GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 31 Mar 2020, 13:45

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A five-digit positive integer N has all digits different and contains

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62380
A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 05 Feb 2020, 02:01
1
7
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

47% (02:28) correct 53% (02:25) wrong based on 51 sessions

HideShow timer Statistics

Competition Mode Question



A five-digit positive integer N has all digits different and contains digits 1, 3, 4, 5, and 6 only. If N is the smallest possible number such that it is divisible by 11, then what is the tens digit of N.

A. 1
B. 3
C. 4
D. 5
E. 6


Are You Up For the Challenge: 700 Level Questions

_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6056
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 05 Feb 2020, 02:47
divisiblity rule of 11 ; sum of odd place of no = sum of even place of no
possible no ; smallest ; 14356 ; IMO d ; 5


A five-digit positive integer N has all digits different and contains digits 1, 3, 4, 5, and 6 only. If N is the smallest possible number such that it is divisible by 11, then what is the tens digit of N.

A. 1
B. 3
C. 4
D. 5
E. 6
Senior Manager
Senior Manager
avatar
G
Joined: 14 Dec 2019
Posts: 483
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Premium Member CAT Tests
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 05 Feb 2020, 03:05
A five-digit positive integer N has all digits different and contains digits 1, 3, 4, 5, and 6 only. If N is the smallest possible number such that it is divisible by 11, then what is the tens digit of N.

A. 1
B. 3
C. 4
D. 5
E. 6

For a number to be divisible by 11 One's digit + Hundred's digit + Ten Thousand's digit - Ten's digit - Thousandth's digit should be divisible by 11.

Because the subtraction requires to be 2 digit number (11) or 0 ->
Try to maximize the addition of 3 numbers
0 is not possible since the maximum addition of 2 numbers is 11 and thus rest of the 3 numbers when added equals 8

4+5+6-1-3 = 11 is the combination

Since N has to be smallest -> N -> 41536 --> Therefore Ten's digit is 3 -> Answer - B
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1351
Location: United States
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 05 Feb 2020, 05:14
Quote:
A five-digit positive integer N has all digits different and contains digits 1, 3, 4, 5, and 6 only. If N is the smallest possible number such that it is divisible by 11, then what is the tens digit of N.

A. 1
B. 3
C. 4
D. 5
E. 6


N: combination{13456} divisible by 11;
A number is div by 11, when:
difference between alternating digits is div by 11;
in this case, we need to find a difference of 11 or 0.

13456: [1+4+6]-[3+5]=11-8=3=invalid
13465: [1+4+5]-[3+6]=10-9=1=invalid
41536: [4,5,6]-[1,3]=15-4=11=valid

Ans (B)
Manager
Manager
avatar
G
Joined: 30 Jul 2019
Posts: 101
Location: Viet Nam
Concentration: Technology, Entrepreneurship
GPA: 2.79
WE: Education (Non-Profit and Government)
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 05 Feb 2020, 06:23
1
N = abcde
N is divisible by 11 => (b+d) - (a+c+e) is divisible by 11
Because (1+3)-(4+5+6) is divisible by 11
=> The minimum value of N is 41536
=> Choice B
Director
Director
User avatar
D
Joined: 07 Mar 2019
Posts: 906
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 05 Feb 2020, 09:57
1
A five-digit positive integer N has all digits different and contains digits 1, 3, 4, 5, and 6 only. If N is the smallest possible number such that it is divisible by 11, then what is the tens digit of N.

A. 1
B. 3
C. 4
D. 5
E. 6

A number is divisible by 11 if difference between sum of digits at odd places and sum of digits in even places is either '0' or divisible be 11.

Here sum of all digits 1,3,4,5 and 6 is 19.
Hence sum of digits at odd places must be '15' and sum of digits at even places must be '4' so that it sums to '19' and differs by '11'.

Now 15 is possible for following combinations:
645
456
564
.....
.....
.....
More importantly digits 1 and 3 cant take odd places eventually to sum '15' as 4 can't take even place to sum '4'. Hence N must start with 4.

Also, the thousand digit(even place) must be smaller than tens digit so that N is smaller.
So, Tens place must be taken by 3.

Hence N = 41536

Answer B.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
VP
VP
avatar
V
Joined: 20 Jul 2017
Posts: 1471
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 05 Feb 2020, 18:52
1
We have to take the difference of alternative digits to check for the divisibility of N.

By trial and error method, the difference can not be be zero and only be +11

So, the set of odd digits and even digits that would satisfy the divisibility rule of 11 is
Odd —> {4, 5, 6} &
Even —> {1, 3}

The smallest number that can be formed using the above is 41536

Ten’s Digit = 3

Option B

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 25 Jan 2020
Posts: 3
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 05 Feb 2020, 19:51
1
N is divisible by 11 only when the difference between the sum of (tens digit + thousands digit) and the sum of (unit digit + hundred digit + ten thousands digit) is divisible by 11. (found on the internet)

We have:
1. the sum of (tens digit + thousands digit) and the sum of (unit digit + hundred digit + ten thousands digit) = 1+3+4+5+6 =19
2. from the above sum, we can say that the difference between the 2 above sum need to be 0 or 11. But 19 is not divisible by 2, so the difference between the two sum need to be 11.

=> the bigger sum is: (11+19)/2 = 15 and the smaller sum is: (19-11)/2 = 4 = 1+3 => the smaller sum must be the sum of (tens digit + thousands digit).

Because the question require the smallest possible value of N => the tens digit must be 3.

=> Answer: B (this question is too evil to me).
CR Forum Moderator
avatar
P
Joined: 18 May 2019
Posts: 800
GMAT ToolKit User Premium Member
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 05 Feb 2020, 21:48
1
From the divisibility rule for 11, either the sum of the even position digits of N must equal to the sum of the odd position digits of N or the difference between the sum of the even position digits and the sum of the odd position digits of N must be divisible by 11.
We know that N is formed from the digits 1, 3, 4, 5, and 6
No combination of the sum of at least two of these numbers (even position digits) is equal to the sum of the remaining three numbers (odd position digits).
However 4+5+6 = 15 (sum of odd position digits of N) and 1+3=4 (sum of even position digits of N)
15-4=11 and 11 is divisible by 11. So we are concerned about the even position digits since we are looking for the tens digit which will occupy an even position in a 5 digit number.
For the smallest possible value, 1 must occupy the first even position. Hence 3 must be the tens digit.

The answer is B.
Director
Director
avatar
P
Joined: 25 Jul 2018
Posts: 639
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 05 Feb 2020, 23:12
1
Let’s say that N= ABCDE.
—> (A+ B+C) —(D+ E )= must be equal to zero or multiple of 11

Now, we have 1,3,4,5,6 for five-digit integer N
—> smallest number should be 41536 ( divisible by 11)
—> (4+5+6)—(1+3) = 15–4 = 11
Tens digit of N is 3

The answer is B

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 13 Jan 2020
Posts: 18
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 06 Feb 2020, 05:44
By trial and error method, the difference can not be zero and only be +11

So, the set of odd digits and even digits that would satisfy the divisibility rule of 11 is
Odd are \({4, 5, 6}\) and
Even are \({1, 3}\)

The smallest number that can be formed using the above is 41536

Ten’s Digit \(= 3\)

Option B
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9906
Location: United States (CA)
Re: A five-digit positive integer N has all digits different and contains  [#permalink]

Show Tags

New post 09 Feb 2020, 05:18
2
Bunuel wrote:

Competition Mode Question



A five-digit positive integer N has all digits different and contains digits 1, 3, 4, 5, and 6 only. If N is the smallest possible number such that it is divisible by 11, then what is the tens digit of N.

A. 1
B. 3
C. 4
D. 5
E. 6


Are You Up For the Challenge: 700 Level Questions


The rule for divisibility by 11 is that the difference between the sum of the odd-numbered digits and the sum of the even-numbered digits must be divisible by 11. For a five-digit integer abcde, this means that (a + c + e) - (b + d) must be divisible by 11.

Notice that the sum of the digits of the number is 1 + 3 + 4 + 5 + 6 = 19. Since 19 is odd, the difference between the alternating sums cannot be 0. Thus, if the five-digit integer is to be divisible by 11, we must have the difference between the alternating sums equal 11 or -11.

Notice that 15 - 4 = 11 and 4 - 15 = -11 (and 15 + 4 = 19). Thus, we will look for two groups of numbers, sums of which are 15 and 4. The only way to obtain a sum of 4 using the given numbers is 1 + 3 = 4; thus the second and fourth digits of the numbers must be 1 and 3. The remaining three numbers are 4, 5 and 6. The smallest five-digit integer we can form using the above restrictions is 41,536 (notice that 41,536 is divisible by 11; we get 41536/11 = 3776), and the tens digit of 41,536 is 3.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
197 Reviews

5-star 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 Bot
Re: A five-digit positive integer N has all digits different and contains   [#permalink] 09 Feb 2020, 05:18
Display posts from previous: Sort by

A five-digit positive integer N has all digits different and contains

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne