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

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SVP
Joined: 08 Jul 2010
Posts: 2120
Location: India
GMAT: INSIGHT
WE: Education (Education)
How many two digit numbers of distinct digits can be formed by us [#permalink]

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Updated on: 04 Aug 2015, 04:48
1
4
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:44) correct 27% (01:18) wrong based on 212 sessions

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Q-2: How many two 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 3?

A) 9
B) 10
C) 11
D) 12
E) 14

Source : http://www.GMATinsight.com

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Originally posted by GMATinsight on 04 Aug 2015, 02:56.
Last edited by GMATinsight on 04 Aug 2015, 04:48, edited 2 times in total.
Current Student
Joined: 20 Mar 2014
Posts: 2641
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: How many two digit numbers of distinct digits can be formed by us [#permalink]

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04 Aug 2015, 04:32
1
GMATinsight wrote:
Q-2: How many two 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 3?

A) 9
B) 10
C) 11
D) 12
E) 13

Source : http://www.GMATinsight.com

Good Questions also deserve Kudos :)

GMATinsight, I am getting 14 possible cases

12
15
21
24
27
36
42
45
51
54
57
63
72
75
SVP
Joined: 08 Jul 2010
Posts: 2120
Location: India
GMAT: INSIGHT
WE: Education (Education)
How many two digit numbers of distinct digits can be formed by us [#permalink]

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04 Aug 2015, 04:50
Engr2012 wrote:
GMATinsight wrote:
Q-2: How many two 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 3?

A) 9
B) 10
C) 11
D) 12
E) 13

Source : http://www.GMATinsight.com

Good Questions also deserve Kudos :)

GMATinsight, I am getting 14 possible cases

12
15
21
24
27
36
42
45
51
54
57
63
72
75

Thank you. Type error. Have corrected.

There are basically 7 cases {12, 15, 24, 27, 36, 45, 57} in forward order and 7 cases after reversing the digits so a total of 14 cases.

Thanks.

P.S. I mentioned Q-# in Subject line intentionally so that reader can differentiate among the different questions with similar starting language

So I would still encourage to mention the same however being a moderator you can take a stand to not to deviate from the rules.
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Bhoopendra Singh and Dr.Sushma Jha
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SVP
Joined: 08 Jul 2010
Posts: 2120
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: How many two digit numbers of distinct digits can be formed by us [#permalink]

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05 Aug 2015, 11:27
GMATinsight wrote:
Q-2: How many two 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 3?

A) 9
B) 10
C) 11
D) 12
E) 14

Source : http://www.GMATinsight.com

Good Questions also deserve Kudos :)

ALTERNATE

CONCEPT: A number will be divisible by 3 if sum of all the digits of the number is divisible by 3

Here the Possible sum of the two distinct digits can be 3, 6, 9 and 12 only in order to satisfy the given condition

If sum of Digits = 3, No. = 12, 21 --- 2 Cases
If sum of Digits = 6, No. = 15, 24, 42, 51 --- 4 Cases
If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases
If sum of Digits = 12, No. = 57, 75 --- 2 Cases

Total Cases = 2+4+6+2 = 14 cases

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GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

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Current Student
Joined: 20 Mar 2014
Posts: 2641
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: How many two digit numbers of distinct digits can be formed by us [#permalink]

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05 Aug 2015, 11:36
GMATinsight wrote:
Engr2012 wrote:
GMATinsight wrote:
Q-2: How many two 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 3?

A) 9
B) 10
C) 11
D) 12
E) 13

Source : http://www.GMATinsight.com

Good Questions also deserve Kudos :)

GMATinsight, I am getting 14 possible cases

12
15
21
24
27
36
42
45
51
54
57
63
72
75

Thank you. Type error. Have corrected.

There are basically 7 cases {12, 15, 24, 27, 36, 45, 57} in forward order and 7 cases after reversing the digits so a total of 14 cases.

Thanks.

P.S. I mentioned Q-# in Subject line intentionally so that reader can differentiate among the different questions with similar starting language

So I would still encourage to mention the same however being a moderator you can take a stand to not to deviate from the rules.

GMATinsight, I completely understand your concern but these rules were made by Bunuel and thus dont want to deviate from them. One way to go around this rule is to rephrase these questions as:

How many two digit numbers divisble by 3 can be formed by using digits 1, 2, 3, 4, 5, 6 and 7? or

Using digits 1, 2, 3, 4, 5, 6 and 7 how many 2 digit numbers can be formed such that the numbers are divisible by 3? etc.
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Joined: 15 Jul 2015
Posts: 110
GPA: 3.62
WE: Corporate Finance (Consulting)
Re: How many two digit numbers of distinct digits can be formed by us [#permalink]

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05 Aug 2015, 11:52
2
GMATinsight wrote:
Q-2: How many two 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 3?

A) 9
B) 10
C) 11
D) 12
E) 14

Source : http://www.GMATinsight.com

Good Questions also deserve Kudos :)

In this case, it probably fastest, just to write out the numbers that satisfy the criteria:
10's - 12, 15
20's - 21, 24, 27
30's - 36 (33 does not satisfy the "disticnt digit" criteria)
40's - 42, 45
50's - 51, 54, 57
60's - 63 (66 does not satisfy the "distinct digit" criteria)
70's - 72, 75

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Joined: 07 Dec 2014
Posts: 1036
How many two digit numbers of distinct digits can be formed by us [#permalink]

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19 Aug 2016, 15:15
1
there are 7*6=42 possible distinct two digit combinations
42/3=14
14
Board of Directors
Joined: 17 Jul 2014
Posts: 2724
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: How many two digit numbers of distinct digits can be formed by us [#permalink]

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07 Sep 2016, 08:22
is there a way to get to the answer without actually counting all the possibilities?
i got:
12 and 21
15 and 51
24 and 42
27 and 72
36 and 63
45 and 54
57 and 75

7 pairs - 14 numbers...
VP
Joined: 07 Dec 2014
Posts: 1036
Re: How many two digit numbers of distinct digits can be formed by us [#permalink]

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07 Sep 2016, 13:07
7/9*6/10*1/3*90=14
Intern
Joined: 08 Jul 2011
Posts: 13
How many two digit numbers of distinct digits can be formed by us [#permalink]

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07 Sep 2016, 22:56
One can also apply , taking X & Y.
X+Y = 3,6,9,12...and so on

where X & Y belongs to (1,2,3,4,5,6,7)

greatest number formed to be divisible by 3 = 75==> 7+5 =12

1. X+ Y = 3 (12,21)
2. X+Y = 6 (24,42,15,51)
3. X+Y = 9 (27,72,36,63,45,54)
4 X+Y =12 (57,75)

Total = 14 pairs

========================================
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Joined: 09 Sep 2013
Posts: 7293
Re: How many two digit numbers of distinct digits can be formed by us [#permalink]

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20 Sep 2017, 19:02
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Re: How many two digit numbers of distinct digits can be formed by us   [#permalink] 20 Sep 2017, 19:02
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