It is currently 23 Jun 2017, 17:44

### 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

# M01 Question 18

Author Message
Manager
Joined: 11 Apr 2009
Posts: 163

### Show Tags

01 Jun 2009, 16:51
1
KUDOS
1
This post was
BOOKMARKED
How many of the three-digit numbers are divisible by 7?

(A) 105
(B) 106
(C) 127
(D) 128
(E) 142

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions
Founder
Joined: 04 Dec 2002
Posts: 15143
Location: United States (WA)
GMAT 1: 750 Q49 V42

### Show Tags

01 Jun 2009, 17:45
4
KUDOS
Expert's post
4
This post was
BOOKMARKED
Is something not clear in the Official Explanation?

Approach One: Divide all of the three-digit numbers $$999 - 100 + 1 = 900$$ (Don't forget to add 1 to get the number of all the 3-digit numbers) by 7, which is 128.57, and then round it off to 128.

Approach Two:
Find the first and the last multiples of 7 WITHIN the range (which is between 105 and 994). Find the positive difference, divide by 7, and add 1:
$$\frac{994-105}{7}+1=128$$
_________________

Founder of GMAT Club

US News Rankings progression - last 10 years in a snapshot - New!
Just starting out with GMAT? Start here...
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

Manager
Joined: 08 Jul 2009
Posts: 170

### Show Tags

04 Jan 2010, 21:02
2
KUDOS
7*15=105
7*142=994

then 142-15+1 = 128
Math Expert
Joined: 02 Sep 2009
Posts: 39622

### Show Tags

20 Sep 2010, 22:55
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
jayasimhaperformer wrote:
a 7*15=105
b 106/7=15.1
c 127/7=18.1
d 128/7=18.12 aprox
e 142/7=20.--- aprox
so a is right & a straight ans as its div by 7*15

Hi, and welcome to Gmat Club.

It seems that you misinterpreted the question.

The question is "How many of the three-digit numbers are divisible by 7?" It's not necessary the answer itself to be divisible by 7

GENERALLY:
$$# \ of \ multiples \ of \ x \ in \ the \ range = \frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1$$.

For example: how many multiples of 5 are there between -7 and 35, not inclusive?

Last multiple of 5 IN the range is 30;
First multiple of 5 IN the range is -5;

$$\frac{30-(-5)}{5}+1=8$$.

OR:
How many multiples of 7 are there between -28 and -1, not inclusive?
Last multiple of 7 IN the range is -7;
First multiple of 7 IN the range is -21;

$$\frac{-7-(-21)}{7}+1=3$$.

Back to the original question:

Last 3-digit multiple of 7 is 994;
First 3-digit multiple of 7 is 105;

So # of 3-digt multiples of 7 is $$\frac{994-105}{7}+1=128$$.

Hope it helps.
_________________
Intern
Joined: 17 May 2010
Posts: 19

### Show Tags

20 Sep 2010, 05:52
1
KUDOS
105 is the first 3 digit number divisible by 7
994 is the last 3 digit number divisible by 7

(994 - 105)/7 + 1 = 128
Math Expert
Joined: 02 Sep 2009
Posts: 39622

### Show Tags

04 Feb 2011, 11:46
1
KUDOS
Expert's post
tinki wrote:
Hello Bunuel, nice explanation as usual
is there any shortcut to find last and first multiples? for example how to find 994 ad 105 of 7?
or we have to use the long method of division?
thx 4 response

Well, it depends multiple of which number you want to find and the range you are looking in. Common sense, and divisibility rules should help you in this but sometimes 'trial and error' is also a good method. Check for example divisibility rules here: math-number-theory-88376.html
_________________
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010

### Show Tags

10 May 2011, 11:11
1
KUDOS
gmatprep09 wrote:
How many of the three-digit numbers are divisible by 7?

(A) 105
(B) 106
(C) 127
(D) 128
(E) 142

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

Description of the technique:

Q: How many 3 digits numbers are divisible by 7
OR
How many multiples of 7 are there between 100 and 999, inclusive?

Choose the first number greater than equal to 100 that is divisible by 7.
Remainder of 100/7 is 2. 100-2+7=105
"105" is the first number greater than equal to 100 that is divisible by 7.

Choose the first number less than equal to 999 that is divisible by 7.
Remainder of 999/7 is 5. 999-5=994
"994" is the first number less than equal to 999 that is divisible by 7.

$$n=\frac{994-105}{7}+1=127+1=128$$

Ans: "D"

************************
This rules hold good for all numbers.

Find the numbers divisible by 3 between 1 and 18, inclusive.

First Number greater than equal to 1 that is divisible by 3 = 3
First Number less than equal to 18 that is divisible by 3 = 18

$$Number of multiples = \frac{18-3}{3}+1=5+1=6$$

Validate:
Count of {3,6,9,12,15,18} = 6

Try it with any number and you should get the count.
_________________
Intern
Joined: 20 May 2009
Posts: 39
3 Digit Numbers Divisible by 7 (and others) [#permalink]

### Show Tags

04 Aug 2009, 00:02
Hi All,

Here’s a question that came up in M01 on the gmatclub tests.

How many of the 3 digit numbers are divisible by 7?

Solution (provided by gmatclub)

Take the first and last multiples of 7 in the range.

They are 105 and 994.

(994 – 105) / 7 + 1 = 128

Does this technique hold true for all numbers in a range? I’ve tried it with a couple of other examples and it seems to work
Manager
Joined: 24 Apr 2009
Posts: 93
Re: 3 Digit Numbers Divisible by 7 (and others) [#permalink]

### Show Tags

04 Aug 2009, 03:17
Aztec wrote:
Hi All,

Here’s a question that came up in M01 on the gmatclub tests.

How many of the 3 digit numbers are divisible by 7?

Solution (provided by gmatclub)

Take the first and last multiples of 7 in the range.

They are 105 and 994.

(994 – 105) / 7 + 1 = 128

Does this technique hold true for all numbers in a range? I’ve tried it with a couple of other examples and it seems to work

yes, it applies to all the numbers in the range..
Manager
Joined: 28 Jul 2009
Posts: 124
Location: India
Schools: NUS, NTU, SMU, AGSM, Melbourne School of Business
Re: 3 Digit Numbers Divisible by 7 (and others) [#permalink]

### Show Tags

10 Aug 2009, 01:00
It should work every time on all the numbers.
_________________

GMAT offended me. Now, its my turn!
Will do anything for Kudos! Please feel free to give one.

Director
Joined: 01 Apr 2008
Posts: 881
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: 3 Digit Numbers Divisible by 7 (and others) [#permalink]

### Show Tags

10 Aug 2009, 02:46
Just to mention,
if it says "excluding" then the formula becomes, (max-min)/divisibility - 1.
SVP
Joined: 05 Jul 2006
Posts: 1747
Re: 3 Digit Numbers Divisible by 7 (and others) [#permalink]

### Show Tags

10 Aug 2009, 02:54
Economist wrote:
Just to mention,
if it says "excluding" then the formula becomes, (max-min)/divisibility - 1.

Great now we have all the rules in one page , thanks
Intern
Joined: 31 Aug 2009
Posts: 5

### Show Tags

01 Oct 2009, 21:55
1) Take all numbers between 1 and 999 divisible by 7: 999/7=142
2) Subtract the number that are not three digits: 99/7=14

142-14=128
Intern
Joined: 25 Nov 2009
Posts: 16
Location: San Francisco
Schools: Wharton West eMBA, Haas EW, Haas eMBA
Re: 3 Digit Numbers Divisible by 7 (and others) [#permalink]

### Show Tags

10 Jan 2010, 17:25
I'm kept my lame questions to a minimum. I see why plus 1 work for inclusive. I don't see for exclusive why minus 1 would work. If both of the end number "excluded" are actually multiples of the number in question it changes it. but that should be the case for inclusive as well. in other words, how many multiples of 7 between 8 and 22 exclusive means 9 to 21 which means the answer is 2. 21-9 is 12 which divided by 7 is 1 so plus 1 = 2. however 7 to 28 exclusive means 8-27 = 19 which is 2 7s which is actually correct.

It makes me very nervous to apply formulas without being crystal clear as to why they're right. Maybe I've misunderstood part of the premise of the question.
Intern
Joined: 03 Aug 2010
Posts: 1

### Show Tags

20 Sep 2010, 21:29
a 7*15=105
b 106/7=15.1
c 127/7=18.1
d 128/7=18.12 aprox
e 142/7=20.--- aprox
so a is right & a straight ans as its div by 7*15
Intern
Joined: 02 Apr 2010
Posts: 47
Location: Mumbai

### Show Tags

25 Sep 2010, 05:09
The range of 3 digit numbers that are divisible by 7 are 105 to 994 inclusive. If we consider the set of these numbers as in Arithmetic Progression, {105, 112, 119 ... 994}, we can find the number of values in the set using the formula; Last term = First term + (n-1)(Common Difference), which implies, 994 = 105 + (n-1)(7). Solving n = 128
_________________

Consider kudos for good explanations.

Manager
Joined: 27 May 2008
Posts: 126

### Show Tags

27 Sep 2010, 04:54
Hi Bunuel nice explanation.
Retired Moderator
Joined: 03 Aug 2010
Posts: 240
Re: 3 Digit Numbers Divisible by 7 (and others) [#permalink]

### Show Tags

28 Dec 2010, 23:23
Can someone solve the same problem with some addtiional details
How many of the 3 digit numbers are divisible by 7?
Nos divisble by 7 = 128
Nos divisible by 5 = 180
Can we find nos divisible by 35 on the basis of above info ( not the traditional formula used for this problem , but using set theory )
_________________

http://www.gmatpill.com/gmat-practice-test/

Amazing Platform

Manager
Joined: 13 Jul 2010
Posts: 167
Re: 3 Digit Numbers Divisible by 7 (and others) [#permalink]

### Show Tags

28 Dec 2010, 23:43
this strategy should work for most of these types of problems. I have never seen an exclusive scenario.

Also to figure out those 3 digit numbers divisible by 35 I would just use the same formula.
Retired Moderator
Joined: 03 Aug 2010
Posts: 240
Re: 3 Digit Numbers Divisible by 7 (and others) [#permalink]

### Show Tags

29 Dec 2010, 00:59
gettinit wrote:
this strategy should work for most of these types of problems. I have never seen an exclusive scenario.

Also to figure out those 3 digit numbers divisible by 35 I would just use the same formula.

Thanks for your reply, i understand that i can find the nos with the same formula

But i wish to understand whethr the same is possible with set theory.. because the q could be asked as a DS question in some different format also
_________________

http://www.gmatpill.com/gmat-practice-test/

Amazing Platform

Re: 3 Digit Numbers Divisible by 7 (and others)   [#permalink] 29 Dec 2010, 00:59

Go to page    1   2    Next  [ 35 posts ]

Similar topics Replies Last post
Similar
Topics:
m01-qs 18 1 26 Dec 2011, 09:15
m01 1 27 May 2009, 11:42
5 M01 27 11 14 Jan 2012, 22:54
19 M01-Q15 20 27 Jun 2014, 11:15
Display posts from previous: Sort by

# M01 Question 18

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.