If n = 14,444, which of the following operations will not yield a number that is divisible by 11?
a. n - 1
b. n + 10
c. n - 100
d. n + 100,000
c. n - 100,000
Is there a quick way to solve this?
divisible by 11
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 135
- Joined: Mon Oct 03, 2011 6:54 am
- Followed by:4 members
GMAT/MBA Expert
- Whitney Garner
- GMAT Instructor
- Posts: 273
- Joined: Tue Sep 21, 2010 5:37 am
- Location: Raleigh, NC
- Thanked: 154 times
- Followed by:74 members
- GMAT Score:770
Hi nidhis.1408!nidhis.1408 wrote:If n = 14,444, which of the following operations will not yield a number that is divisible by 11?
a. n - 1
b. n + 10
c. n - 100
d. n + 100,000
c. n - 100,000
Is there a quick way to solve this?
I don't know that this is really QUICK, but it is faster than long division! Also, I believe that one of your choices is wrong (E) or else we get 2 answers that meet the criteria (will NOT yield a number that is divisible by 11), so I'm thinking it should be -10,000 NOT -100,000 and I will solve it as such).
So the "trick" to tell divisibility by 11 is to go backwards through the digits of the number alternately subtracting then adding its digits. This can be a bit complicated to explain so let me use a dummy number:
123,456
To test if this number is divisible by 11, I go backwards alternating between subtract and add (always start with subtract)
6-5+4-3+2-1 = 1+1+1 = 3 which is NOT divisible by 11, so neither is this number.
What about 31834:
4-3+8-1+3 = 11 which is divisible by 11 and so is 31,834.
Now we can check the number you have been given:
14444... 4-4+4-4+1 = 1 so this number is NOT divisible by 11 (it is 1 off).
(a) 14443... 3-4+4-4+1 = 0 so this number IS divisible by 11!
(b) 14454... 4-5+4-4+1 = 0 so this number IS divisible by 11! (notice that both A and B made alterations that resulted in a negative 1...3-4 and 4-5 to cancel with that +1 that was making us not divisible by 11
(c) 14544... 4-4+5-4+1 = 2 so this number IS NOT divisible by 11 (notice that this alteration ADDED an additional 1 (because the 5 was in a SUM position) so it didn't cancel with our 1 we were off originally)
(d) 114444... 4-4+4-4+1-1=0 so this number IS divisible by 11!
(e) 4,444... 4-4+4-4=0 so this number IS divisible by 11!
That means that our answer is [spoiler]C[/spoiler]!
Hope this helps!
Whit
Whitney Garner
GMAT Instructor & Instructor Developer
Manhattan Prep
Contributor to Beat The GMAT!
Math is a lot like love - a simple idea that can easily get complicated
GMAT Instructor & Instructor Developer
Manhattan Prep
Contributor to Beat The GMAT!
Math is a lot like love - a simple idea that can easily get complicated
- LalaB
- Master | Next Rank: 500 Posts
- Posts: 425
- Joined: Wed Dec 08, 2010 9:00 am
- Thanked: 56 times
- Followed by:7 members
- GMAT Score:690
answer choice C says n minus 100 ; 14444-100=14344 it is divisible by 11 (check it by summing up digits in odd places,then digits in even places. if the sum of digits in odd places is equal to the sum of digits in even places, then the number is divisible by 11)
1+3+4=4+4 so, 14544 is divisible by 11
answer choice E is not divisible by 11
1+3+4=4+4 so, 14544 is divisible by 11
answer choice E is not divisible by 11
Happy are those who dream dreams and are ready to pay the price to make them come true.(c)
In order to succeed, your desire for success should be greater than your fear of failure.(c)
In order to succeed, your desire for success should be greater than your fear of failure.(c)
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
Another approach. We can solve this question by first determining the remainder when 14,444 is divided by 11.nidhis.1408 wrote:If n = 14,444, which of the following operations will not yield a number that is divisible by 11?
a. n - 1
b. n + 10
c. n - 100
d. n + 100,000
c. n - 100,000
Here's one strategy: find a multiple of 11 that's close to (but less than) 14,444
Well, we know 11,000 is a multiple of 11.
Now subtract 11,000 from 14,444 to get 3444
Now find a multiple of 11 that's close to (but less than) 3444
Well, we know 3300 is a multiple of 11.
Now subtract 3300 from 3444 to get 144
Now find a multiple of 11 that's close to (but less than) 144
Well, we know 110 is a multiple of 11.
Now subtract 110 from 144 to get 34
Now find a multiple of 11 that's close to (but less than) 34
Well, we know 33 is a multiple of 11.
Now subtract 33 from 34 to get 1
Great, we now know that, when we divide 14,444 by 11, the remainder is 1.
IMPORTANT: We can now say that 14,444 = 11k + 1 for some integer value of k.
In other words, n = 11k + 1 for some integer value of k.
Notice that we don't need to know the value of k here.
Okay, now let's check the answer choices:
A) n - 1
If n = 11k + 1, then n-1 = 11k
Since 11k is definitely divisible by 11, we can eliminate A.
B) n + 10
If n = 11k + 1, then n+10 = 11k + 11 = 11(k+1)
Since 11(k+1) is definitely divisible by 11, we can eliminate B.
C) n - 100
If n = 11k + 1, then n-100 = 11k - 99 = 11(k-9)
Since 11(k-9) is definitely divisible by 11, we can eliminate C.
D) n + 100,000
If n = 11k + 1, then n+100,000 = 11k + 100,001 = 11(k + 9091)
Since 11(k + 9091) is definitely divisible by 11, we can eliminate D.
This leaves us with answer choice E?
Are we going to check to see whether it's divisible by 11?
No. We don't have the luxury of time to do so.
Take E and move on!
Cheers,
Brent
-
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Sat Sep 22, 2012 8:56 am
- Thanked: 1 times
Another approach:
Lets assume n-1 is divisible by 11 and check other ans to find which one is not divisible by 11 as following
n+10 = (n-1)+11 =divisible as both n-1 and 11 are divisible
Same way;
n-100= (n-1)-99= divisible
n+100000 = (n-1) + 100001 = divisible
n-100000 = (n-1)- 99999 = not divisible as 99999 is not divisible by 11
So the and is E
Lets assume n-1 is divisible by 11 and check other ans to find which one is not divisible by 11 as following
n+10 = (n-1)+11 =divisible as both n-1 and 11 are divisible
Same way;
n-100= (n-1)-99= divisible
n+100000 = (n-1) + 100001 = divisible
n-100000 = (n-1)- 99999 = not divisible as 99999 is not divisible by 11
So the and is E
- AIM TO CRACK GMAT
- Senior | Next Rank: 100 Posts
- Posts: 80
- Joined: Sat Sep 15, 2012 1:07 am
- Thanked: 1 times
- Followed by:1 members
Brent@GMATPrepNow wrote:Another approach. We can solve this question by first determining the remainder when 14,444 is divided by 11.nidhis.1408 wrote:If n = 14,444, which of the following operations will not yield a number that is divisible by 11?
a. n - 1
b. n + 10
c. n - 100
d. n + 100,000
c. n - 100,000
Here's one strategy: find a multiple of 11 that's close to (but less than) 14,444
Well, we know 11,000 is a multiple of 11.
Now subtract 11,000 from 14,444 to get 3444
Now find a multiple of 11 that's close to (but less than) 3444
Well, we know 3300 is a multiple of 11.
Now subtract 3300 from 3444 to get 144
Now find a multiple of 11 that's close to (but less than) 144
Well, we know 110 is a multiple of 11.
Now subtract 110 from 144 to get 34
Now find a multiple of 11 that's close to (but less than) 34
Well, we know 33 is a multiple of 11.
Now subtract 33 from 34 to get 1
Great, we now know that, when we divide 14,444 by 11, the remainder is 1.
IMPORTANT: We can now say that 14,444 = 11k + 1 for some integer value of k.
In other words, n = 11k + 1 for some integer value of k.
Notice that we don't need to know the value of k here.
Okay, now let's check the answer choices:
A) n - 1
If n = 11k + 1, then n-1 = 11k
Since 11k is definitely divisible by 11, we can eliminate A.
B) n + 10
If n = 11k + 1, then n+10 = 11k + 11 = 11(k+1)
Since 11(k+1) is definitely divisible by 11, we can eliminate B.
C) n - 100
If n = 11k + 1, then n-100 = 11k - 99 = 11(k-9)
Since 11(k-9) is definitely divisible by 11, we can eliminate C.
D) n + 100,000
If n = 11k + 1, then n+100,000 = 11k + 100,001 = 11(k + 9091)
Since 11(k + 9091) is definitely divisible by 11, we can eliminate D.
This leaves us with answer choice E?
Are we going to check to see whether it's divisible by 11?
No. We don't have the luxury of time to do so.
Take E and move on!
Cheers,
Brent
Brent its a gud method but dnt u think its 2 long?????????? is der any other quicker method 2 solve d same... i liked the way u elaborated al d steps!!! could u suggest a quicker method?
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 don't think this approach would take more than 2 minutes. Perhaps it looks longer because I list every little step. But most of the work can be done quickly in your head.AIM TO CRACK GMAT wrote: Brent its a gud method but dnt u think its 2 long?????????? is der any other quicker method 2 solve d same... i liked the way u elaborated al d steps!!! could u suggest a quicker method?
Another option is to memorize the rule for divisibility by 11 (I'm just not very good at memorizing things . . . just ask my wife )
Cheers,
Brent
- LalaB
- Master | Next Rank: 500 Posts
- Posts: 425
- Joined: Wed Dec 08, 2010 9:00 am
- Thanked: 56 times
- Followed by:7 members
- GMAT Score:690
I am not a wife,but I already posted the rule for divisibility by 11
the quickest method is to guess and move on (kidding!)
Brent, I liked ur post. This shows again that most of the gmat questions can be solved in multiple ways. that is why we love (do we!? I am a liar hehe) the gmat )))
the quickest method is to guess and move on (kidding!)
Brent, I liked ur post. This shows again that most of the gmat questions can be solved in multiple ways. that is why we love (do we!? I am a liar hehe) the gmat )))
Happy are those who dream dreams and are ready to pay the price to make them come true.(c)
In order to succeed, your desire for success should be greater than your fear of failure.(c)
In order to succeed, your desire for success should be greater than your fear of failure.(c)
-
- Legendary Member
- Posts: 1085
- Joined: Fri Apr 15, 2011 2:33 pm
- Thanked: 158 times
- Followed by:21 members
I've looked through all posts, I guess santusri2001 has posted similar ideanidhis.1408 wrote:If n = 14,444, which of the following operations will not yield a number that is divisible by 11?
a. n - 1
b. n + 10
c. n - 100
d. n + 100,000
c. n - 100,000
Is there a quick way to solve this?
From the first look, it's clear 4,444 all digits of four are repeated, hence the number is divisible by 11. By dealing with 10,000 we can check the choices for divisibility by 11 further. The divisibility by 11 of non-repeated and non-adjacent digit numbers (unlike 3333 or 4444) in itself is checked against the number to contain certain quantity of tens and ones (as units), e.g. 100101 contains 10^5, 10^2 and 1. So by multiplying 11 onto (10^5 + 10^2 +1) we get the whole number equal to 100101.
a. n - 1 <=> 10,000-1 is divisible by 11 because in 9,999 all digits are replicated and adjacent
b. n + 10 <=> 10,000+10 is divisible by 11 because we have 10^4 + 10 quantity of tens and zero ones
c. n - 100 <=> 9,900 is divisible by 11 because we have two digits replicated and adjacent
d. n + 100,000 <=> 110,000 is divisible by 11 because we have two digits replicated and adjacent
e. n - 100,000 <=> -90,000 isn't divisible by 11 because in a new number (90,000) the other digit(s) following (neither adjacent nor in the ten's unit) is not replicated <--- major takeaway from this question.
in e) if it were n - 109,000 we would have divisibility by 11 Or if it were n - 100,090 again the number would be divisible by 11. But not in case of n - 100,009 as we have no replication in the ten's unit.
Success doesn't come overnight!