January 22, 2019 January 22, 2019 10:00 PM PST 11:00 PM PST In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one. January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52385

How many 4digit positive integers are there in which all 4 digits are
[#permalink]
Show Tags
30 Sep 2016, 05:28
Question Stats:
65% (01:07) correct 35% (01:23) wrong based on 353 sessions
HideShow timer Statistics



Manager
Joined: 08 Aug 2015
Posts: 55

Re: How many 4digit positive integers are there in which all 4 digits are
[#permalink]
Show Tags
30 Sep 2016, 06:03
Positive integers  2,4,6,8,0
Let the integers of a four digit positive number be ABCD
A can take four values (2,4,6,8) B can take five values (0,2,4,6,8) C can take five values (0,2,4,6,8) D can take five values (0,2,4,6,8)
The total is 5*5*5*4
The answer according to me is 500



SVP
Joined: 06 Nov 2014
Posts: 1877

Re: How many 4digit positive integers are there in which all 4 digits are
[#permalink]
Show Tags
30 Sep 2016, 08:44
Bunuel wrote: How many 4digit positive integers are there in which all 4 digits are even?
A. 625 B. 600 C. 500 D. 400 E. 256 The 4  digit integer should be comprised of the following digits: 2, 4 ,6, 8, 0 For it to be a 4 digits integer, the first digit cannot be zero. Hence the following scenarios are possible 1st digit: (2,4,6,8) 2nd digit: (0,2,4,6,8) 3rd digit: (0,2,4,6,8) 4th digit: (0,2,4,6,8) Total numbers possible = 4*5*5*5 = 500 Correct Option: C



Intern
Joined: 26 Jul 2014
Posts: 12

Re: How many 4digit positive integers are there in which all 4 digits are
[#permalink]
Show Tags
30 Sep 2016, 08:50
E. 256
In the first place ( thousand place), i can choose 4 numbers : 2, 4, 6, 8 ( recall 0 is neither positive nor negative although O is even integer , don't confuse even with positive integer ) 2nd place ( hundred place) can also be filled up by 4 number : 2, 4, 6, 8 and same logic applies to 3rd ( 10th ) and 4th( unit) . so number of ways is 4*4*4*4= 256 ways .
Important concepts : if a task has two steps , step 1 can be done in n ways and step 2 can be done in m ways , then number of easy the task can be done is n*m ways . Same concept applies in above question.



Intern
Joined: 01 Jul 2014
Posts: 26
Location: India
GPA: 3.2

How many 4digit positive integers are there in which all 4 digits are
[#permalink]
Show Tags
30 Sep 2016, 12:46
We need to find: # of 4digit positive integers, all 4digits are even
Digits can be : 0,2,4,6,8 (0 is an even number) 4 digit integer = "_ _ _ _"
first place (Thousands place ) can be filled with 4 even integers : 2,4,6,8 (Why not 0?? > then the number will be a 3 digit number) second place (Hundreds Place) can be filled with 5 even integers : 0,2,4,6,8 (there is no restriction on repetition of digits) third place (Tens Place) can be filled with 5 even integers : 0,2,4,6,8 fourth place (Unit Place) can be filled with 5 even integers : 0,2,4,6,8
Hence total # : 4*5*5*5 =500
Hence C



Current Student
Joined: 26 Jan 2016
Posts: 103
Location: United States
GPA: 3.37

Re: How many 4digit positive integers are there in which all 4 digits are
[#permalink]
Show Tags
30 Sep 2016, 13:16
4 options for digit 1 (2,4,6,8), 5 options for digits 2,3,&4 (2,4,6,8,0)
4*5*5*5=500 C



Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 533
Location: India

Re: How many 4digit positive integers are there in which all 4 digits are
[#permalink]
Show Tags
01 Mar 2017, 01:09
Even digits: 0,2,4,6,8 The thousands place can be filled in 4 ways The hundreds place can be filled in 5 ways The tens place can be filled in 5 ways The ones place can be filled in 5 ways Therefore total number of numbers = 4*5*5*5 = 500. Option C
_________________
GMAT Mentors



Manager
Joined: 21 Jun 2017
Posts: 83

Re: How many 4digit positive integers are there in which all 4 digits are
[#permalink]
Show Tags
06 Mar 2018, 22:23
Bunuel wrote: How many 4digit positive integers are there in which all 4 digits are even?
A. 625 B. 600 C. 500 D. 400 E. 256 Even Digits: 0,2,4,6,8 (Five digits total) A 4digit positive integer starts out the thousandths place. In the thousandths place, the digit cannot be 0, because this makes the number a three digit, rather than four digit. Therefore, in the thousandths place, there is 4 possible options. in the hundreds place, we have 5 possible options; the same goes for the tens and singles. This information translates into this: 4x5x5x5 = 500 (C) Hope this helps



Intern
Joined: 04 May 2018
Posts: 1

Re: How many 4digit positive integers are there in which all 4 digits are
[#permalink]
Show Tags
08 Jul 2018, 01:25
sajib2126 wrote: E. 256
In the first place ( thousand place), i can choose 4 numbers : 2, 4, 6, 8 ( recall 0 is neither positive nor negative although O is even integer , don't confuse even with positive integer ) 2nd place ( hundred place) can also be filled up by 4 number : 2, 4, 6, 8 and same logic applies to 3rd ( 10th ) and 4th( unit) . so number of ways is 4*4*4*4= 256 ways .
Important concepts : if a task has two steps , step 1 can be done in n ways and step 2 can be done in m ways , then number of easy the task can be done is n*m ways . Same concept applies in above question. Can anyone refer to this excellent point highlited? zero is neither a negative or a positive number! How come the answer considers 0 as positive?




Re: How many 4digit positive integers are there in which all 4 digits are &nbs
[#permalink]
08 Jul 2018, 01:25






