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

 It is currently 17 Nov 2018, 09:23

# Join here

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

November 18, 2018

November 18, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
• ### 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.

# Let A be the vent that a randomly selected two digit number

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 Aug 2015
Posts: 2
Let A be the vent that a randomly selected two digit number  [#permalink]

### Show Tags

Updated on: 16 Aug 2015, 11:34
4
00:00

Difficulty:

25% (medium)

Question Stats:

80% (02:10) correct 20% (02:56) wrong based on 114 sessions

### HideShow timer Statistics

Let A be the event that a randomly selected two digit number is divisible by 3 and let B be the event that a randomly selected two digit number is divisible by 5. What is P(A and B)?

A. 1/18
B. 1/15
C. 1/5
D. 1/3
E. 1/2

Originally posted by tonytran14896 on 06 Aug 2015, 11:58.
Last edited by Bunuel on 16 Aug 2015, 11:34, edited 2 times in total.
Edited the question and moved to PS forum.
CEO
Joined: 20 Mar 2014
Posts: 2635
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Let A be the vent that a randomly selected two digit number  [#permalink]

### Show Tags

06 Aug 2015, 12:22
1
tonytran14896 wrote:
Let A be the event that a randomly selected two digit number is divisible by 3 and let B be the event that a randomly selected two digit number is divisible by 5. What is P(A and B)?
a. 1/18
b.1/15
c.1/5
d.1/3
e.1/2

I know the answer is b:1/15 but i don't know how to explain it. Please clarify for me. Thanks.

Please format the question properly and mention anything related to the solution either in another post or put it under "spoiler" as shown above.

For 2 independent events ,

P(A and B) = P(A)*P(B)

where
P(A) = selecting a multiple of 3 in all the 2 digit numbers = Favorable cases/ Total cases = 30/90 = 1/3
P(B) = selecting a multiple of 5 in all the 2 digit numbers = Favorable cases/ Total cases = 18/90 = 1/5

Thus, P(A and B) = P(A)*P(B) = (1/3)(1/5) = 1/15 . B is the correct answer.
Manager
Joined: 20 Jul 2011
Posts: 80
GMAT 1: 660 Q49 V31
Re: Let A be the vent that a randomly selected two digit number  [#permalink]

### Show Tags

10 Aug 2015, 11:09
tonytran14896 wrote:
Let A be the event that a randomly selected two digit number is divisible by 3 and let B be the event that a randomly selected two digit number is divisible by 5. What is P(A and B)?
a. 1/18
b.1/15
c.1/5
d.1/3
e.1/2

b:1/15
but i don't know how to explain it. Please clarify for me. Thanks.

We know that

P(A and B) = P(A) * P(B)

Event where a two digit no is divisible by 3 => 30 (12 to 99)
Total two digit no.s = 90
Hence P(A) = 30/90 => 1/3

Similarly, Event where a two digit no is divisible by 5 => 18 (10 to 95)
P(B) = 18/90 => 1/5

P(A and B) = 1/3 * 1/5 => 1/15

Option B
Intern
Joined: 01 Nov 2015
Posts: 36
Location: India
Concentration: Marketing, Entrepreneurship
WE: Engineering (Computer Software)
Re: Let A be the vent that a randomly selected two digit number  [#permalink]

### Show Tags

30 Nov 2015, 18:37
Given that P(A) be the probability that a number divisible by 3 and P(B) be the probability that a number is divisible by 5

=> P ( A and B ) is the number divisible by both 3 and 5

the Numbers are 15, 30, 45, 60, 75, 90 => 6

Total No of Events = Count (10 to 99) = 90

Therefore $$P(A and B) = \frac{Favorable Events}{Total Events}$$$$= \frac{6}{90} = \frac{1}{15}$$

Ans: B
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6517
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Let A be the vent that a randomly selected two digit number  [#permalink]

### Show Tags

30 Nov 2015, 23:36
1
2
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

Let A be the event that a randomly selected two digit number is divisible by 3 and let B be the event that a randomly selected two digit number is divisible by 5. What is P(A and B)?

A. 1/18
B. 1/15
C. 1/5
D. 1/3
E. 1/2

The event A and B means that a randomly selected two digit number is divisible by both 3 and 5. Since the least common multiple of 3 and 5 is 15, that event is same as a randomly selected two digit number is divisible by 15.

The total number of two digit number is 90(from 10 to 99 inclusively). The number of the multiples of 15 from 10 to 99 is [100/15]=6.

So P(A and B) = 6/90 = 3/45 = 1/15. So the answer is B.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Board of Directors
Joined: 17 Jul 2014
Posts: 2645
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Let A be the vent that a randomly selected two digit number  [#permalink]

### Show Tags

27 Apr 2016, 19:28
1
can't believe I missed this one because of a silly mistake...
we have 90 numbers.
we need positive outcomes when the numbers are divisible by 3 and 5.
we have: 15, 30, 45, 60, 75, 90 - 6 numbers.
6/90 = 1/15
Non-Human User
Joined: 09 Sep 2013
Posts: 8801
Re: Let A be the vent that a randomly selected two digit number  [#permalink]

### Show Tags

17 Jul 2018, 02:50
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.
_________________
Re: Let A be the vent that a randomly selected two digit number &nbs [#permalink] 17 Jul 2018, 02:50
Display posts from previous: Sort by