GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Nov 2018, 16:57

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

The integers from 1 to 100 inclusive are each written on a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
User avatar
Joined: 15 Jul 2004
Posts: 69
The integers from 1 to 100 inclusive are each written on a  [#permalink]

Show Tags

New post 09 Apr 2005, 00:13
3
12
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

62% (01:27) correct 38% (01:22) wrong based on 775 sessions

HideShow timer Statistics

The integers from 1 to 100 inclusive are each written on a single slip of paper and dropped into a jar. If one slip of paper is removed at random, approximately what is the probability that the number on it is neither even nor a multiple of 3?

A. 83%
B. 67%
C. 50%
D. 33%
E. 17%

_________________

===========================
Let us make hay while the sun shines.
Don Quixote. Part i. Book. iii. Chap. xi.

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

Show Tags

New post 19 Mar 2012, 02:48
2
4
Zem wrote:
The integers from 1 to 100 inclusive are each written on a single slip of paper and dropped into a jar. If one slip of paper is removed at random, approximately what is the probability that the number on it is neither even nor a multiple of 3?

A. 83%
B. 67%
C. 50%
D. 33%
E. 17%


# of multiples of 2 in the range (100-2)/2+1=50 (check this: totally-basic-94862.html#p730075);
# of multiples of 3 in the range (99-3)/3+1=33;
# of multiples of both 2 and 3, so multiples of 6, in the range (96-6)/6+1=16 (to get the overlap of above two sets);

Hence there are total of 50+33-16=67 numbers from 1 to 100, inclusive, which are multiples of 2 or 3, which means that the probability of selecting neither multiple of 2 nor multiple of 3 is 1-67/100=33/100=33%.

Answer: D.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
VP
VP
avatar
Joined: 30 Sep 2004
Posts: 1435
Location: Germany
  [#permalink]

Show Tags

New post 09 Apr 2005, 00:44
1
67%...

50/100 (all multiples of 2) + 33/100 (all multiples of 3) - 1650/10000 (multiples of 3 and 2) =6650/10000=67%...
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Senior Manager
Senior Manager
avatar
Joined: 19 Feb 2005
Posts: 461
Location: Milan Italy
  [#permalink]

Show Tags

New post 09 Apr 2005, 01:39
1
odd multiples of 3 are 17/100
3 3+6 3+6+6 3+6+6+6 etc
50/100+17/100=67/100
Senior Manager
Senior Manager
avatar
Joined: 15 Mar 2005
Posts: 405
Location: Phoenix
  [#permalink]

Show Tags

New post 09 Apr 2005, 02:20
2
1
Nither even nor a multiple of 3.

Even numbers between 1 and 100 are 2, 4, 6 ... 100 (50 numbers).

Numbers that are multiple of 3 are 3, 6, 9 ... 99. However, all even multiples of 3 have been counted already in even numbers. Therefore, this set includes 3, 9, 15, 21 ... 99. (17 numbers).

Thus total numbers that are to be excluded = 50 + 17 = 67.

Therefore probability that a randomly picked number is nither even nor a multiple of 3 = 33%
_________________

Who says elephants can't dance?

Senior Manager
Senior Manager
avatar
Joined: 19 Feb 2005
Posts: 461
Location: Milan Italy
  [#permalink]

Show Tags

New post 09 Apr 2005, 02:23
why I added instead of subtracting? :wall

Options >=50% should be ruled out soon because numbers range from 1 to 100, and thus subtracting 50 even you can't have more than 49 (you know at least that 3 is an odd multiple of 3, son you have at least 1 in 50 remaining numbers)

This question is asking nothing more than:
"how many odd numbers are in the first 100 positive ones that are not multiple of 3?"
Senior Manager
Senior Manager
avatar
Joined: 15 Mar 2005
Posts: 405
Location: Phoenix
  [#permalink]

Show Tags

New post 10 Apr 2005, 02:37
thearch wrote:
why I added instead of subtracting? :wall

Options >=50% should be ruled out soon because numbers range from 1 to 100, and thus subtracting 50 even you can't have more than 49 (you know at least that 3 is an odd multiple of 3, son you have at least 1 in 50 remaining numbers)

This question is asking nothing more than:
"how many odd numbers are in the first 100 positive ones that are not multiple of 3?"


Careful theArch, that wall is rather fragile !!!

Btw what're you saying? Your answer matches mine?
_________________

Who says elephants can't dance?

Senior Manager
Senior Manager
avatar
Joined: 19 Feb 2005
Posts: 461
Location: Milan Italy
  [#permalink]

Show Tags

New post 10 Apr 2005, 02:46
1
My first answer was 67/100.
However, I was deceived by christoph, because I calculated 67/100 and then I looked at answers already given, and forgot to subtract. This wouldn't happen in the actual test :)
Manager
Manager
avatar
Joined: 17 Dec 2004
Posts: 71
  [#permalink]

Show Tags

New post 10 Apr 2005, 05:49
2
33%

100 slips of paper: 50 are even, and 17 are odd multiples of 3

100-(50+17)=33
Director
Director
avatar
Joined: 18 Feb 2005
Posts: 641
  [#permalink]

Show Tags

New post 10 Apr 2005, 05:59
thearch wrote:
why I added instead of subtracting? :wall

Options >=50% should be ruled out soon because numbers range from 1 to 100, and thus subtracting 50 even you can't have more than 49 (you know at least that 3 is an odd multiple of 3, son you have at least 1 in 50 remaining numbers)

This question is asking nothing more than:
"how many odd numbers are in the first 100 positive ones that are not multiple of 3?"


This happens with many of us....We get there to the answer and forget subtracting.......GMAT has both the answers as a trap and we should be careful enough not to fall in it........
Senior Manager
Senior Manager
avatar
Joined: 15 Mar 2005
Posts: 405
Location: Phoenix
  [#permalink]

Show Tags

New post 11 Apr 2005, 11:24
Zem wrote:
but how you found the number: 17?


Zem, we are trying to find the numbers that are nither divisible by 2 nor 3.

If you take the numbers that are divisible by 2 away, you've taken all even numbers between 1 and 100 away. They are (100-1)/2 = 50 numbers.

We could repeat the same process with 3. However, there are numbers that are common to 2 and 3, and we don't have to take them out (they were accounted for in the even numbers list anyway).

So we see what are these numbers we're looking at (odd multiples of 3).
They are 3, 9, 15, 21 and so on.

There're a plathora of ways to figuring out how many such numbers would exist between 1 and 100. I'd list out two here.

One is the way of sequences.

the last number in this list would be 99.
99 = 3 + (n - 1) 6 => n = 17.

Else do a 100/16 = 16.xxx. 16*6 = 96. but since it starts at 3, the 16th multiple would be 99. 16 multiples, and add one (for 3) and you've 17.

Thus we have the number 17.

Hope that helps.
_________________

Who says elephants can't dance?

VP
VP
User avatar
Joined: 13 Jun 2004
Posts: 1080
Location: London, UK
Schools: Tuck'08
  [#permalink]

Show Tags

New post 11 Apr 2005, 19:30
I think that in this problem it's easier to find directly the prob than to use the formula 1-(opposite prob)

from 1 to 100 : 100 numbers
even numbers : 50
multiples of 3 : 33 (3*1, 3*2, ...3*33) however in those 33 numbers there are already even numbers and you have to be careful to not repeat the even numbers you've already taken out so finally you will get 17 odd and 16 even (you can see that everytime 3 is multiply by an even number the final result is obviously even so 1/2 of the multiples of 3 will be even and 1/2 odd, howver the last one is odd so there is an additionnal odd one)

17 odd multiples of 3 + 50 even numbers = 67

100-67 = 33 :wink:
Manager
Manager
avatar
Joined: 22 Jan 2012
Posts: 81
Location: India
Concentration: General Management, Technology
GPA: 3.3
WE: Engineering (Consulting)
Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

Show Tags

New post 18 Mar 2012, 19:56
1
Simple to solve using P(n) = 1-X concept

P = 1 - [ P(even 0r multiples of 2)+P(multiples of 3) - P(multiples of 2 and 3 or multiples of 6)]
P = (1 - [ 50/100+33/100 - 16/100]) = 33%
_________________

Press +1 Kudos rather than saying thanks
which is more helpful infact..

Ill be posting good questions as many as I can...

Towards Success

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1745
Concentration: Finance
GMAT ToolKit User
Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

Show Tags

New post 10 Dec 2013, 05:19
Zem wrote:
The integers from 1 to 100 inclusive are each written on a single slip of paper and dropped into a jar. If one slip of paper is removed at random, approximately what is the probability that the number on it is neither even nor a multiple of 3?

A. 83%
B. 67%
C. 50%
D. 33%
E. 17%


Bunuel is this approach correct?

Ballparking from 1 to 10 there are only 3 numbers that satisfy these conditions: 1,5 and 7. Then 3/10 so approximately 30% only answer choice that is close is D

If you do it for other ranges you are basically going to have 4,3,4,3,4,3 so in theory it would be something like 3.5/10 or between 30% and 35%

Cheers
J :)
Director
Director
User avatar
S
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 526
Location: India
GMAT 1: 780 Q51 V46
Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

Show Tags

New post 10 Dec 2013, 05:22
Zem wrote:
The integers from 1 to 100 inclusive are each written on a single slip of paper and dropped into a jar. If one slip of paper is removed at random, approximately what is the probability that the number on it is neither even nor a multiple of 3?

A. 83%
B. 67%
C. 50%
D. 33%
E. 17%


Multiple of 3: 100/3 = 33 numbers
Multiple of 2: 100/2 = 50 numbers

Multiple of 6: 100/6= 16 numbers

Total numbers divisible by 2 or 3: 50 + 33 - 16 = 67

Neither = 100 - 67 = 33

Probability = 33/100

Pushpinder Gill
_________________

For more info on GMAT and MBA, follow us on @AskCrackVerbal

Intern
Intern
avatar
Joined: 31 Oct 2015
Posts: 33
Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

Show Tags

New post 03 Jan 2016, 08:46
Even numbers = 100/2 = 50
Numbers divisible by 3 = 99/3 = 33
Even or divisible by 3 =
50 + 33 - duplicates(divisible by 3 and even)
Duplicates = 32/2 = 16
Even or divisible by 3 = 50 + 33 - 16
= 67
Numbers that are not even or divisible by 3 = 100 - 67 = 33
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2633
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

Show Tags

New post 14 Mar 2016, 00:12
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8818
Premium Member
Re: The integers from 1 to 100 inclusive are each written on a  [#permalink]

Show Tags

New post 20 Oct 2018, 04:06
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: The integers from 1 to 100 inclusive are each written on a &nbs [#permalink] 20 Oct 2018, 04:06
Display posts from previous: Sort by

The integers from 1 to 100 inclusive are each written on a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

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®.