Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

 It is currently 30 Mar 2017, 04:01

### 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

# What is the number of multiples of 6 between 60 and 100

Author Message
SVP
Joined: 05 Jul 2006
Posts: 1743
Followers: 6

Kudos [?]: 343 [0], given: 49

What is the number of multiples of 6 between 60 and 100 [#permalink]

### Show Tags

12 Sep 2006, 12:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the number of multiples of 6 between 60 and 100 inclusive and exclusive?

CEO
Joined: 20 Nov 2005
Posts: 2909
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 25

Kudos [?]: 279 [0], given: 0

### Show Tags

12 Sep 2006, 12:59
Inclusive:
(96-60)/6 + 1
= 7

Exclusive:
(96-66)/6 + 1
= 6
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

VP
Joined: 02 Jun 2006
Posts: 1266
Followers: 2

Kudos [?]: 83 [0], given: 0

### Show Tags

12 Sep 2006, 15:47

Number of multiples of 7 between 237 and 489 inclusive?
Senior Manager
Joined: 31 Jul 2006
Posts: 440
Followers: 3

Kudos [?]: 47 [0], given: 0

### Show Tags

12 Sep 2006, 18:33
haas_mba07 wrote:

Number of multiples of 7 between 237 and 489 inclusive?

can we do (489-237)/7+1=37?

BTW why do we add 1 at the end?
Senior Manager
Joined: 20 Feb 2006
Posts: 373
Followers: 1

Kudos [?]: 29 [0], given: 0

### Show Tags

12 Sep 2006, 18:44
Yes 37 is correct.

You add the 1 when stated for the inclusive to include the first term, because after you've substracted, the first term effectively becomes 0.

So multiples of 6 between 60 and 100:

100-60/6 = 40/6 6r4 However, this does not include the original term of 60 which is divisible by 6. Hence 6+1
VP
Joined: 02 Jun 2006
Posts: 1266
Followers: 2

Kudos [?]: 83 [0], given: 0

### Show Tags

12 Sep 2006, 18:54
But note that neither of 489 or 237 are divisible by 7.

The smallest number greater than 237 divisible by 7, is 238.
The greatest number less than 437 divisible by 7 is, 434.

Is the answer still 37? Or is it 36? Or is it something else?

Yes 37 is correct.

You add the 1 when stated for the inclusive to include the first term, because after you've substracted, the first term effectively becomes 0.

So multiples of 6 between 60 and 100:

100-60/6 = 40/6 6r4 However, this does not include the original term of 60 which is divisible by 6. Hence 6+1
Senior Manager
Joined: 20 Feb 2006
Posts: 373
Followers: 1

Kudos [?]: 29 [0], given: 0

### Show Tags

12 Sep 2006, 19:05
Actually, I stand corrected - it's 36 because the first term isn't divisible by 7.

Correct?
VP
Joined: 02 Jun 2006
Posts: 1266
Followers: 2

Kudos [?]: 83 [0], given: 0

### Show Tags

12 Sep 2006, 19:05
What about the last one? Its not divisible by 7 either...

Actually, I stand corrected - it's 36 because the first term isn't divisible by 7.

Correct?
VP
Joined: 25 Jun 2006
Posts: 1168
Followers: 3

Kudos [?]: 151 [0], given: 0

### Show Tags

12 Sep 2006, 20:07
it is 7.

60 is divisible by 6.
96 is divisible by 6.

so just take these 2 numbers, because 100 is not divisible by 6 and it is excluded anyway.

(96-60)/6 + 1 = 7.

so it is 7.
Senior Manager
Joined: 14 Aug 2006
Posts: 363
Followers: 1

Kudos [?]: 46 [0], given: 0

### Show Tags

12 Sep 2006, 21:39
haas_mba07 wrote:
What about the last one? Its not divisible by 7 either...

Actually, I stand corrected - it's 36 because the first term isn't divisible by 7.

Correct?

There are 252 numbers from 237 - 489
489-237 = 252
252/7 = 36.

So there are 36 numbers divisible by 7
Senior Manager
Joined: 20 Feb 2006
Posts: 373
Followers: 1

Kudos [?]: 29 [0], given: 0

### Show Tags

13 Sep 2006, 04:21
Number of multiples of 7 between 237 and 489 inclusive?

(489-237)/7 could be rewritten as 489/7 - 237/7 = 69 - 33 = 36

We add the "1" if the number excluded by the subtraction is divisible by n.

ie if it had been (490-237))/7 = 36 + 1 (490 is divisible by 7)

or (489-231)/7 = 36 +1 (231 is divisible by 7)

If both upper and lower terms are divisible eg multiples of 7 between 7-28 inclusive then you still add "1" because you only effectively exclude one of the terms:

(28-14)/7 = 2 But there are 3 numbers divisible by 7; 7,14,21 so "+1"
= 2 +1

I'm sure this is a long winded explanation and that one of the more math fluent members can do a better job of explaining this.[/quote]
Senior Manager
Joined: 31 Jul 2006
Posts: 440
Followers: 3

Kudos [?]: 47 [0], given: 0

### Show Tags

13 Sep 2006, 05:56
Great stuff! Thank you.
13 Sep 2006, 05:56
Display posts from previous: Sort by