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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
Question Stats:
40% (02:17) correct 60% (02:42) wrong based on 109 sessions
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Q4: 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.comGood Questions also deserve Kudos :)
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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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How many three digit numbers of distinct digits can be formed by [#permalink]
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Updated on: 05 Aug 2015, 11:33
GMATinsight wrote: Q4: 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.comGood Questions also deserve Kudos :) Did by counting 132 143 154 165 176 231 253 264 275 341 352 374 451 462 473 517 561 572 627 671 715 726 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
What about 726/627?



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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....



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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
Cadaver wrote: 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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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



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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
GMATinsight wrote: Q4: 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.comGood 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 3Digit 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 casesTotal Cases = 2+2+2+2+4+4+6 = 22 casesAnswer: option E
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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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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



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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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Re: How many three digit numbers of distinct digits can be formed by [#permalink]
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22 Sep 2017, 18:54
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 timeconsuming, that's the best approach to solve it, however, even using that it took me 3 mins or more, to doublecheck 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, nonstandard divisibility patterns)




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