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

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GMATinsight
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How many two digit numbers of distinct digits can be formed by [#permalink] New post   Updated on: 04 Aug 2015, 04:28
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Q-1: 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 4?

A) 7
B) 8
C) 9
D) 10
E) 11

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D

Originally posted by GMATinsight on 04 Aug 2015, 02:55.
Last edited by ENGRTOMBA2018 on 04 Aug 2015, 04:28, edited 1 time in total.
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How many two digit numbers of distinct digits can be formed by [#permalink] New post   04 Aug 2015, 04:20
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GMATinsight wrote:
Q-1: 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 4?

A) 7
B) 8
C) 9
D) 10
E) 11

Source : https://www.GMATinsight.com

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Counting the different combinations possible is the easiest method as the options tell you that the correct number is a relatively small number.

The total cases possible are:
12
16
24
32
36
44 (not counted as we need distinct digits)
52
56
64
72
76

Edit: Total: 10

D is the correct answer.
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Re: How many two digit numbers of distinct digits can be formed by [#permalink] New post   04 Aug 2015, 06:30
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GMATinsight wrote:
Q-1: 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 4?

A) 7
B) 8
C) 9
D) 10
E) 11

Source : https://www.GMATinsight.com

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12,16,24,32,36,52,56,64,72,76
Answer D=10
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Re: How many two digit numbers of distinct digits can be formed by [#permalink] New post   22 Apr 2016, 20:28
GMATinsight wrote:
Q-1: 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 4?

A) 7
B) 8
C) 9
D) 10
E) 11

Source : https://www.GMATinsight.com

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we don't have many possibilities: 6*7 = 42 possible numbers. making some assumptions, numbers in which 1, 3, 5, 7 are units digit can't be taken into consideration. we have 6 of each - total 24 numbers. we are left with 18. out of the 18, we can list those that can't be divisible by 4: 42, 62, 14, 34, 54, 74, 26, 46. 8 numbers. thus - answer is 18-8=10

another way, list all possible numbers:
12
16
24
32
36
52
56
64
72
76

we have 10 numbers.
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Re: How many two digit numbers of distinct digits can be formed by [#permalink] New post   22 Apr 2016, 20:53
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GMATinsight wrote:
Q-1: 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 4?

A) 7
B) 8
C) 9
D) 10
E) 11

Source : https://www.GMATinsight.com

Good Questions also deserve Kudos :)


hi,
we don't require to do any calculations but understand the properties involved..

here for a number to be div by 4, the last 2-digits should be div by 4 and this gives us two cases--
1) If the first digit is ODD, the units digit should be non multiple of 4 EVEN number..
so hundreds digit can be any of 4 - 1,3,5,7- and units digit any of 2 - 2,6--
total 4*2=8..
2) If the first digit is EVEN, the units digit should be multiple of 4..
so hundreds digit can be ONLY 1 - 4 - and units digit any of 2 - 2,6-- since 4 will make both digits identical
total 1*2=2.

TOTAL = 8+2=10
D

May help when there are lot of combinations possible..
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Re: How many two digit numbers of distinct digits can be formed by [#permalink] New post   07 Jul 2019, 02:00
GMATinsight wrote:
Q-1: 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 4?

A) 7
B) 8
C) 9
D) 10
E) 11

Source : https://www.GMATinsight.com

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for a no to be divisible by 4 ; the digit should be twice divisible by 2 ; in this case possible unit digits value can be only 4,6 and the tens digit can be taken by other 5 digits
so total combinations ; 5*2 ; 10
IMO D :)
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Re: How many two digit numbers of distinct digits can be formed by [#permalink] New post   07 Jul 2019, 02:38
GMATinsight wrote:
Q-1: 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 4?

A) 7
B) 8
C) 9
D) 10
E) 11

Source : https://www.GMATinsight.com

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The nos are- 12, 16, 24, 32, 36, 52, 56, 64, 72, 76.
The answer to this question is 10
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Re: How many two digit numbers of distinct digits can be formed by [#permalink] New post   06 Feb 2021, 20:45
I might be missing something in the approach....


but the Units Digit does NOT have to be only 4 and 6

12 or 32 are 2 example that work fine also

it ended up as the right answer, but is this approach correct?







Archit3110 wrote:
GMATinsight wrote:
Q-1: 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 4?

A) 7
B) 8
C) 9
D) 10
E) 11

Source : https://www.GMATinsight.com

Good Questions also deserve Kudos :)


for a no to be divisible by 4 ; the digit should be twice divisible by 2 ; in this case possible unit digits value can be only 4,6 and the tens digit can be taken by other 5 digits
so total combinations ; 5*2 ; 10
IMO D :)
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Re: How many two digit numbers of distinct digits can be formed by [#permalink] New post   06 Feb 2021, 21:21
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Fdambro294 wrote:
I might be missing something in the approach....


but the Units Digit does NOT have to be only 4 and 6

12 or 32 are 2 example that work fine also

it ended up as the right answer, but is this approach correct?







Archit3110 wrote:
GMATinsight wrote:
Q-1: 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 4?

A) 7
B) 8
C) 9
D) 10
E) 11

Source : https://www.GMATinsight.com

Good Questions also deserve Kudos :)


for a no to be divisible by 4 ; the digit should be twice divisible by 2 ; in this case possible unit digits value can be only 4,6 and the tens digit can be taken by other 5 digits
so total combinations ; 5*2 ; 10
IMO D :)



No, that is not the correct approach.
By this method 14, 34 are also multiple of 4, but they are not.
Also 12, 32, 72 are not, while they are.
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Re: How many two digit numbers of distinct digits can be formed by [#permalink] New post   14 Apr 2024, 07:09
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