Last visit was: 25 Dec 2024, 05:42 It is currently 25 Dec 2024, 05:42

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 30490
Own Kudos [?]: 36851 [6]
Given Kudos: 26106
Send PM
Most Helpful Community Reply
avatar
Intern
Intern
Joined: 09 Oct 2019
Posts: 1
Own Kudos [?]: 5 [5]
Given Kudos: 0
Send PM
General Discussion
Retired Moderator
Joined: 09 Jun 2020
Posts: 205
Own Kudos [?]: 235 [0]
Given Kudos: 34
GPA: 3.21
Send PM
avatar
Intern
Intern
Joined: 25 Aug 2020
Posts: 17
Own Kudos [?]: 13 [2]
Given Kudos: 0
Send PM
Re: How many positive integers less than 5,000 are multiple [#permalink]
2
You are asked to see how many values less than 5000 are multiples of 7. The first 6 numbers (1,2,3,4,5,6) can't be multiples of 7 so 7 is your first number. 5000 is not divisible by 7 so you got to find the last value that is a multiple of 7. I like to do this by dividing 5000 by 7 and then multiplying it by whatever number they gave me (if it's a whole number then that's a multiple, if it's a decimal then that means it is not a multiple). 5000/7= 714.28 so multiply 7 by 714 and you'll get 4998 as your answer. This is in fact a multiple of 7 and we can conclude that the numbers we are working with are in the range of 7-4998. From here I subtract 7 from 4998 and then divide it by 7 to see how many integers are multiples of 7. I came out with 714 possible values. From here it asks you to see which one of these multiples of 7 is also the product of 11 and an even number. The lowest possible value that could be is 11*2= 22. So look at the multiples of 22 until you see one that is a multiple of 7. It took 7 tries for me to realize that the seventh multiple of 22 is also a multiple of 7 (154). Find the range again by the same technique used to find the range for 7 and you get a range of possible values from 22-4994. Again subtract 22 from 4994 and you get 226+1 for a total of 227 multiples of 22. From here we need to find out which multiples of 22 are multiples of 7. Again our range is now from 7 to 224 so subtract 7 from 224 and you get 217. Divide that value by 7 and you get 31 values. Don't forget to add +1 and your final answer is 32!. We add +1 to include the last value of the range. The way i like to think about it is asking yourself "How many integers are in 1-10?" Well obviously 10 but if we subtract 1 from 10 our answer is 9 so don't forget to include the last value of the set to get that total of 10! Sorry for making this so long, but i wanted to be as descriptive as possible. Cheers!
avatar
Intern
Intern
Joined: 10 Sep 2020
Posts: 26
Own Kudos [?]: 9 [0]
Given Kudos: 0
Send PM
Re: How many positive integers less than 5,000 are multiple [#permalink]
1
I saw this as a patterns and sequences type problem. I found that there are 14 multiples of 7 between 0-100. 7 of those multiples are even numbers. 100-200, 200-300, and 300-400 do as well. Then when we get to 400-500 we need to worry about going over 5,000. 11*406, 11*420, 11*434 and 11*448 all stay under. So we end up with 4 groups of 7 plus the 4 from the last group.
Manager
Manager
Joined: 06 Nov 2020
Posts: 85
Own Kudos [?]: 69 [2]
Given Kudos: 101
Send PM
Re: How many positive integers less than 5,000 are multiple [#permalink]
2
the positive integers must contain at least 7,11 and 2 primes thus, 7*11*2 =154 will be the first integer that satisfies the mentioned conditions.
and the subsequent positive integers are n*154, where, n=1,2,3,4,5,6....... up to 32. Because 32*154= 4928 the highest integer less than 5000.
So the answer is 32.
Alternative way: just divide 5000 by 154, 5000/154=32.47, therefore, 32 is the answer
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5093
Own Kudos [?]: 76 [0]
Given Kudos: 0
Send PM
Re: How many positive integers less than 5,000 are multiple [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
Re: How many positive integers less than 5,000 are multiple [#permalink]
Moderators:
GRE Instructor
88 posts
GRE Forum Moderator
37 posts
Moderator
1115 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne