February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT February 24, 2019 February 24, 2019 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1207
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
10 Nov 2018, 09:30
Question Stats:
28% (02:44) correct 72% (02:44) wrong based on 187 sessions
HideShow timer Statistics
GMATbuster's Weekly Quant Quiz#8 Ques #10 For Questions from earlier quizzes: Click HereA certain computer program generates 4digit even numbers using the following numbers: O, 1, 2, 3, 4, and 5. If the digits can be repeated, what Is the probability that a number formed by this program will be a multiple of 4? A) 16.7% B) 25% C) 33.3% D) 50% E) 75%
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Win GMAT CLUB Test Weekly Quant Quiz Contest Weekly Quant Quiz Questions Direct Download SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS



Intern
Joined: 05 Mar 2017
Posts: 5

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
10 Nov 2018, 09:46
C . Total ways 540. Favourable ways 180, p= 33.35%



Manager
Joined: 09 Jun 2018
Posts: 189
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
10 Nov 2018, 09:47
Let number formed be X X X X. First three spots can be taken by 6 digits each. Last spot can be taken by 0, 2, 4 only for it to form an even number. So total possible = 6*6*6*3 For number to be multiple of 4, we need last two digits to be 00,04,12,20,24,32,40,44,52, so 9 possible values. First two spots can be taken by 6 digits each. So number of values = 6*6*9 Probability = 6*6*9/6*6*6*3 = 1/2 = 50% Hence D
_________________
If you found this relevant and useful, please Smash that Kudos button!



Manager
Joined: 04 Jun 2018
Posts: 156
GMAT 1: 610 Q48 V25 GMAT 2: 690 Q50 V32 GMAT 3: 710 Q50 V36

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
10 Nov 2018, 09:53
A certain computer program generates 4digit even numbers using the following numbers: O, 1, 2, 3, 4, and S. If the digits can be repeated, what Is the probability that a number formed by this program will be a multiple of 4?
We have O,1,2,3,4,S
Repetition is allowed
Total no. of cases: 6*6*6*2= 432(we multiply by 2 since the no. of even numbers =2,4)
Total no. of cases where it is divisible by 4:
Cases last 2 digits are div by 4: 24,44 (42 and 22 not eligible)
6*6*2=72
72/432=16.7
Option A Ans



RC Moderator
Joined: 24 Aug 2016
Posts: 681
Location: Canada
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28 GMAT 2: 540 Q49 V16

A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
10 Nov 2018, 10:09
I would like to go with the solution below : The question basically asks a us : (numbers div by 4 out of those generated from 0,1,2,3,4 & 5) / (numbers div by 2 out of those generated from 0,1,2,3,4 & 5) . Say , the numbers div by 2 out of those generated from 0,1,2,3,4 & 5 is x. Definitely numbers div by 4 out of those generated from 0,1,2,3,4 & 5 is x/2 ( as in every two consecutive even integers , one is div by 4 and the other is not ) Hence , P = (x/2)/x=1/2 =50% Ans D.
_________________
Please let me know if I am going in wrong direction. Thanks in appreciation.



Intern
Joined: 31 Oct 2018
Posts: 10

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
10 Nov 2018, 10:34
even numbers divisible by 4::
00 04 12 32 40 44 52
=(7*5*6/6*6*6*6)*100= ans A



Intern
Joined: 09 Nov 2018
Posts: 27

A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
Updated on: 13 Nov 2018, 00:00
Total possible number of 4 digit even numbers with the given number = 5*6*6*3 =540 If a number is to be divisible by 4, then the last 2 digits should be divisible by 4. If the 3rd digit is 0, the possible values for 4th digit are 0 or 4. so, possibilities of a number divisible by 4 and ending in even when 3rd digit is 0 = 5*6*1*2 = 60 If the 3rd digit is 1, the possible value for 4th digit is 2. so, possibilities of a number divisible by 4 and ending in even when 3rd digit is 1 = 5*6*1*1 = 30 If the 3rd digit is 2, the possible values for 4th digit are 0 or 4. so, possibilities of a number divisible by 4 and ending in even when 3rd digit is 2 = 5*6*1*2 = 60 If the 3rd digit is 3, the possible value for 4th digit is 2. so, possibilities of a number divisible by 4 and ending in even when 3rd digit is 3 = 5*6*1*1 = 30 If the 3rd digit is 4, the possible values for 4th digit are 0 or 4. so, possibilities of a number divisible by 4 and ending in even when 3rd digit is 4 = 5*6*1*2 = 60 If the 3rd digit is 5, the possible value for 4th digit is 2. so, possibilities of a number divisible by 4 and ending in even when 3rd digit is 5 = 5*6*1*1 = 30 Total possibilities of a 4 digit number divisible by 4 and ending in even = (60+30+60+30+60+30)=270 probability= 270/540 = 50%
OPTION D
Originally posted by sowmiyav on 10 Nov 2018, 11:11.
Last edited by sowmiyav on 13 Nov 2018, 00:00, edited 1 time in total.



Intern
Joined: 30 Sep 2018
Posts: 16

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
10 Nov 2018, 17:17
We know that there are in all, total of 6 digits to choose from.
Letter O, 1, 2, 3, 4, and letter S.
1st case: (different numbers that are a multiple and hence divisible by 4)
For any number to be divisible by 4, the rule is that it's last two digits have to be divisible by 4.
_ _ _ _ (4 digit numbers that can be formed)
Using the digits available and knowing that repetition is allowed, we have only two different ways of filling the last two spots  24 44
Therefore, the number of ways in which we can have the 4 digit number divisible by 4 is
6 6 2 (since first two places are allowed repetition and there are 6 digits to choose from)
6*6*2 ways
2nd case (total number of even 4 digit numbers that can be formed)
From the digits available, the last digit has to either be 2 or 4 for the 4digit number to be even.
Therefore, number of ways possible  6*6*6*2 ways
Concluding the solution
Probability of having a 4digit number divisible by 4, therefore, can be calculated as below
= (6*6*2 / 6*6*6*2) * 100 = (1/6) * 100 = 16.67%
Ans. (A) 16.67%
Posted from my mobile device



Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1207
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
11 Nov 2018, 08:14



Intern
Joined: 23 Feb 2018
Posts: 1

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
12 Nov 2018, 13:03
No calculations needed I guess:
Every second even number can be divided by 4. That means 50%.



Manager
Joined: 29 May 2017
Posts: 128
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
14 Nov 2018, 17:56
MichaelGolth wrote: No calculations needed I guess:
Every second even number can be divided by 4. That means 50%. Hello... very interesting......can you elaborate on this please? regards



Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1207
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
15 Dec 2018, 04:36
MichaelGolth, Mansoor50"MichaelGolth wrote: No calculations needed I guess:
Every second even number can be divided by 4. That means 50%."Above approach is valid only when number of even numbers are even.
For example, suppose set of even numbers are (2,4,6). Here no of multiple of 4 is not half the total no of even numbers.
_________________
Win GMAT CLUB Test Weekly Quant Quiz Contest Weekly Quant Quiz Questions Direct Download SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS



Intern
Joined: 16 Jul 2018
Posts: 28

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
14 Jan 2019, 05:40
Gladiator59, Hi gladi,just a prompt question for you, based on a divisibility rule (it is also written in the OA) if the last 2 digits of a number are divisible by 4 then the whole number is divisible by 4 right? However I was wondering why in this case the choices which end in 00 are also included is it also part of a rule or just an assumption?



Math Expert
Joined: 02 Sep 2009
Posts: 53067

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
14 Jan 2019, 05:44



Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 722

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
14 Jan 2019, 05:54
Hi UNSTOPPABLE12, Hope you are doing great! Please find my responses in red to your specific questions  UNSTOPPABLE12 wrote: Gladiator59, Hi gladi,just a prompt question for you, based on a divisibility rule (it is also written in the OA) if the last 2 digits of a number are divisible by 4 then the whole number is divisible by 4 right? Perfect  this is the divisibility test of 4 However I was wondering why in this case the choices which end in 00 are also included is it also part of a rule or just an assumption? 00 is also divisible by 4  0 in fact is divisible by all integers Also, have you checked out the more elegant solution by u1983? Once we confirm that an even number of total even 4digit numbers are present it becomes obvious that half of them will be divisible by 4. Why am I putting this additional rule? Let's say we have 2,4,6 ... only 4 is divisible by 4. But if we have 2,4,6,8  2/4 or 50% are divisible by 4. As long as the total even numbers are even, and consecutive ( which is exactly the case here) we can directly say 50% without computing the actual number of even diivisble by 4. Even just the method shown in OE is sufficient to get the question in under 2 mins. Hope it helps.
_________________
Regards, Gladi
“Do. Or do not. There is no try.”  Yoda (The Empire Strikes Back)



Intern
Joined: 16 Jul 2018
Posts: 28

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
14 Jan 2019, 05:58
Thank you Bunuel and Gladiator59 really helpful remarks.



Intern
Status: when you say,"I can or I can't", Both times you are right!
Joined: 26 Nov 2018
Posts: 9

A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
21 Jan 2019, 09:03
UNSTOPPABLE12 wrote: Gladiator59, Hi gladi,just a prompt question for you, based on a divisibility rule (it is also written in the OA) if the last 2 digits of a number are divisible by 4 then the whole number is divisible by 4 right? However I was wondering why in this case the choices which end in 00 are also included is it also part of a rule or just an assumption? the number ends with 00 always divisible by 4.



Intern
Joined: 22 Feb 2017
Posts: 23
Location: India
GPA: 3.6
WE: Engineering (Manufacturing)

A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
21 Jan 2019, 20:37
nkin wrote: Let number formed be X X X X. First three spots can be taken by 6 digits each. Last spot can be taken by 0, 2, 4 only for it to form an even number. So total possible = 6*6*6*3
For number to be multiple of 4, we need last two digits to be 00,04,12,20,24,32,40,44,52, so 9 possible values. First two spots can be taken by 6 digits each. So number of values = 6*6*9
Probability = 6*6*9/6*6*6*3 = 1/2 = 50%
Hence D The 1st spot can't be taken by '0' coz its clearly mentioned that the digit is '4digit' => 0441, 0532 these are 3digits ; So, total such no.s with repetitions allowed = 5x6x6x3 Similarly to be multiple of 4 the last 2digits can be 00,04,12,20,24,32,40,44,52. As you mentioned ; First spot can be taken here as well by '5digits' and not '6' [0 doesn't counts] So, total such no.s = 5x6x9 P (divisible by 4) = [5x6x6x3] / [5x6x9] = 1/2 or 50% [NOTE The answer will be same as in both cases '6' or '5' gets cancelled. ]



Intern
Joined: 21 Jan 2019
Posts: 1

Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
Show Tags
21 Jan 2019, 23:00
mishugarg wrote: even numbers divisible by 4::
00 04 12 32 40 44 52
=(7*5*6/6*6*6*6)*100= ans A What about 20? It’s also divisible by 4. Posted from my mobile device




Re: A certain computer program generates 4digit even numbers using the f
[#permalink]
21 Jan 2019, 23:00






