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# How many three digit numbers of distinct digits can be formed by

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CEO
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How many three digit numbers of distinct digits can be formed by  [#permalink]

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Updated on: 05 Aug 2015, 10:51
5
16
00:00

Difficulty:

95% (hard)

Question Stats:

35% (02:35) correct 65% (02:54) wrong based on 123 sessions

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Q-4: How many three digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 11?

A) 14
B) 16
C) 18
D) 20
E) 22

Source : http://www.GMATinsight.com

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Originally posted by GMATinsight on 04 Aug 2015, 02:58.
Last edited by GMATinsight on 05 Aug 2015, 10:51, edited 3 times in total.
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Re: How many three digit numbers of distinct digits can be formed by  [#permalink]

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05 Aug 2015, 10:49
7
6
GMATinsight wrote:
Q-4: How many three digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 11?

A) 14
B) 16
C) 18
D) 20
E) 22

Source : http://www.GMATinsight.com

Good Questions also deserve Kudos :)

CONCEPT: A number is divisible by 11 when Difference of Sums of even place digits and odd place digits is either zero or a multiple of 11.

i.e. a 3-Digit Number abc will be divisible by 11 if (a+c) - b = 0 or multiple of 11

@b=1, a+c should be 1 or 12 i.e. (a,c) can be (5, 7), (7, 5) --- 2 cases

@b=2, a+c should be 2 or 13 i.e. (a,c) can be (6, 7), (7, 6) ---- 2 cases

@b=3, a+c should be 3 or 14 i.e. (a,c) can be (1, 2), (2, 1) ---- 2 cases

@b=4, a+c should be 4 or 15 i.e. (a,c) can be (1, 3), (3, 1) ---- 2 cases

@b=5, a+c should be 5 or 16 i.e. (a,c) can be (1, 4), (2, 3), (3, 2), (4, 1) ---- 4 cases

@b=6, a+c should be 6 or 17 i.e. (a,c) can be (1, 5), (2, 4), (4, 2), (5, 1) ---- 4 cases

@b=7, a+c should be 7 or 18 i.e. (a,c) can be (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) ---- 6 cases

Total Cases = 2+2+2+2+4+4+6 = 22 cases

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##### General Discussion
CEO
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How many three digit numbers of distinct digits can be formed by  [#permalink]

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Updated on: 05 Aug 2015, 11:33
1
GMATinsight wrote:
Q-4: How many three digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 11?

A) 8
B) 10
C) 12
D) 14
E) 16

Source : http://www.GMATinsight.com

Good Questions also deserve Kudos :)

Did by counting

132
143
154
165
176
231
253
264
275
341
352
374
451
462
473
517
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627
671
715
726
GMATinsight, Total should be 22.

Originally posted by ENGRTOMBA2018 on 04 Aug 2015, 04:35.
Last edited by ENGRTOMBA2018 on 05 Aug 2015, 11:33, edited 4 times in total.
Updated the possible cases from 18 to 22.
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Re: How many three digit numbers of distinct digits can be formed by  [#permalink]

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04 Aug 2015, 07:23
1
Manager
Joined: 03 Oct 2014
Posts: 126
Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
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Re: How many three digit numbers of distinct digits can be formed by  [#permalink]

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04 Aug 2015, 08:10
462/264 , 143/34, 132/231,154/451 repitition??

There must be some easy way out....
CEO
Joined: 20 Mar 2014
Posts: 2548
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
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Re: How many three digit numbers of distinct digits can be formed by  [#permalink]

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04 Aug 2015, 08:48
462/264 , 143/34, 132/231,154/451 repitition??

There must be some easy way out....

When a question talks about distinct digits it means that the digits in 1 number should be distinct and not that they need to unique thoroughout.

Example, 110 is not an acceptable case as 1 is repeated but 132 and 231 will be 2 good values. 'Distinct' does not apply (usually) apply to different numbers.
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Joined: 03 Aug 2015
Posts: 1
Re: How many three digit numbers of distinct digits can be formed by  [#permalink]

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05 Aug 2015, 10:26
it should be 10.
231
341
451
561
671
352
462
572
374
726
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3033
Location: India
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How many three digit numbers of distinct digits can be formed by  [#permalink]

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05 Aug 2015, 10:55
Engr2012 wrote:

Did by counting

132
143
154
165
176
231
243
264
275
341
352
374
451
462
473
517
671
761

GMATinsight, Total should be 18.

Did multiple mistakes due to mental calculations. Have updated options. There are 22 cases.

Thanks for notifying about my mistake.
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CEO
Joined: 20 Mar 2014
Posts: 2548
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: How many three digit numbers of distinct digits can be formed by  [#permalink]

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05 Aug 2015, 11:08
GMATinsight wrote:
Engr2012 wrote:

Did by counting

132
143
154
165
176
231
243
264
275
341
352
374
451
462
473
517
671
761

GMATinsight, Total should be 18.

Did multiple mistakes due to mental calculations. Have updated options. There are 22 cases.

Thanks for notifying about my mistake.

I missed 4 cases :

The total cases are: 22. Your method is very useful.

132
143
154
165
176
231
253
264
275
341
352
374
451
462
473
517
561
572
627
671
715
726
Current Student
Joined: 12 Aug 2015
Posts: 2548
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: How many three digit numbers of distinct digits can be formed by  [#permalink]

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23 Aug 2016, 08:34
Engr2012 wrote:
GMATinsight wrote:
Engr2012 wrote:

Did by counting

132
143
154
165
176
231
243
264
275
341
352
374
451
462
473
517
671
761

GMATinsight, Total should be 18.

Did multiple mistakes due to mental calculations. Have updated options. There are 22 cases.

Thanks for notifying about my mistake.

I missed 4 cases :

The total cases are: 22. Your method is very useful.

132
143
154
165
176
231
253
264
275
341
352
374
451
462
473
517
561
572
627
671
715
726

CAN we Solve it in under 2 minutes on the test.!!!
I really doubt that.

P.S => i counted the cases and it took me 5 minutes upwards
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Posts: 115
Re: How many three digit numbers of distinct digits can be formed by  [#permalink]

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22 Sep 2017, 18:54
1
the best approach to go via rule if a number is divisible by 11 then take every 2nd digit (in our case the 1 in the middle) and subtract it from the sum of the rest digits, if the result is 0 or a multiple of 11 then we are settled
number x1x possible combination 7 and 5 (2 options as it could be 5 and 7)
number x2x possible combination 7 and 6 (2 options)
number x3x possible combination 1 and 2 (2 options)
number x4x possible combination 1 and 3 (2 options)
number x5x possible combination 3 and 2 also 4 and 1 (4 options)
number x6x possible combination 5 and 1 also 4 and 2 (4 options)
number x7x possible combination 5 and 2 also 4 and 3 also 6 and 1 (6 options)
Anyways, I found this question a bit time-consuming, that's the best approach to solve it, however, even using that it took me 3 mins or more, to double-check the responses as all answers are pretty much close to each other

I'm curious what are the odd to get that kind of question on GMAT? (instead of 11 that can be 7 or 13, non-standard divisibility patterns)
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Re: How many three digit numbers of distinct digits can be formed by  [#permalink]

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10 Dec 2019, 09:34
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Re: How many three digit numbers of distinct digits can be formed by   [#permalink] 10 Dec 2019, 09:34
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