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A certain computer program generates 4digit even numbers using the f
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10 Nov 2018, 10:30
Question Stats:
29% (02:44) correct 71% (02:43) wrong based on 194 sessions
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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%
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Re: A certain computer program generates 4digit even numbers using the f
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10 Nov 2018, 10:46
C . Total ways 540. Favourable ways 180, p= 33.35%



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Re: A certain computer program generates 4digit even numbers using the f
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10 Nov 2018, 10:47
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
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Re: A certain computer program generates 4digit even numbers using the f
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10 Nov 2018, 10:53
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



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A certain computer program generates 4digit even numbers using the f
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10 Nov 2018, 11:09
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.
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Re: A certain computer program generates 4digit even numbers using the f
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10 Nov 2018, 11:34
even numbers divisible by 4::
00 04 12 32 40 44 52
=(7*5*6/6*6*6*6)*100= ans A



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A certain computer program generates 4digit even numbers using the f
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Updated on: 13 Nov 2018, 01:00
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, 12:11.
Last edited by sowmiyav on 13 Nov 2018, 01:00, edited 1 time in total.



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Re: A certain computer program generates 4digit even numbers using the f
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10 Nov 2018, 18:17
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%
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Re: A certain computer program generates 4digit even numbers using the f
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11 Nov 2018, 09:14
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Re: A certain computer program generates 4digit even numbers using the f
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12 Nov 2018, 14:03
No calculations needed I guess:
Every second even number can be divided by 4. That means 50%.



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Re: A certain computer program generates 4digit even numbers using the f
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14 Nov 2018, 18:56
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



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Re: A certain computer program generates 4digit even numbers using the f
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15 Dec 2018, 05:36
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.
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Re: A certain computer program generates 4digit even numbers using the f
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14 Jan 2019, 06:40
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?



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Re: A certain computer program generates 4digit even numbers using the f
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14 Jan 2019, 06:44
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? Because 00 or simply 0 is also divisible by 4. Recall that 0 is divisible by every integer except 0 itself.
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Re: A certain computer program generates 4digit even numbers using the f
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14 Jan 2019, 06:54
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.
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Re: A certain computer program generates 4digit even numbers using the f
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14 Jan 2019, 06:58
Thank you Bunuel and Gladiator59 really helpful remarks.



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A certain computer program generates 4digit even numbers using the f
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21 Jan 2019, 10:03
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.



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A certain computer program generates 4digit even numbers using the f
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21 Jan 2019, 21:37
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. ]
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Re: A certain computer program generates 4digit even numbers using the f
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22 Jan 2019, 00:00
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
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