Mar 20 07:00 AM PDT  09:00 AM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Mar 20 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Wednesday, March 20th at 9 PM EDT Mar 23 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 13 Oct 2015
Posts: 17

If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
Show Tags
Updated on: 06 Jun 2016, 22:42
Question Stats:
62% (02:21) correct 38% (02:16) wrong based on 105 sessions
HideShow timer Statistics
If an integer is randomly chosen from the numbers 250 to 449, inclusive, what is the probability that all the digits of the number are even? (A) 3/5 (B) 17/50 (C) 1/8 (D) 51/199 (E) 1/4
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by DrAB on 06 Jun 2016, 21:10.
Last edited by DrAB on 06 Jun 2016, 22:42, edited 1 time in total.



Manager
Joined: 29 Nov 2011
Posts: 92

Re: If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
Show Tags
06 Jun 2016, 21:57
I took C as answer but it wrong...I dont know what am i missing keeping 2 as first digit , we can 6 and 8 at the second digit and 0,2,4,6,8 as third digit so ultimately , 2*5 = 10
keeping 4 at the first digit we can have 0 , 2,4 at the second, and third can be any of the 5 even. so we will have 15 total will be 25/200 = 1/8. so i guess C should be the answer.
Had it been chosen from only even then i would have think of 25/100 = 1/4



Math Expert
Joined: 02 Aug 2009
Posts: 7419

Re: If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
Show Tags
06 Jun 2016, 22:32
sudhirmadaan wrote: I took C as answer but it wrong...I dont know what am i missing keeping 2 as first digit , we can 6 and 8 at the second digit and 0,2,4,6,8 as third digit so ultimately , 2*5 = 10
keeping 4 at the first digit we can have 0 , 2,4 at the second, and third can be any of the 5 even. so we will have 15 total will be 25/200 = 1/8. so i guess C should be the answer.
Had it been chosen from only even then i would have think of 25/100 = 1/4 HI, I do not think there is anything wrong in your approach... Another way of doing it is 1)The hundreds digit can be choosen from 2,3, and 4 but number of 3s in hundreds digit is equal to total number of 2s and 4s.. so prob of picking an even number is 1/2.... 2) Probability of picking even TENS digit is 1/2 ........ 5 even from total 10 digits 3) Prbability of picking even UNITS digit is 1/2 ........ 5 even from total 10 digits.... So probability = 1/2*1/2*1/2 = 1/8 C
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert



Manager
Joined: 18 May 2016
Posts: 67
Concentration: Finance, International Business
GPA: 3.7
WE: Analyst (Investment Banking)

Re: If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
Show Tags
06 Jun 2016, 23:00
I chose to solve this question by finding the total of numbers in the range and of numbers that fulfil the criteria, i.e. all digits are even. Total of numbers in the provided range: 449  250 +1 = 200 From 250: 1*2*5 = 10 300: none 400 to 449 = 1*3*5 = 15 Total: 12+8 = 25 Probability = \(\frac{25}{200} = \frac{5}{40} = \frac{1}{8}\)
_________________
Please kindly +Kudos if my posts or questions help you!
My debrief: Selfstudy: How to improve from 620(Q39,V36) to 720(Q49,V39) in 25 days!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8997
Location: Pune, India

Re: If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
Show Tags
06 Jun 2016, 23:10
DrAB wrote: If an integer is randomly chosen from the numbers 250 to 449, inclusive, what is the probability that all the digits of the number are even?
(A) 3/5 (B) 17/50 (C)1/8 (D) 51/199 (E) 1/4 Another method is to enumerate the hundreds and tens digits which are acceptable: 26 __ 28 __ 40 __ 42 __ 44 __ In each case, any of the 5 even digits (0, 2, 4, 6, 8) can take the units place. So acceptable cases = 5*5 = 25 Total number of integers = 200 Probability = 25/200 = 1/8
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 534
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

Re: If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
Show Tags
06 Jun 2016, 23:48
fantaisie wrote: I chose to solve this question by finding the total of numbers in the range and of numbers that fulfil the criteria, i.e. all digits are even.
Total of numbers in the provided range: 449  250 +1 = 200
From 250: 1*2*5 = 10 300: none 400 to 449 = 1*3*5 = 15
Total: 12+8 = 25
Probability = \(\frac{25}{200} = \frac{5}{40} = \frac{1}{8}\) Nice approach I did the problem on probability approach: Probability of getting even number in the UNIT digit= (\(\frac{(299250+1)+(449400+1)}{449250+1}\))=\(\frac{100}{200}\)=\(\frac{1}{2}\) Probability of f getting even number in the tens digit=\(\frac{(3+2)}{3+2+5}\)=\(\frac{5}{10}\)=\(\frac{1}{2}\) Probability of f getting even number in the Hundred digit=\(\frac{1}{2}\) So the probablity of getting Even number in all digits within this range=\(\frac{1}{2}\)*\(\frac{1}{2}\)*\(\frac{1}{2}\)=\(\frac{1}{8}\) Correct answer C
_________________
Md. Abdur Rakib
Please Press +1 Kudos,If it helps Sentence CorrectionCollection of Ron Purewal's "elliptical construction/analogies" for SC Challenges



Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 534
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)

Re: If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
Show Tags
06 Jun 2016, 23:56
VeritasPrepKarishma wrote: DrAB wrote: If an integer is randomly chosen from the numbers 250 to 449, inclusive, what is the probability that all the digits of the number are even?
(A) 3/5 (B) 17/50 (C)1/8 (D) 51/199 (E) 1/4 Another method is to enumerate the hundreds and tens digits which are acceptable: 26 __ 28 __ 40 __ 42 __ 44 __ In each case, any of the 5 even digits (0, 2, 4, 6, 8) can take the units place. So acceptable cases = 5*5 = 25 Total number of integers = 200 Probability = 25/200 = 1/8 Nice approach. I didn't get your approach easily first May I know this approach more broadly ?
_________________
Md. Abdur Rakib
Please Press +1 Kudos,If it helps Sentence CorrectionCollection of Ron Purewal's "elliptical construction/analogies" for SC Challenges



Manager
Joined: 18 May 2016
Posts: 67
Concentration: Finance, International Business
GPA: 3.7
WE: Analyst (Investment Banking)

If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
Show Tags
07 Jun 2016, 00:17
AbdurRakib wrote: VeritasPrepKarishma wrote: DrAB wrote: If an integer is randomly chosen from the numbers 250 to 449, inclusive, what is the probability that all the digits of the number are even?
(A) 3/5 (B) 17/50 (C)1/8 (D) 51/199 (E) 1/4 Another method is to enumerate the hundreds and tens digits which are acceptable: 26 __ 28 __ 40 __ 42 __ 44 __ In each case, any of the 5 even digits (0, 2, 4, 6, 8) can take the units place. So acceptable cases = 5*5 = 25 Total number of integers = 200 Probability = 25/200 = 1/8 Nice approach. I didn't get your approach easily first May I know this approach more broadly ? I think this is the same approach as the one I presented above, just more of a shortcut. She first evaluates how many different combinations of the two first digits are possible, thus the list of 2 digit combinations (hundrends and tenths) which in total equals to 5 different combinations that satisfy the requirements given by the range and also that all digits are even. She then checks how many different numbers would be applicable to each combination of digits, which is also five. So every 2 digit combination will have 5 options for the last digit, eg: 260, 262, 264, 266, 268 280, 282, 284, 286, 288 I hope it helps!
_________________
Please kindly +Kudos if my posts or questions help you!
My debrief: Selfstudy: How to improve from 620(Q39,V36) to 720(Q49,V39) in 25 days!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8997
Location: Pune, India

Re: If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
Show Tags
07 Jun 2016, 22:54
AbdurRakib wrote: VeritasPrepKarishma wrote: DrAB wrote: If an integer is randomly chosen from the numbers 250 to 449, inclusive, what is the probability that all the digits of the number are even?
(A) 3/5 (B) 17/50 (C)1/8 (D) 51/199 (E) 1/4 Another method is to enumerate the hundreds and tens digits which are acceptable: 26 __ 28 __ 40 __ 42 __ 44 __ In each case, any of the 5 even digits (0, 2, 4, 6, 8) can take the units place. So acceptable cases = 5*5 = 25 Total number of integers = 200 Probability = 25/200 = 1/8 Nice approach. I didn't get your approach easily first May I know this approach more broadly ? Here is the way I thought about it: The number has to be chosen from 250 to 449. All digits have to be even. Let's consider the acceptable hundreds and tens digits : 26 __  The units digit can be any even digit since all numbers in the range 260 to 269 are included. 28 __  The units digit can be any even digit since all numbers in the range 280 to 289 are included. 3 __ __  All such numbers are not acceptable since 3 is odd. Move on to 4 __ __ 40 __  The units digit can be any even digit since all numbers in the range 400 to 409 are included. 42 __  The units digit can be any even digit since all numbers in the range 420 to 429 are included. 44 __  The units digit can be any even digit since all numbers in the range 440 to 449 are included. Each of the acceptable 5 options have further 5 options for the units digit: 260, 262, 264, 266, 268 280, 282, 284, 286, 288 ... and so on So there will be 25 such numbers.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



NonHuman User
Joined: 09 Sep 2013
Posts: 10152

Re: If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
Show Tags
05 Jan 2019, 10:50
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If an integer is randomly chosen from the numbers 250 to 449, inclusiv
[#permalink]
05 Jan 2019, 10:50






