 It is currently 24 Oct 2020, 10:04 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # A number is randomly chosen from the first 100 positive inte  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2971 , given: 394

A number is randomly chosen from the first 100 positive inte [#permalink]
Expert's post 00:00

Question Stats: 76% (00:19) correct 23% (00:50) wrong based on 51 sessions
A number is randomly chosen from the first 100 positive integers. What is the probability that it is a multiple of 3??

A. $$\frac{32}{100}$$
B. $$\frac{33}{100}$$
C. $$\frac{1}{3}$$
D. $$\frac{34}{100}$$
E. $$\frac{2}{3}$$
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2971  , given: 394

Re: A number is randomly chosen from the first 100 positive inte [#permalink]
1
KUDOS
Expert's post
Explanation

The first 100 positive integers comprise the set of numbers containing the integers 1 to 100.

Of these numbers, the only ones that are divisible by 3 are {3, 6, 9, …, 96, 99}, which adds up to exactly 33 numbers. This can be determined in several ways. One option is to count the multiples of 3, but that’s a bit slow. Alternatively, compute $$\frac{99}{3}= 33$$ and realize that there are 33 multiples of 3 up to and including 99.

The number 100 is not divisible by 3, so the correct answer is $$\frac{33}{100}$$.

Alternatively, use the “add one before you’re done” trick, subtracting the first multiple of 3 from the last multiple of 3, dividing by 3 and then adding 1: $$\frac{99-3}{3}+ 1 = 33$$.

Then, since probability is determined by the number of desired options divided by the total number of options, the probability that the number chosen is a multiple of 3 is $$\frac{33}{100}$$.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Manager  Joined: 06 Jun 2018
Posts: 94
Followers: 2

Kudos [?]: 80  , given: 0

Re: A number is randomly chosen from the first 100 positive inte [#permalink]
1
KUDOS
sandy wrote:
A number is randomly chosen from the first 100 positive integers. What is the probability that it is a multiple of 3??

A. $$\frac{32}{100}$$
B. $$\frac{33}{100}$$
C. $$\frac{1}{3}$$
D. $$\frac{34}{100}$$
E. $$\frac{2}{3}$$

Total numbers = 100

Total multiple of 3 = 33*3 = 99. It means there are 33 multiple of 3 up to 100.

Probability = 33 / 100. GRE Instructor Joined: 10 Apr 2015
Posts: 3871
Followers: 158

Kudos [?]: 4640  , given: 70

Re: A number is randomly chosen from the first 100 positive inte [#permalink]
1
KUDOS
Expert's post
sandy wrote:
A number is randomly chosen from the first 100 positive integers. What is the probability that it is a multiple of 3??

A. $$\frac{32}{100}$$
B. $$\frac{33}{100}$$
C. $$\frac{1}{3}$$
D. $$\frac{34}{100}$$
E. $$\frac{2}{3}$$

The multiples of 3 are as follows: 3, 6, 9, 12, .....96, 99

Notice that:
3 = 3(1)
6 = 3(2)
9 = 3(3)
12 = 3(4)
.
.
.
96 = 3(32)
99 = 3(33)

So, we can see that there are 33 multiples of 3 between 1 and 100.

So, P(chosen number is multiple of 3) = 33/100

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Re: A number is randomly chosen from the first 100 positive inte   [#permalink] 09 Apr 2020, 10:02
Display posts from previous: Sort by

# A number is randomly chosen from the first 100 positive inte  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.