Multiples and integers between : GMAT Quantitative Section
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 Feb 2017, 07:32

### GMAT 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

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

Practice
Pays

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Multiples and integers between

Author Message
TAGS:

### Hide Tags

Director
Joined: 28 Jul 2011
Posts: 563
Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 3

Kudos [?]: 220 [0], given: 16

### Show Tags

08 Jan 2012, 17:50
1
This post was
BOOKMARKED
I have one concern regarding this How many multiples and how many integers?

How many of the three-digit numbers are divisible by 7?

Generally we do--->999-100= 899

so 899/7=128 so we need to include both digits so we add 1 to total so it is 128+1

but the answer is only 128,How is that possible?????

As per our knowledge we know that

->If the question says both inclusive we add +1 at the last, For eg

How many of the three-digit numbers are divisible by 7?

Generally we do--->999-100= 899

so 899/7=128 so we need to include both digits so we add 1 to total so it is 128+1

->If the question says both not inclusive we add -1 at the last, For eg

How many of the three-digit numbers are divisible by 7?

Generally we do--->999-100= 899

so 899/7=128 so we need to include both digits so we add 1 to total so it is 128-1

->If the question says one inclusive we only subtract two extremes, for Eg

How many of the three-digit numbers are divisible by 7?

Generally we do--->999-100= 899

so 899/7=128, so 128 is the answer.....

Anything wrong with my concept???????Please explain i am totally confused with this...............

If anything wrong,please explain how to with these kind of problems, Like How many integers between two numbers? and How many integers between two multiples?
_________________

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 3861
Followers: 1334

Kudos [?]: 6138 [1] , given: 73

Re: Multiples and integers between [#permalink]

### Show Tags

08 Jan 2012, 22:18
1
KUDOS
Expert's post
Hi, there. I'm happy to help with this.

First of all, the "add one" thing for inclusive counting only works after subtracting biggest from smallest on a list. If you divide or do some other calculation first, then you can't just add one to that result and call it inclusive counting. You divided by 7, then added one. That's not bonafide inclusive counting.

Next, notice that there are not 899 three digits numbers --- there are actually 900, because you have to count 100. That is genuine inclusive counting --- 999 - 100 + 1 = 900.

Now, for multiples, first find out about the other factors.
7*14 = 98
7*15 = 105, so 7*15 is the first multiple of 7 that's a three-digit number.

1000/7 = 142 and change, so
7*142 = 994
7*143 = 1001, so 7*142 is the last multiple of 7 that's a three-digit number.

How many multiples from 7*15 to 7*142? That's equivalent to: how many integers from 15 to 142? That's where inclusive counting comes in again:

142 - 15 + 1 = 128

Does that make sense? Please let me know if you have any questions about what I've said here.

Here's another similar question for practice.

http://gmat.magoosh.com/questions/846

The question at that link should be followed by a video explanation of the answer.

Mike
_________________

Mike McGarry
Magoosh Test Prep

Director
Joined: 28 Jul 2011
Posts: 563
Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 3

Kudos [?]: 220 [0], given: 16

Re: Multiples and integers between [#permalink]

### Show Tags

08 Jan 2012, 23:31
mikemcgarry wrote:
Hi, there. I'm happy to help with this.

First of all, the "add one" thing for inclusive counting only works after subtracting biggest from smallest on a list. If you divide or do some other calculation first, then you can't just add one to that result and call it inclusive counting. You divided by 7, then added one. That's not bonafide inclusive counting.

Next, notice that there are not 899 three digits numbers --- there are actually 900, because you have to count 100. That is genuine inclusive counting --- 999 - 100 + 1 = 900.

Now, for multiples, first find out about the other factors.
7*14 = 98
7*15 = 105, so 7*15 is the first multiple of 7 that's a three-digit number.

1000/7 = 142 and change, so
7*142 = 994
7*143 = 1001, so 7*142 is the last multiple of 7 that's a three-digit number.

How many multiples from 7*15 to 7*142? That's equivalent to: how many integers from 15 to 142? That's where inclusive counting comes in again:

142 - 15 + 1 = 128

Does that make sense? Please let me know if you have any questions about what I've said here.

Here's another similar question for practice.

http://gmat.magoosh.com/questions/846

The question at that link should be followed by a video explanation of the answer.

Mike

+1 Kudos for you
_________________

Director
Joined: 28 Jul 2011
Posts: 563
Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 3

Kudos [?]: 220 [0], given: 16

Re: Multiples and integers between [#permalink]

### Show Tags

08 Jan 2012, 23:41
mikemcgarry wrote:
Hi, there. I'm happy to help with this.

First of all, the "add one" thing for inclusive counting only works after subtracting biggest from smallest on a list. If you divide or do some other calculation first, then you can't just add one to that result and call it inclusive counting. You divided by 7, then added one. That's not bonafide inclusive counting.

Next, notice that there are not 899 three digits numbers --- there are actually 900, because you have to count 100. That is genuine inclusive counting --- 999 - 100 + 1 = 900.

Now, for multiples, first find out about the other factors.
7*14 = 98
7*15 = 105, so 7*15 is the first multiple of 7 that's a three-digit number.

1000/7 = 142 and change, so
7*142 = 994
7*143 = 1001, so 7*142 is the last multiple of 7 that's a three-digit number.

How many multiples from 7*15 to 7*142? That's equivalent to: how many integers from 15 to 142? That's where inclusive counting comes in again:

142 - 15 + 1 = 128

Does that make sense? Please let me know if you have any questions about what I've said here.

Here's another similar question for practice.

http://gmat.magoosh.com/questions/846

The question at that link should be followed by a video explanation of the answer.

Mike

Can you please refer this link in this link For not inclusive problem "Bunnel"(Gmat user) has added 1 at the last is that correct??....i think there we need to subtract 1 from the count right??

and can you also please throw some light on both not inclusive and 1 inclusive problem...

_________________

Senior Manager
Joined: 13 May 2011
Posts: 317
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Followers: 21

Kudos [?]: 253 [0], given: 11

Re: Multiples and integers between [#permalink]

### Show Tags

09 Jan 2012, 00:05
1st digit: 105
last digit: 994
994=105+(n-1)*7 [AP, nth term]
n=128
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14002
Followers: 592

Kudos [?]: 168 [0], given: 0

Re: Multiples and integers between [#permalink]

### Show Tags

20 Oct 2014, 16:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
_________________
Re: Multiples and integers between   [#permalink] 20 Oct 2014, 16:29
Similar topics Replies Last post
Similar
Topics:
Even and Odd Integers Multiplication Combinations 2 24 Dec 2015, 09:13
2 Should we 0 count as a multiple of all integers in the gmat? 4 09 Apr 2013, 22:14
9 How many multiples of 7 between 100 and 150? 12 10 May 2012, 04:45
2 Fast Multiplication 0 21 May 2010, 09:05
5 Multiple modulus inequalities 8 19 Dec 2009, 01:01
Display posts from previous: Sort by