Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

 It is currently 06 Jun 2020, 19:14

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If in a six-digit integer N , F(k) is the value of

Author Message
TAGS:

### Hide Tags

Manager
Joined: 05 Oct 2008
Posts: 207
If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

02 Dec 2009, 11:52
5
24
00:00

Difficulty:

95% (hard)

Question Stats:

42% (02:32) correct 58% (02:46) wrong based on 240 sessions

### HideShow timer Statistics

If in a six-digit integer $$N$$, $$F(k)$$ is the value of the $$k-th$$ digit, is $$N$$ divisible by 7 (For example, $$F(4)$$ is the value of the hundreds digit of $$N$$)?

(1) $$F(1) = F(4), F(2) = F(5), F(3) = F(6)$$

(2) $$F(1) = F(2) = ... = F(6)$$

M15-29
Manager
Joined: 04 Nov 2009
Posts: 63
WE 1: Research
WE 2: Corporate Strat
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

03 Dec 2009, 23:23
7
7
From the question stem, F(k) gives us the k-th digit in the k-th place. Since F(4) is the hundredths digit, we are counting the digits from the left for the 6-digit number N.
So F(1) gives us the 1st digit, F(2) the 2nd digit and so on.

Stmt 1.
Let $$F(1) = x, F(2) = y, F(3) = z$$, where x,y,z are any of the digits from 0 to 9.
So the first 3 digits are x,y,z.
From the statement, the next 3 digits are the same as these. So the number is the form xyzxyz (e.g. 123123 or 375375)
Now a number like 123123 can be written as $$123*1000 + 123$$
$$123123 = 123*1000 + 123 = 1001*123$$
So $$xyzxyz = 1001*xyz$$

The key thing here is that 1001 is divisible by 7. So that means the other side of the above equation is also divisible by 7 i.e. the number xyzxyz is divisible by 7.
So if the first 3 digits are the same as the last 3, it is divisible by 7.

SUFF

Stmt 2.
This says that all the digits are the same e.g. (111111,444444,55555 etc). This is just a special case of the same principle in Stmt 1. Here too, the first 3 digits are equal to last 3 digits. (in addition, all are equal)

SUFF

So D.

------------------------------------------

This can lead into a nice test for checking whether a number is divisible by 7. Take the digits of the number from the right three at a time and take the alternating sum. If that sum is divisible, then the number is divisible too.

E.g. Is 12348763 divisible by 7?
Take numbers in groups of 3 from the right: 12, 348, 763
Alternately add and subtract each group $$= 12-348+763 = 427$$, which is divisible by 7.
So 12348763 is divisible by 7.
##### General Discussion
Intern
Joined: 31 Oct 2009
Posts: 22
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

02 Dec 2009, 14:24
The answer is D that both are sufficient, but I don't really know why...
Manager
Joined: 25 Aug 2009
Posts: 97
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

04 Dec 2009, 13:12
5
1
My Solution is same as above, however I would never base my answers on a single set of sample numbers i.e. 123. Instead we can work with the number xyzxyz
this can be written as z+1000z+10y+10,000y+100x+100,000x
=1001z+1001*10y+1001*100x
=1001(z+10y+100x)

Now we can lead to the same conclusion that 1001 is divisible by 7.
SVP
Joined: 29 Aug 2007
Posts: 1733
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

05 Dec 2009, 11:52
Thats a nice work..

+1.

4test1 wrote:
From the question stem, F(k) gives us the k-th digit in the k-th place. Since F(4) is the hundredths digit, we are counting the digits from the left for the 6-digit number N.
So F(1) gives us the 1st digit, F(2) the 2nd digit and so on.

Stmt 1.
Let $$F(1) = x, F(2) = y, F(3) = z$$, where x,y,z are any of the digits from 0 to 9.
So the first 3 digits are x,y,z.
From the statement, the next 3 digits are the same as these. So the number is the form xyzxyz (e.g. 123123 or 375375)
Now a number like 123123 can be written as $$123*1000 + 123$$
$$123123 = 123*1000 + 123 = 1001*123$$
So $$xyzxyz = 1001*xyz$$

The key thing here is that 1001 is divisible by 7. So that means the other side of the above equation is also divisible by 7 i.e. the number xyzxyz is divisible by 7.
So if the first 3 digits are the same as the last 3, it is divisible by 7.

SUFF

Stmt 2.
This says that all the digits are the same e.g. (111111,444444,55555 etc). This is just a special case of the same principle in Stmt 1. Here too, the first 3 digits are equal to last 3 digits. (in addition, all are equal)

SUFF

So D.

------------------------------------------

This can lead into a nice test for checking whether a number is divisible by 7. Take the digits of the number from the right three at a time and take the alternating sum. If that sum is divisible, then the number is divisible too.

E.g. Is 12348763 divisible by 7?
Take numbers in groups of 3 from the right: 12, 348, 763
Alternately add and subtract each group $$= 12-348+763 = 427$$, which is divisible by 7.
So 12348763 is divisible by 7.
Manager
Joined: 05 Oct 2008
Posts: 207
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

24 May 2010, 00:32
Beware..This rule doesn't really work with all numbers. Could be a false check.

For eg: 111111

111+111= 222

222 is not divisible by 7, but 111111 is!
Retired Moderator
Joined: 05 Sep 2010
Posts: 590
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

07 Nov 2014, 05:17
if F(k) gives us the k-th digit in the k-th place then how F(4) gives hundredth place? F (4) should give thousandth place !!
Math Expert
Joined: 02 Sep 2009
Posts: 64322
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

07 Nov 2014, 05:28
1
1
if F(k) gives us the k-th digit in the k-th place then how F(4) gives hundredth place? F (4) should give thousandth place !!

123,456
1 - HUNDRED THOUSANDS
2 - TEN THOUSANDS
3 - THOUSANDS
4 - HUNDREDS
5 - TENS
6 - UNITS
_________________
Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 86
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

27 Jan 2015, 13:32
Dear Bunuel, I answered the above question by using this way: Anumber is divisible by 7 if the difference between its units digit multiplied by 2 and the rest of the number is a multiple of 7 so I tried by using the number 523523
52352-3*2=52346
5234-6*2=5222
522-2*2=518
51-8*2=35
3-5*2=7
I found this way in Kaplan book but I need to be sure that I unberstand the way correctly and whether it is the same the way that I found in Gmat club Math book where in this book they said that take the last digit and double it and subtract it from the rest of the number, if the answer is divisible by 7 , then the number is divisible by 7. Does the last digit mean units digit?
Math Expert
Joined: 02 Sep 2009
Posts: 64322
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

28 Jan 2015, 00:52
23a2012 wrote:
Dear Bunuel, I answered the above question by using this way: Anumber is divisible by 7 if the difference between its units digit multiplied by 2 and the rest of the number is a multiple of 7 so I tried by using the number 523523
52352-3*2=52346
5234-6*2=5222
522-2*2=518
51-8*2=35
3-5*2=7
I found this way in Kaplan book but I need to be sure that I unberstand the way correctly and whether it is the same the way that I found in Gmat club Math book where in this book they said that take the last digit and double it and subtract it from the rest of the number, if the answer is divisible by 7 , then the number is divisible by 7. Does the last digit mean units digit?

Yes, its units digit.

For example, let's check whether 1519 is divisible by 7: 151-2*9=133. Since 133 is divisible by 7 (133=7*19), then so is 1,519.
_________________
Intern
Joined: 07 Mar 2014
Posts: 14
Location: India
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

24 Feb 2016, 15:42
is N divisible by 7?

Statement 1: F(1) = F(4), F(2) = F(5), F(3) = F(6)

Taking any example 123,123 is divisible by 7 = yes
146,146 is divisble by 7 = yes

clearly sufficient

Statement 2:

F(1) = F(2) = F(3)........= F(6)

Clearly sufficient

VP
Joined: 12 Dec 2016
Posts: 1419
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

29 Sep 2017, 09:42
yup, this question frequently appears in test prep.

st: abcabc = abc * 1001 is divisible 7
st 2 is true
Non-Human User
Joined: 09 Sep 2013
Posts: 15106
Re: If in a six-digit integer N , F(k) is the value of  [#permalink]

### Show Tags

28 Mar 2020, 03:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If in a six-digit integer N , F(k) is the value of   [#permalink] 28 Mar 2020, 03:18