Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 27 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

CEO
Joined: 12 Sep 2015
Posts: 3854
Location: Canada

Re: How many fivedigit numbers can be formed from the digits 0,
[#permalink]
Show Tags
29 Aug 2018, 16:25
rodri102 wrote: Hi Bunuel. Could you clarify why we can't use 0 as the first digit? The question doesn't mention this as a restriction. Thanks! A 5digit number can't have 0 in the ten thousands position. For example, 03212 is not considered a 5digit number. If we allowed the first digit to be zero, then even a basic number like 1 could be a 2digit number (01), a 3digit number (001), a 4digit number (0001), etc Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Intern
Joined: 16 Jun 2018
Posts: 15

Re: How many fivedigit numbers can be formed from the digits 0,
[#permalink]
Show Tags
23 Sep 2018, 13:23
Hi, we need to form 5 digit number , if we start with 0 then we would only be able to form a 4 digit number. (restriction mentioned in question stem). Hope it helps. rodri102 wrote: Hi Bunuel. Could you clarify why we can't use 0 as the first digit? The question doesn't mention this as a restriction. Thanks!



Intern
Joined: 28 Aug 2016
Posts: 11

Re: How many fivedigit numbers can be formed from the digits 0,
[#permalink]
Show Tags
15 Jan 2019, 20:07
guerrero25 wrote: How many fivedigit numbers can be formed from the digits 0, 1, 2, 3, 4, and 5, if no digits can repeat and the number must be divisible by 4?
A. 36 B. 48 C. 72 D. 96 E. 144 I believe if we just calculate outcome for the first three digits  we will get 5*5*4 or 100 (first digit  we can't use zero, next digit with zero as a possibility, next =4 as the first 2 digits are used). Calculating for any more possibilities should be more than 100, leaving only E as an option.



Senior Manager
Joined: 12 Sep 2017
Posts: 298

Re: How many fivedigit numbers can be formed from the digits 0,
[#permalink]
Show Tags
24 Jan 2019, 17:05
Hello!
Can someone please explain to me why are not we taking the following last two digits?
48, 36, 16, etc...?
Why just must be 04, 12, 20, 24, 32, 40, or 52.
Kind regards!



Intern
Joined: 28 Aug 2016
Posts: 11

Re: How many fivedigit numbers can be formed from the digits 0,
[#permalink]
Show Tags
24 Jan 2019, 18:59
jfranciscocuencag wrote: Hello!
Can someone please explain to me why are not we taking the following last two digits?
48, 36, 16, etc...?
Why just must be 04, 12, 20, 24, 32, 40, or 52.
Kind regards! because we don't really have number 6 here: "How many fivedigit numbers can be formed from the digits 0, 1, 2, 3, 4, and 5, if no digits can repeat and the number must be divisible by 4?"



Intern
Joined: 04 Oct 2016
Posts: 17

Re: How many fivedigit numbers can be formed from the digits 0,
[#permalink]
Show Tags
24 Jan 2019, 19:47
rodri102 wrote: Hi Bunuel. Could you clarify why we can't use 0 as the first digit? The question doesn't mention this as a restriction. Thanks! The question says 5 digit number. Did we ever hear a 5digit number with a zero in the starting? something like 02367? It becomes a 4 digit number, not 5. It is not necessary to explicitly mention that 0 cannot be the first digit. That's the ground rule. Hope you understood!



Intern
Joined: 06 Feb 2018
Posts: 5
Location: Uzbekistan
GPA: 3.5

Re: How many fivedigit numbers can be formed from the digits 0,
[#permalink]
Show Tags
09 Mar 2019, 14:57
matcarvalho wrote: guerrero25 wrote: How many fivedigit numbers can be formed from the digits 0, 1, 2, 3, 4, and 5, if no digits can repeat and the number must be divisible by 4?
A. 36 B. 48 C. 72 D. 96 E. 144 My approach: Total of 600 possible number: 5x5x4x3x2x1 (zero can't be the 1st digit) Of those 600 number, 300 are even, because you have 3 odd and 3 even numbers. Of those 300 even numbers, about half are multiple of 4. So answer choice E. This way is faster than Bunuel's solutions! Btw you could count even numbers this way: 4*4*3*2*3=288



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6967
Location: United States (CA)

Re: How many fivedigit numbers can be formed from the digits 0,
[#permalink]
Show Tags
13 Apr 2019, 19:06
guerrero25 wrote: How many fivedigit numbers can be formed from the digits 0, 1, 2, 3, 4, and 5, if no digits can repeat and the number must be divisible by 4?
A. 36 B. 48 C. 72 D. 96 E. 144 To be divisible by 4, the last two digits of the number must be divisible by 4. Therefore, they can be 04, 12, 20, 24, 32, 40, and 52. We can split these into two groups: 1) 04, 20, 40, and 2) 12, 24, 32, 52 Group 1: If the last two digits are 04, then there are 4 choices for the first (or tenthousands) digit, 3 choices for the second (or thousands) digit, and 2 choices for the third (or hundreds) digit. So we have 4 x 3 x 2 = 24 such numbers if the last two digits are 04. Also there should be 24 numbers if the last two digits are 20 or 40. So we have 24 x 3 = 72 numbers in this group. Group 2: If the last two digits are 12, then there are 3 choices for the first (or tenthousands) digit (since it can’t be 0), 3 choices for the second (or thousands) digit, and 2 choices for the third (or hundreds) digit. So we have 3 x 3 x 2 = 18 such numbers if the last two digits are 12. Also there should be 18 numbers if the last two digits are 24, 32 or 52. So we have 18 x 4 = 72 numbers in this group also. Therefore, there are a total of 72 + 72 = 144 numbers. Answer: E
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4260
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: How many fivedigit numbers can be formed from the digits 0,
[#permalink]
Show Tags
22 Apr 2019, 04:35
guerrero25 wrote: How many fivedigit numbers can be formed from the digits 0, 1, 2, 3, 4, and 5, if no digits can repeat and the number must be divisible by 4?
A. 36 B. 48 C. 72 D. 96 E. 144 a good question for a no to be divisible by 4 , the last 2 digits have to be divisible by 4 possible options 04,12,20,24,32,40,52 we have three options with 0 as units or tens place so pair possible 4*3*2*1 = 24 and three such pairs are there so 24 * 3 ; 72 also for rest 4 sets ; possible pairs without 0 ; 3*3*2*1 = 18 * 4 ; 72 total pairs; 72 + 72 ; 144 IMO E
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.




Re: How many fivedigit numbers can be formed from the digits 0,
[#permalink]
22 Apr 2019, 04:35



Go to page
Previous
1 2
[ 29 posts ]



