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

Question

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 :  https://www.GMATinsight.com

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ENGRTOMBA2018 · Answer

GMATinsight , I am getting 14 possible cases

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

GMATinsight · Answer

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 · Answer

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

Answer: option E

ENGRTOMBA2018 · Answer

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.

VeritasPrepDennis · Answer

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

Correct answer is E) 14

gracie · Answer

there are 7*6=42 possible distinct two digit combinations
42/3=14
14

mvictor · Answer

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...

gracie · Answer

7/9*6/10*1/3*90=14

ASHARAN · Answer

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

========================================

PinakiRDas · Answer

Can anyone please confirm if this can be done using Combination approach too?

bumpbot · Answer

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

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

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