A natural number consists of only 0's and 1's. If the number is divisible by 375, then what is the least possible number of 0's and 1's in the number respectively?
(a) 6 and 3 (b) 3 and 6 (c) 6 and 9 (d) 3 and 4 e) None of these
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
Number system
This topic has expert replies
-
batwaraanirudh
- Junior | Next Rank: 30 Posts
- Posts: 10
- Joined: Thu Mar 28, 2013 5:26 am
- Thanked: 1 times
Prime factors of 375 = 5*5*5*3A natural number consists of only 0's and 1's. If the number is divisible by 375, then what is the least possible number of 0's and 1's in the number respectively?
So the natural number that we are talking about should be divisible by 3
For any number to be divisible by the sum of the digits should be divisible by 3. Since the digits can be only 0s or 1s, minimum number of 1s require is 3.
the number should also be divisible by three 5s. So the number should have atleast 3 0s at the end. Since we cannot have any 5s.
Therefore the least possible number is 111000. This number is divisible by 375
Therefore choose E
-
ganeshrkamath
- Master | Next Rank: 500 Posts
- Posts: 283
- Joined: Sun Jun 23, 2013 11:56 pm
- Location: Bangalore, India
- Thanked: 97 times
- Followed by:26 members
- GMAT Score:750
375 = 125 * 3sanjoy18 wrote:A natural number consists of only 0's and 1's. If the number is divisible by 375, then what is the least possible number of 0's and 1's in the number respectively?
(a) 6 and 3 (b) 3 and 6 (c) 6 and 9 (d) 3 and 4 e) None of these
So the number has to end with 3 zeros and the sum of the digits of the number should be a multiple of 3.
The least such number = 111000
Choose E
Cheers
Every job is a self-portrait of the person who did it. Autograph your work with excellence.
Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi All,
I'm sure this goes without saying, but since it's been happening a lot as of late, this is NOT a GMAT question.
GMAT assassins aren't born, they're made,
Rich
I'm sure this goes without saying, but since it's been happening a lot as of late, this is NOT a GMAT question.
GMAT assassins aren't born, they're made,
Rich
-
ani781
- Master | Next Rank: 500 Posts
- Posts: 141
- Joined: Fri Jun 24, 2011 4:35 am
- Location: Edison
- Thanked: 12 times
- Followed by:1 members
Hi Rich,
Just curious, how do you earmark the questions as being GMAT or Non-GMAT ?
And based on the same chores, do you find this question above or below GMAT level ?
Regards.
Just curious, how do you earmark the questions as being GMAT or Non-GMAT ?
And based on the same chores, do you find this question above or below GMAT level ?
Regards.
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
I initially thought this question was out of scope until I saw ganeshrkamath's and batwaraanirudh's great solutions. I just want to elaborate on their solutions a bit so that others can see how they reached their conclusions.
Since 375 = (3)(125), we know that the answer must be divisible by both 125 and 3.
Let's take a closer look at numbers that are divisible by 125.
Notice that:
(1)(125) = 125
(2)(125) = 250
(3)(125) = 375
(4)(125) = 500
(5)(125) = 625
(6)(125) = 750
(7)(125) = 875
(8)(125) = 000
(9)(125) = 1125
.
.
.
So, as you can see, the last 3 digits of numbers divisible by 125 must be 125, 250, 375, 500, 625, 750, 875, or 000
Notice that ONLY ONE of these cases is such that the number consists of only 0's and 1's
So, the number in question must end in 000
Since the number in question is ALSO divisible by 3, the sum of its digits must be divisible by 3.
So, the least possible number must be 111000
Answer: E
Cheers,
Brent
Since 375 = (3)(125), we know that the answer must be divisible by both 125 and 3.
Let's take a closer look at numbers that are divisible by 125.
Notice that:
(1)(125) = 125
(2)(125) = 250
(3)(125) = 375
(4)(125) = 500
(5)(125) = 625
(6)(125) = 750
(7)(125) = 875
(8)(125) = 000
(9)(125) = 1125
.
.
.
So, as you can see, the last 3 digits of numbers divisible by 125 must be 125, 250, 375, 500, 625, 750, 875, or 000
Notice that ONLY ONE of these cases is such that the number consists of only 0's and 1's
So, the number in question must end in 000
Since the number in question is ALSO divisible by 3, the sum of its digits must be divisible by 3.
So, the least possible number must be 111000
Answer: E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
-
rahul.sehgal@btgchampion
- Senior | Next Rank: 100 Posts
- Posts: 40
- Joined: Thu Mar 03, 2011 11:27 am
- Location: New Delhi, India
- Thanked: 3 times
- Followed by:7 members
Brent@GMATPrepNow wrote:I initially thought this question was out of scope until I saw ganeshrkamath's and batwaraanirudh's great solutions. I just want to elaborate on their solutions a bit so that others can see how they reached their conclusions.
Since 375 = (3)(125), we know that the answer must be divisible by both 125 and 3.
Let's take a closer look at numbers that are divisible by 125.
Notice that:
(1)(125) = 125
(2)(125) = 250
(3)(125) = 375
(4)(125) = 500
(5)(125) = 625
(6)(125) = 750
(7)(125) = 875
(8)(125) = 000
(9)(125) = 1125
.
.
.
So, as you can see, the last 3 digits of numbers divisible by 125 must be 125, 250, 375, 500, 625, 750, 875, or 000
Notice that ONLY ONE of these cases is such that the number consists of only 0's and 1's
So, the number in question must end in 000
Since the number in question is ALSO divisible by 3, the sum of its digits must be divisible by 3.
So, the least possible number must be 111000
Answer: E
Cheers,
Brent
As always, excellent explaination Brent. I have been learning a lot from you.
As I was reading through your explaination, I was just thinking - would that help if we can add a 1 before the zeroes while answering - (8) (125) to make it go with your statement - 'Notice that ONLY ONE of these cases is such that the number consists of only 0's and 1's'.
Just my 2 cents. Please do let me know in case I am missing anything here.
Best Regards,
Rahul Sehgal
Rahul Sehgal
