NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 02:30 It is currently 24 Apr 2024, 02:30
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

How many integers between 100 and 150, inclusive, cannot be

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
shaneforu
Intern
Intern
Joined: 11 Jan 2007
Posts: 29
Own Kudos [?]: 157 [28]
Given Kudos: 4
Location: United States
Concentration: Marketing, Healthcare
Schools: Stern PT '14 Booth '14 Kellogg PT '14
GMAT 1: 600 Q49 V25
GMAT 2: 650 Q49 V32
GPA: 3.5
WE:Pharmaceuticals (Consulting)
Send PM
How many integers between 100 and 150, inclusive, cannot be [#permalink] New post   24 May 2010, 10:53
28
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

45% (02:25) correct 55% (02:31) wrong based on 315 sessions
Hide Show timer Statistics
How many integers between 100 and 150, inclusive, cannot be evenly divided by 3 nor 5?

A. 35
B. 27
C. 25
D. 26
E. 28
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618681 [15]
Given Kudos: 81586
Send PM
CAT Tests Forum Quiz Mode
Re: Iintegers between 100 and 150 - Common Counting problem [#permalink] New post   24 May 2010, 11:33
6
Kudos
9
Bookmarks
Expert Reply
shaneforu wrote:
17) How many integers between 100 and 150, inclusive, cannot be evenly divided by 3 nor 5?

a) 35
b) 27
c) 25
d) 26
e) 28

Please explain the answer

Show Spoiler
B


Total # between 100 and 150, inclusive = 51;

Multiples of 3 = (Last in the range - First in the range)/3+1=(150-102)/3+1=17;
Multiples of 5 = (Last in the range - First in the range)/5+1=(150-100)/5+1=11;

But these 17+11=28 numbers will include overlaps (meaning that some number are counted twice, for instance: 105). Numbers counted twice would be the numbers which are divisible by both 3 and 5 or by 15. Multiples of 15 = (Last in the range - First in the range)/15+1=(150-105)/15+1=4.

So total # = 51-17-11+4=27.

Answer: B.
General Discussion
User avatar
bibha
Manager
Manager
Joined: 14 Apr 2010
Posts: 99
Own Kudos [?]: 960 [0]
Given Kudos: 1
Send PM
Re: Iintegers between 100 and 150 - Common Counting problem [#permalink] New post   11 Jun 2010, 21:02
Bunuel,
Is this a formula? Can we apply in other similar problems?
Multiples of 3 = (Last in the range - First in the range)/3+1=(150-102)/3+1=17;
Multiples of 5 = (Last in the range - First in the range)/5+1=(150-100)/5+1=11;
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618681 [4]
Given Kudos: 81586
Send PM
CAT Tests Forum Quiz Mode
How many integers between 100 and 150, inclusive, cannot be [#permalink] New post   12 Jun 2010, 04:48
3
Kudos
1
Bookmarks
Expert Reply
bibha wrote:
Bunuel,
Is this a formula? Can we apply in other similar problems?
Multiples of 3 = (Last in the range - First in the range)/3+1=(150-102)/3+1=17;
Multiples of 5 = (Last in the range - First in the range)/5+1=(150-100)/5+1=11;


Yes. it is.

\(Number \ of \ multiples \ of \ x \ in \ the \ range = \)

\(=\frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1\).

How many multiples of 4 are there between 12 and 96, inclusive?

Last multiple of 4 IN the range is 96;
First multiple of 4 IN the range is 12;

\(\frac{96-12}{4}+1=22\).

OR: 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;

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

Hope it helps.
avatar
Nschiloff
Intern
Intern
Joined: 26 Feb 2011
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: Iintegers between 100 and 150 - Common Counting problem [#permalink] New post   23 Jul 2011, 06:13
By the way, if range goes from negative to positive, would zero also be a multiple? For example if it was "how many multiples of 7 are there between -28 and 28, inclusive?"
User avatar
WishMasterUA
Manager
Manager
Joined: 02 May 2011
Status:GMAT BATTLE - WIN OR DIE
Posts: 84
Own Kudos [?]: 235 [0]
Given Kudos: 13
Concentration: General Management, Entrepreneurship
GMAT Date: 12-22-2011
GPA: 3.81
WE:General Management (Hospitality and Tourism)
Send PM
Re: Iintegers between 100 and 150 - Common Counting problem [#permalink] New post   25 Jul 2011, 08:33
thanks for clear explanation
avatar
Ameya85
Intern
Intern
Joined: 10 Apr 2008
Posts: 23
Own Kudos [?]: 17 [0]
Given Kudos: 110
Location: India
GMAT 1: 560 Q39 V28
WE:Consulting (Computer Software)
Send PM
GMAT ToolKit User
Re: How many integers between 100 and 150, inclusive, cannot be [#permalink] New post   25 Nov 2014, 06:14
Bunuel

I did not understand what you added 4 here > 51-17-11 + 4 > why +4? I calculated other numbers correctly, but i added them all and was not able to find the answer in the options. Can you please explain what is my mistake? For overlapping set we use the formula Total = Group1 + Group 2 + Group 3 - (Common in 2 Groups) - 2 * (Common in all three groups) + None. How can this formula be used for question involving 2 groups instead of three?

Ameya
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92901
Own Kudos [?]: 618681 [2]
Given Kudos: 81586
Send PM
CAT Tests Forum Quiz Mode
Re: How many integers between 100 and 150, inclusive, cannot be [#permalink] New post   25 Nov 2014, 07:10
2
Kudos
Expert Reply
Ameya85 wrote:
Bunuel

I did not understand what you added 4 here > 51-17-11 + 4 > why +4? I calculated other numbers correctly, but i added them all and was not able to find the answer in the options. Can you please explain what is my mistake? For overlapping set we use the formula Total = Group1 + Group 2 + Group 3 - (Common in 2 Groups) - 2 * (Common in all three groups) + None. How can this formula be used for question involving 2 groups instead of three?

Ameya


{Total} = {Group 1} + {Group 1} - {Both} + {Neither}

51 = 17 + 11 - 4 + x
x = 27

Hope it's clear.
User avatar
B
law258
Senior Manager
Senior Manager
Joined: 05 Sep 2016
Status:DONE!
Posts: 274
Own Kudos [?]: 101 [0]
Given Kudos: 283
Send PM
Re: How many integers between 100 and 150, inclusive, cannot be [#permalink] New post   30 Nov 2016, 10:18
150-100+1 = 51 (total numbers)

(1) We need to calculate how many multiples of 3 are in 51

51/3 = 17

(2) Now let's calculate how many multiples of 5 are in 51

51/5 = 10

(3) Lastly, we need to look at how many multiples of 15 (3x5) are in 51 and add them back in

51/15 = 3

Overall: 51-(10+17)+3 = 27

B.
avatar
B
VP1030
Intern
Intern
Joined: 10 Mar 2022
Posts: 8
Own Kudos [?]: 0 [0]
Given Kudos: 25
Send PM
Re: How many integers between 100 and 150, inclusive, cannot be [#permalink] New post   22 Mar 2022, 09:58
Why is the word evenly used in the question?
GMAT Club Bot
gmatclubot
Re: How many integers between 100 and 150, inclusive, cannot be [#permalink]
22 Mar 2022, 09:58
Moderators:
Bunuel
Math Expert
92901 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions