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# A four digit number using the digits 3,4,6 and 7 without repetition

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Manager
Joined: 15 Dec 2015
Posts: 115

Kudos [?]: 140 [0], given: 72

GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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31 Jul 2017, 13:05
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Difficulty:

95% (hard)

Question Stats:

46% (01:29) correct 54% (09:12) wrong based on 111 sessions

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A four digit number using the digits 3,4,6 and 7 without repetition is formed.All the possible numbers so formed are added and the sum is equal to P, which of the following is the value of P?

A.133200
B.123320
C.133220
D.133320
E.None of these.
[Reveal] Spoiler: OA

Kudos [?]: 140 [0], given: 72

Math Expert
Joined: 02 Aug 2009
Posts: 5536

Kudos [?]: 6441 [5], given: 122

Re: A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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31 Jul 2017, 17:58
5
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Expert's post
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DH99 wrote:
A four digit number using the digits 3,4,6 and 7 without repetition is formed.All the possible numbers so formed are added and the sum is equal to P, which of the following is the value of P?

A.133200
B.123320
C.133220
D.133320
E.None of these.

hi..
what will be the SUM of digits in each..
in each position, each of 3,4,6,7 will stay for 3! ways...WHY?
say 3 is in units digit... how many such number are possible..
thousands digit.. any of 3
humdreds digit.. any of remaining 2
tens digit remaining one
units digit.. digit 3

so $$3*2*1=3!=6$$..

so SUM is $$6*(3+4+6+7)=120..$$

so number = 120*thousand+120*hundred+120*ten+120*one=120*1000+120*100+120*10+120*1=133320
D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Kudos [?]: 6441 [5], given: 122

Director
Joined: 07 Dec 2014
Posts: 884

Kudos [?]: 308 [1], given: 17

A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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31 Jul 2017, 19:55
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This post was
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DH99 wrote:
A four digit number using the digits 3,4,6 and 7 without repetition is formed.All the possible numbers so formed are added and the sum is equal to P, which of the following is the value of P?

A.133200
B.123320
C.133220
D.133320
E.None of these.

least value=3,467
greatest value=7,643
3,467+7,643=11,110
11,110/2=5,555
4*6*5,555=133,320
D

Kudos [?]: 308 [1], given: 17

Manager
Joined: 15 Dec 2015
Posts: 115

Kudos [?]: 140 [1], given: 72

GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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31 Jul 2017, 21:38
1
KUDOS
chetan2u wrote:
DH99 wrote:
A four digit number using the digits 3,4,6 and 7 without repetition is formed.All the possible numbers so formed are added and the sum is equal to P, which of the following is the value of P?

A.133200
B.123320
C.133220
D.133320
E.None of these.

hi..
what will be the SUM of digits in each..
in each position, each of 3,4,6,7 will stay for 3! ways...WHY?
[highlight]say 3 is in units digit... how many such number are possible..

thousands digit.. any of 3
humdreds digit.. any of remaining 2
tens digit remaining one
units digit.. digit 3
[/highlight]
so $$3*2*1=3!=6$$..

so SUM is $$6*(3+4+6+7)=120..$$

so number = 120*thousand+120*hundred+120*ten+120*one=120*1000+120*100+120*10+120*1=133320
D

Hi chetan2u: Can you please elaborate the highlighted part.Thank you

Kudos [?]: 140 [1], given: 72

Manager
Joined: 18 Jun 2017
Posts: 60

Kudos [?]: 2 [0], given: 166

Re: A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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02 Aug 2017, 04:05
gracie wrote:
DH99 wrote:
A four digit number using the digits 3,4,6 and 7 without repetition is formed.All the possible numbers so formed are added and the sum is equal to P, which of the following is the value of P?

A.133200
B.123320
C.133220
D.133320
E.None of these.

least value=3,467
greatest value=7,643
3,467+7,643=11,110
11,110/2=5,555
4*6*5,555=133,320
D

4*6*5,555=133,320
How do you come to the conclusion on the multiplication factors 4*6

Kudos [?]: 2 [0], given: 166

Intern
Joined: 15 Jun 2013
Posts: 47

Kudos [?]: 14 [0], given: 33

Schools: Ivey '19 (I)
GMAT 1: 690 Q49 V35
GPA: 3.82
Re: A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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02 Aug 2017, 10:50
DH99 wrote:
chetan2u wrote:
DH99 wrote:
A four digit number using the digits 3,4,6 and 7 without repetition is formed.All the possible numbers so formed are added and the sum is equal to P, which of the following is the value of P?

A.133200
B.123320
C.133220
D.133320
E.None of these.

hi..
what will be the SUM of digits in each..
in each position, each of 3,4,6,7 will stay for 3! ways...WHY?
[highlight]say 3 is in units digit... how many such number are possible..

thousands digit.. any of 3
humdreds digit.. any of remaining 2
tens digit remaining one
units digit.. digit 3
[/highlight]
so $$3*2*1=3!=6$$..

so SUM is $$6*(3+4+6+7)=120..$$

so number = 120*thousand+120*hundred+120*ten+120*one=120*1000+120*100+120*10+120*1=133320
D

Hi chetan2u: Can you please elaborate the highlighted part.Thank you

Why? it is part of combinatorics. You have 3 digits (after one of 3,4, 6,7 is chosen) and all possible combinations for these digits in one number is 3!.

Kudos [?]: 14 [0], given: 33

Director
Joined: 07 Dec 2014
Posts: 884

Kudos [?]: 308 [0], given: 17

A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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02 Aug 2017, 12:05
FB2017 wrote:
gracie wrote:
DH99 wrote:
A four digit number using the digits 3,4,6 and 7 without repetition is formed.All the possible numbers so formed are added and the sum is equal to P, which of the following is the value of P?

A.133200
B.123320
C.133220
D.133320
E.None of these.

least value=3,467
greatest value=7,643
3,467+7,643=11,110
11,110/2=5,555
4*6*5,555=133,320
D

4*6*5,555=133,320
How do you come to the conclusion on the multiplication factors 4*6

hi FB2017,
I put 3 in the first position and counted 6 possible arrangements for 4,6,7.
hence, 4*6
I hope this helps
gracie

Kudos [?]: 308 [0], given: 17

Manager
Joined: 07 Jun 2017
Posts: 109

Kudos [?]: 3 [0], given: 454

Re: A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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04 Aug 2017, 02:22
gracie wrote:

hi FB2017,
I put 3 in the first position and counted 6 possible arrangements for 4,6,7.
hence, 4*6
I hope this helps
gracie

Dear Gracie,
I understand why you time 6
but I don't understand why you time 4?
Thank you very much

Kudos [?]: 3 [0], given: 454

Intern
Joined: 17 Mar 2017
Posts: 9

Kudos [?]: 0 [0], given: 15

GMAT 1: 510 Q47 V15
GMAT 2: 600 Q49 V22
A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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07 Aug 2017, 02:13
each number will be represented 6 times (for the unit, tenth , hundred etc..)

Sum of unit Digit: 6 (7+6+4+3)=120
Sum of tenth Digit: 6 (7+6+4+3)=120
Sum of hundred Digit: 6 (7+6+4+3)=120
...

..120000
+..12000
+....1200
+......120
---------
...133320

Kudos [?]: 0 [0], given: 15

Director
Joined: 07 Dec 2014
Posts: 884

Kudos [?]: 308 [0], given: 17

A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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07 Aug 2017, 09:23
pclawong wrote:
gracie wrote:

hi FB2017,
I put 3 in the first position and counted 6 possible arrangements for 4,6,7.
hence, 4*6
I hope this helps
gracie

Dear Gracie,
I understand why you time 6
but I don't understand why you time 4?
Thank you very much

hi pclawong,
I multiplied by 4 because there are 4 digits,
each giving 6 possible arrangements of the other 3
I hope this helps
gracie

Kudos [?]: 308 [0], given: 17

Intern
Joined: 11 Oct 2016
Posts: 2

Kudos [?]: 1 [0], given: 123

GMAT 1: 720 Q49 V38
GPA: 3.5
Re: A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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07 Aug 2017, 16:35
hey gracie, why did you divide 11110/2?

Kudos [?]: 1 [0], given: 123

Director
Joined: 07 Dec 2014
Posts: 884

Kudos [?]: 308 [1], given: 17

A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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07 Aug 2017, 18:26
1
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aspreneur wrote:
hey gracie, why did you divide 11110/2?

hi aspreneur,

to find the arithmetic mean of the the lowest and highest value combinations,
to multiply it by the number of possible combinations
I hope this helps
gracie

Kudos [?]: 308 [1], given: 17

Intern
Joined: 08 Apr 2017
Posts: 2

Kudos [?]: 1 [0], given: 14

Re: A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

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26 Aug 2017, 09:20
DH99 wrote:
A four digit number using the digits 3,4,6 and 7 without repetition is formed.All the possible numbers so formed are added and the sum is equal to P, which of the following is the value of P?

A.133200
B.123320
C.133220
D.133320
E.None of these.

Here is a formula:
(n-1)!*(Sum of n digits)*(1111...n times)
Thus, in this case: n = 4, Sum of 4 digits = 20; therefore Total Sum = 3!*20*1111 which is equal to 133320

Kudos [?]: 1 [0], given: 14

Re: A four digit number using the digits 3,4,6 and 7 without repetition   [#permalink] 26 Aug 2017, 09:20
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