## Multiples, odd numbers, divisibility, primes

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
theawkwardcellist
Posts: 2
Joined: Wed Jun 13, 2012 11:12 pm
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### Multiples, odd numbers, divisibility, primes

2. For the first 1,000 positive integers, how many integers are multiples of 3 or 4?
(A)470
(B)480
(C)500
(D)520
(E)550

3. Between 300 and 800, how many integers are multiples of 5 and 8?
(A)10
(B)12
(C)300
(D)799
(E)800

4. How many 4 digit numbers between 5,000 and 10,000 are odd numbers?
(A)200
(B)400
(C)1000
(D)2500
(E)3000

5. If k is divisible by 2,3, and 15, which of the following is also divisible by these numbers?
(A)k+10
(B)k+15
(C)k+20
(D)k+30
(E)k+40

6. Which of the following numbers is divisible by the largest prime factor?
(A)250
(B)260
(C)300
(D)320
(E)400

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
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### Re: Multiples, odd numbers, divisibility, primes

2. For the first 1,000 positive integers, how many integers are multiples of 3 or 4?
How many are multiples of 3? (Hint: Divide!) How many are multiples of 4? (Hint: Divide!) Since any multiple of 3*4=12 is a duplicate, you'll need to toss those out. How many are multiples of 12? (Hint: Divide!) What do you get?
3. Between 300 and 800, how many integers are multiples of 5 and 8?
This one works just like the previous one.
4. How many 4 digit numbers between 5,000 and 10,000 are odd numbers?
Where are you stuck in dividing by 2?
5. If k is divisible by 2,3, and 15, which of the following is also divisible by these numbers?
(A)k+10
(B)k+15
(C)k+20
(D)k+30
(E)k+40
Using the fact that 15=3*5, what can you figure out about these expressions?
6. Which of the following numbers is divisible by the largest prime factor?
(A)250
(B)260
(C)300
(D)320
(E)400
What did you get when you factored each number?