It is currently 18 Oct 2017, 02:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 15 Dec 2015
Posts: 114

Kudos [?]: 111 [0], given: 70

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]

### Show Tags

31 Jul 2017, 14:05
9
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

46% (01:30) correct 54% (09:25) wrong based on 108 sessions

### HideShow timer Statistics

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 [?]: 111 [0], given: 70

Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4967

Kudos [?]: 5457 [5], given: 112

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

### Show Tags

31 Jul 2017, 18:58
5
KUDOS
Expert's post
3
This post was
BOOKMARKED
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

Kudos [?]: 5457 [5], given: 112

Director
Joined: 07 Dec 2014
Posts: 812

Kudos [?]: 247 [1], given: 12

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

### Show Tags

31 Jul 2017, 20:55
1
KUDOS
1
This post was
BOOKMARKED
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 [?]: 247 [1], given: 12

Manager
Joined: 15 Dec 2015
Posts: 114

Kudos [?]: 111 [1], given: 70

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]

### Show Tags

31 Jul 2017, 22:38
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 [?]: 111 [1], given: 70

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]

### Show Tags

02 Aug 2017, 05:05
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: 45

Kudos [?]: 7 [0], given: 33

GMAT 1: 690 Q49 V35
GPA: 3.82
WE: Management Consulting (Manufacturing)
Re: A four digit number using the digits 3,4,6 and 7 without repetition [#permalink]

### Show Tags

02 Aug 2017, 11:50
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 [?]: 7 [0], given: 33

Director
Joined: 07 Dec 2014
Posts: 812

Kudos [?]: 247 [0], given: 12

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

### Show Tags

02 Aug 2017, 13:05
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 [?]: 247 [0], given: 12

Manager
Joined: 07 Jun 2017
Posts: 111

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

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

### Show Tags

04 Aug 2017, 03:22
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: 3

Kudos [?]: 0 [0], given: 8

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

### Show Tags

07 Aug 2017, 03:13
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: 8

Director
Joined: 07 Dec 2014
Posts: 812

Kudos [?]: 247 [0], given: 12

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

### Show Tags

07 Aug 2017, 10:23
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 [?]: 247 [0], given: 12

Intern
Joined: 11 Oct 2016
Posts: 1

Kudos [?]: [0], given: 122

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

### Show Tags

07 Aug 2017, 17:35
hey gracie, why did you divide 11110/2?

Kudos [?]: [0], given: 122

Director
Joined: 07 Dec 2014
Posts: 812

Kudos [?]: 247 [1], given: 12

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

### Show Tags

07 Aug 2017, 19:26
1
KUDOS
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 [?]: 247 [1], given: 12

Intern
Joined: 09 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]

### Show Tags

26 Aug 2017, 10:20
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, 10:20
Display posts from previous: Sort by