## 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: 350
Joined: Mon Dec 08, 2008 12:32 am
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### Re: Multiples, odd numbers, divisibility, primes

theawkwardcellist wrote: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?

theawkwardcellist wrote:3. Between 300 and 800, how many integers are multiples of 5 and 8?

This one works just like the previous one.

theawkwardcellist wrote:4. How many 4 digit numbers between 5,000 and 10,000 are odd numbers?

Where are you stuck in dividing by 2?

theawkwardcellist wrote: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?

theawkwardcellist wrote: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?