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What is the sum of all four digit integers formed using the digits 1,

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What is the sum of all four digit integers formed using the digits 1, [#permalink]

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What is the sum of all four digit integers formed using the digits 1, 2, 3 and 4 (repetition is allowed)

A) 444440
B) 610000
C) 666640
D) 711040
E) 880000
[Reveal] Spoiler: OA

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What is the sum of all four digit integers formed using the digits 1, [#permalink]

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n = 4 * 4 * 4 * 4 = 256

<x> = (4444 + 1111) / 2 = 2777.5

Sum = number of integers x average value

n * <x> = 256 * 2777.5 = 711040

answer = D

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Re: What is the sum of all four digit integers formed using the digits 1, [#permalink]

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New post 24 Feb 2016, 05:33
Bunuel wrote:
What is the sum of all four digit integers formed using the digits 1, 2, 3 and 4 (repetition is allowed)

A) 444440
B) 610000
C) 666640
D) 711040
E) 880000


Total Numbers that can be formed by using digits 1, 2, 3 and 4 = 4x4x4x4 = 256

Now sum of all these numbers can be calculated by looking at an observation that

Any digit can come at any of the 4 places i.e. each digit will appear at unit digit 256/4 = 64 times

i.e. 1 will be used as Unit digit in 64 numbers
i.e. 2 will be used as Unit digit in 64 numbers
i.e. 3 will be used as Unit digit in 64 numbers
i.e. 4 will be used as Unit digit in 64 numbers

i.e. Sum of Unit digits of all the number = 64(1+2+3+4) = 640

i.e. Number becomes _ _ _ 0 AND 64 GOES AS CARRY FORWARD


Any digit can come at any of the 4 places i.e. each digit will appear at ten's digit 256/4 = 64 times

i.e. 1 will be used as Tens digit in 64 numbers
i.e. 2 will be used as Tens digit in 64 numbers
i.e. 3 will be used as Tens digit in 64 numbers
i.e. 4 will be used as Tens digit in 64 numbers

i.e. Sum of Tens digits of all the number = 64(1+2+3+4) = 640
with carry forward 64, the sum becomes (640+64=704)

i.e. Number becomes _ _ 4 0 AND 70 GOES AS CARRY FORWARD
Any digit can come at any of the 4 places i.e. each digit will appear at Hundreds digit 256/4 = 64 times

i.e. 1 will be used as Hundreds digit in 64 numbers
i.e. 2 will be used as Hundreds digit in 64 numbers
i.e. 3 will be used as Hundreds digit in 64 numbers
i.e. 4 will be used as Hundreds digit in 64 numbers

i.e. Sum of Hundreds digits of all the number = 64(1+2+3+4) = 640
with carry forward 64, the sum becomes (640+70=710)

i.e. Number becomes _ 0 4 0 AND 71 GOES AS CARRY FORWARD

Any digit can come at any of the 4 places i.e. each digit will appear at Thousands digit 256/4 = 64 times

i.e. 1 will be used as Thousands digit in 64 numbers
i.e. 2 will be used as Thousands digit in 64 numbers
i.e. 3 will be used as Thousands digit in 64 numbers
i.e. 4 will be used as Thousands digit in 64 numbers

i.e. Sum of Thousands digits of all the number = 64(1+2+3+4) = 640
with carry forward 64, the sum becomes (640+71=711)

i.e. Number becomes 7 1 1 0 4 0

Answer: option D
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Re: What is the sum of all four digit integers formed using the digits 1, [#permalink]

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New post 27 Feb 2016, 05:52
GMATinsight wrote:
Bunuel wrote:
What is the sum of all four digit integers formed using the digits 1, 2, 3 and 4 (repetition is allowed)

A) 444440
B) 610000
C) 666640
D) 711040
E) 880000


Total Numbers that can be formed by using digits 1, 2, 3 and 4 = 4x4x4x4 = 256

Now sum of all these numbers can be calculated by looking at an observation that

Any digit can come at any of the 4 places i.e. each digit will appear at unit digit 256/4 = 64 times

i.e. 1 will be used as Unit digit in 64 numbers
i.e. 2 will be used as Unit digit in 64 numbers
i.e. 3 will be used as Unit digit in 64 numbers
i.e. 4 will be used as Unit digit in 64 numbers

i.e. Sum of Unit digits of all the number = 64(1+2+3+4) = 640

i.e. Number becomes _ _ _ 0 AND 64 GOES AS CARRY FORWARD


Any digit can come at any of the 4 places i.e. each digit will appear at ten's digit 256/4 = 64 times

i.e. 1 will be used as Tens digit in 64 numbers
i.e. 2 will be used as Tens digit in 64 numbers
i.e. 3 will be used as Tens digit in 64 numbers
i.e. 4 will be used as Tens digit in 64 numbers

i.e. Sum of Tens digits of all the number = 64(1+2+3+4) = 640
with carry forward 64, the sum becomes (640+64=704)

i.e. Number becomes _ _ 4 0 AND 70 GOES AS CARRY FORWARD
Any digit can come at any of the 4 places i.e. each digit will appear at Hundreds digit 256/4 = 64 times

i.e. 1 will be used as Hundreds digit in 64 numbers
i.e. 2 will be used as Hundreds digit in 64 numbers
i.e. 3 will be used as Hundreds digit in 64 numbers
i.e. 4 will be used as Hundreds digit in 64 numbers

i.e. Sum of Hundreds digits of all the number = 64(1+2+3+4) = 640
with carry forward 64, the sum becomes (640+70=710)

i.e. Number becomes _ 0 4 0 AND 71 GOES AS CARRY FORWARD

Any digit can come at any of the 4 places i.e. each digit will appear at Thousands digit 256/4 = 64 times

i.e. 1 will be used as Thousands digit in 64 numbers
i.e. 2 will be used as Thousands digit in 64 numbers
i.e. 3 will be used as Thousands digit in 64 numbers
i.e. 4 will be used as Thousands digit in 64 numbers

i.e. Sum of Thousands digits of all the number = 64(1+2+3+4) = 640
with carry forward 64, the sum becomes (640+71=711)

i.e. Number becomes 7 1 1 0 4 0

Answer: option D


Are you kidding me!!!!!!!! :shock: :shock:
Shocking solution process.
Who's gonna understand that for d day?
Aren't you gonna give us something of value for GMAT?

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Re: What is the sum of all four digit integers formed using the digits 1, [#permalink]

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New post 27 Feb 2016, 20:03
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Expert's post
Nez wrote:
GMATinsight wrote:
Bunuel wrote:
What is the sum of all four digit integers formed using the digits 1, 2, 3 and 4 (repetition is allowed)

A) 444440
B) 610000
C) 666640
D) 711040
E) 880000


Total Numbers that can be formed by using digits 1, 2, 3 and 4 = 4x4x4x4 = 256

Now sum of all these numbers can be calculated by looking at an observation that

Any digit can come at any of the 4 places i.e. each digit will appear at unit digit 256/4 = 64 times

i.e. 1 will be used as Unit digit in 64 numbers
i.e. 2 will be used as Unit digit in 64 numbers
i.e. 3 will be used as Unit digit in 64 numbers
i.e. 4 will be used as Unit digit in 64 numbers

i.e. Sum of Unit digits of all the number = 64(1+2+3+4) = 640

i.e. Number becomes _ _ _ 0 AND 64 GOES AS CARRY FORWARD


Any digit can come at any of the 4 places i.e. each digit will appear at ten's digit 256/4 = 64 times

i.e. 1 will be used as Tens digit in 64 numbers
i.e. 2 will be used as Tens digit in 64 numbers
i.e. 3 will be used as Tens digit in 64 numbers
i.e. 4 will be used as Tens digit in 64 numbers

i.e. Sum of Tens digits of all the number = 64(1+2+3+4) = 640
with carry forward 64, the sum becomes (640+64=704)

i.e. Number becomes _ _ 4 0 AND 70 GOES AS CARRY FORWARD
Any digit can come at any of the 4 places i.e. each digit will appear at Hundreds digit 256/4 = 64 times

i.e. 1 will be used as Hundreds digit in 64 numbers
i.e. 2 will be used as Hundreds digit in 64 numbers
i.e. 3 will be used as Hundreds digit in 64 numbers
i.e. 4 will be used as Hundreds digit in 64 numbers

i.e. Sum of Hundreds digits of all the number = 64(1+2+3+4) = 640
with carry forward 64, the sum becomes (640+70=710)

i.e. Number becomes _ 0 4 0 AND 71 GOES AS CARRY FORWARD

Any digit can come at any of the 4 places i.e. each digit will appear at Thousands digit 256/4 = 64 times

i.e. 1 will be used as Thousands digit in 64 numbers
i.e. 2 will be used as Thousands digit in 64 numbers
i.e. 3 will be used as Thousands digit in 64 numbers
i.e. 4 will be used as Thousands digit in 64 numbers

i.e. Sum of Thousands digits of all the number = 64(1+2+3+4) = 640
with carry forward 64, the sum becomes (640+71=711)

i.e. Number becomes 7 1 1 0 4 0

Answer: option D


Are you kidding me!!!!!!!! :shock: :shock:
Shocking solution process.
Who's gonna understand that for d day?
Aren't you gonna give us something of value for GMAT?


Logic and basic approaches only help on D-Day... I have much more experience with D-Days... :)

So a suggestion is that don't get tricked with "Tricky ways"' to solve maths on D-Day ;)

Fort he question above, All I can say is that it's simple addition written in detail.
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e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
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Re: What is the sum of all four digit integers formed using the digits 1, [#permalink]

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New post 01 Mar 2016, 04:11
Quote:
Logic and basic approaches only help on D-Day... I have much more experience with D-Days... :)

So a suggestion is that don't get tricked with "Tricky ways"' to solve maths on D-Day ;)

Fort he question above, All I can say is that it's simple addition written in detail.


Hi GMATinsight,
Could "Logic and Basic Approach" help me on D day, if I didn't hone in on the LABA skill before the D day?
If I solve like high school math teacher alone, how will that help me on gmat's 2 minutes test?
Thanks for providing another approach to the solution.
Just learning, and i'm a big fluke.

Kudos [?]: 173 [0], given: 211

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Re: What is the sum of all four digit integers formed using the digits 1, [#permalink]

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New post 01 Mar 2016, 04:32
Nez wrote:
Quote:
Logic and basic approaches only help on D-Day... I have much more experience with D-Days... :)

So a suggestion is that don't get tricked with "Tricky ways"' to solve maths on D-Day ;)

Fort he question above, All I can say is that it's simple addition written in detail.


Hi GMATinsight,
Could "Logic and Basic Approach" help me on D day, if I didn't hone in on the LABA skill before the D day?
If I solve like high school math teacher alone, how will that help me on gmat's 2 minutes test?
Thanks for providing another approach to the solution.
Just learning, and i'm a big fluke.


Yes, Basic approaches (Like High schools maths) are good enough but the idea is "To Be Lazy" and reduce as many steps as possible. "Think More" and "Write Less" and soon you will see that your speed has improved substantially and your mental calculations have improved significantly. :)

Make sure that you don't miss on basic aptitude of

1) Using Options in most of the PS questions and eliminate wrong options to get right Option
2) Do the reverse engineering and validate the questions with Options to find the correct option at the earliest. E.g. in the question above we could have stopped right after calculating Thousands digit of the sum as it is applicable only with one option (correct one) and after calculation of tens digit of sum you could have eliminated 2 options already.
3) Data Sufficiency needs to be practised and the basic need to be understood that you don't have to reach to final value of unknown variable but you have to just stop immediately when you have figured that statement is SUFFICIENT or NOT

I hope that helps!
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Re: What is the sum of all four digit integers formed using the digits 1, [#permalink]

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New post 17 Nov 2016, 10:13
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Total no. of possibilities: 4^4

Sum of digits = 10

As each digit has an equal chance of occurring and since there are 4 digits, Each digit will appear 4^4 / 4 = 4^3 = 64

Sum of units digits = 10 * 1 * 64 = 640
tens digit = 10 * 10 * 64 = 6400
hundreds digit = 10 * 100 * 64 = 64,000
thousands = 10 * 1000 * 64 = 640,000

total = 640000 + 64000 + 6400 + 640 = 711,040

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Re: What is the sum of all four digit integers formed using the digits 1, [#permalink]

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Re: What is the sum of all four digit integers formed using the digits 1,   [#permalink] 28 Dec 2017, 15:19
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