
4 and the first one of the last 4) must be the same
for it to remain a palindrome, like this: 793NN297.
That number (N) is _____.
3. So, the next palindromic number is ________ and it is _____ more than the first number.
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5) Quint bought a car. He sold it to Rachael for 5/6 of the price he paid for it. Rachael sold
it to Shawn for 1/5 less than she paid for it. Shawn sold it to Teddy for 3/4 of what he paid.
Teddy paid $1200 for it. How much did Quint pay for it originally?
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Work this problem backwards:
Use Q for Quint, R for Rachael, S for Shawn and T for Teddy.
1. If Teddy paid $1200 for the car and it was 3/4
of what Shawn paid, then 1200 = (3/4) x S.
So S = ______
2. Rachael sold it to Shawn for 4/5 of what she paid Quint for it, so
(4/5) R = S, and R = ____.
3. Continue this logic until you solve for Q = _____
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