It is currently 20 Nov 2017, 12:30

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The sum of the digits used to write the sum 10 + 11 + 12 + 1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

4 KUDOS received
Director
Director
User avatar
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 602

Kudos [?]: 637 [4], given: 298

Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 26 Dec 2013, 19:06
4
This post received
KUDOS
32
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (02:13) correct 55% (02:02) wrong based on 388 sessions

HideShow timer Statistics

The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001
[Reveal] Spoiler: OA

_________________

Like my post Send me a Kudos :) It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html


Last edited by Bunuel on 01 Jul 2014, 03:50, edited 1 time in total.
Edited the OA.

Kudos [?]: 637 [4], given: 298

Manager
Manager
avatar
Joined: 05 Nov 2012
Posts: 163

Kudos [?]: 40 [0], given: 57

Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 26 Dec 2013, 20:09
1
This post was
BOOKMARKED
I did not understand the question....
Sum of any arithmatic series is \(\frac{n}{2}(2a+(n-1)d)\)
So sum of 10, 11, 12, 13 is 64, so sum of digits of 64 is 10.... makes sense until now....
Likewise, sum of 1,2,... 110 is \(\frac{110}{2}((2*1)+(110-1)1)\) = 55*(2+109) = 55*111 = 6105.... So sum of digits of 6105 is 12.... What is the question even asking then? :shock: :? :?

Kudos [?]: 40 [0], given: 57

Director
Director
User avatar
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 602

Kudos [?]: 637 [0], given: 298

Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 26 Dec 2013, 21:01
Amateur wrote:
I did not understand the question....
Sum of any arithmatic series is \(\frac{n}{2}(2a+(n-1)d)\)
So sum of 10, 11, 12, 13 is 64, so sum of digits of 64 is 10.... makes sense until now....
Likewise, sum of 1,2,... 110 is \(\frac{110}{2}((2*1)+(110-1)1)\) = 55*(2+109) = 55*111 = 6105.... So sum of digits of 6105 is 12.... What is the question even asking then? :shock: :? :?



what is the sum of digit of following-
10, 11

1+0+1+1 = 3
_________________

Like my post Send me a Kudos :) It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Kudos [?]: 637 [0], given: 298

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42269

Kudos [?]: 132809 [4], given: 12378

The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 27 Dec 2013, 02:59
4
This post received
KUDOS
Expert's post
15
This post was
BOOKMARKED
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


We need to find the sum of all digits used in the following expression: 1 + 2 + 3 + 4 + ... + 109 + 110.

Look at the sum from 1 to 99, inclusive:
01
02
03
...
98
99

Each digit above is used 10 times for units digits and 10 times for tens digits, so 20 times in total. Therefore the sum of the digits used to write the sum of the integers from 1 to 99, inclusive is 20(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = (something with 0 as units digit).

Now, the sum of the digits used to write the sum of the integers from 100 to 110, inclusive (100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110) is 11 + 1 + (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 57.

Total: (something with 0 as units digit) + 57 = (something with 7 as units digit).

Answer: D.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132809 [4], given: 12378

Manager
Manager
avatar
Joined: 05 Nov 2012
Posts: 163

Kudos [?]: 40 [0], given: 57

Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 27 Dec 2013, 12:13
honchos wrote:
what is the sum of digit of following-
10, 11

1+0+1+1 = 3

Then shouldn't the question structure be sum of digits of first 110 positive integers..... or sum of digits of integers between 1 and 110.....

By stating "The sum of the digits used to write the sum of " what is used to write the sum of 10,11,12,13? Number 64....
Gmat is trying to kill my time by using ambiguous statements.... So I boycott the Verbal section, please ask GMAT to take that section away from my exam :lol:

Kudos [?]: 40 [0], given: 57

Expert Post
3 KUDOS received
SVP
SVP
User avatar
G
Joined: 08 Jul 2010
Posts: 1851

Kudos [?]: 2345 [3], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 02 Aug 2015, 12:20
3
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


Break the Numbers into multiple pieces

From 0 - 9 Sum of the digits = 45
From 10 - 19 Sum of the UNIT digits = 45
From 20 - 29 Sum of the UNIT digits = 45
and so on...
i.e. There are 11 such series of 10 numbers from 1 through 110 and
Sum of the Unit digits in all 11 series = 11*45 = 495


From 0 - 9 Sum of the TENS digits = 0
From 10 - 19 Sum of the TENS digits = 1*10 = 10
From 20 - 29 Sum of the TENS digits = 2*10 = 20
From 30 - 39 Sum of the TENS digits = 3*10 = 30
and so on...
i.e. There are 11 such series of 10 numbers from 1 through 110 and
Sum of the TENS digits in all 11 series = 10+20+30+40+50+60+70+80+90+1(100 to 110)=451

Sum of HUNDREDS digit from Numbers from 1 through 110 = 11 (only 100 to 110 have Hundreds Digit)

TOTAL DIGIT SUM = 495+451+11 = 957

Answer: Option D
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2345 [3], given: 51

Manager
Manager
User avatar
Joined: 13 Apr 2015
Posts: 76

Kudos [?]: 22 [0], given: 325

Concentration: General Management, Strategy
GMAT 1: 620 Q47 V28
GPA: 3.25
WE: Project Management (Energy and Utilities)
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 15 Aug 2015, 09:56
Can anyone tell why cant we use (n-1)! X Sum of digits X 111...N in this question.

Kudos [?]: 22 [0], given: 325

Intern
Intern
avatar
Joined: 10 Jun 2013
Posts: 19

Kudos [?]: 16 [0], given: 25

Concentration: General Management, Technology
GMAT Date: 06-26-2015
WE: Corporate Finance (Venture Capital)
GMAT ToolKit User
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 16 Aug 2015, 03:47
1 digit numbers
Sum for 1 digit numbers is 5 in average
9 one digit numbrs
9x5 = 45

2 digits numbers
90 numbers
On average, sum of digits is 9,5
=855

3 digit numbers
11 numbers x 1 (hundredth)
+9x5
+1 for the last non accounted 1 in (110)
=57


Sum is 957

Kudos [?]: 16 [0], given: 25

Manager
Manager
User avatar
Joined: 10 Jun 2015
Posts: 126

Kudos [?]: 30 [0], given: 0

The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 16 Aug 2015, 04:34
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001

sum from 1 to 9 = 45
sum from 10 to 19 = 45+10=55
sum from 20 to 29 = 45+20=65
Therefore sum from 1 to 99 = 45+55+65+75+.....+135=5*(45+135)=5*180=900
sum from 100 to 110=45+1+11=57
Hence, sum of all digits = 957
The correct option is D

alternative method

sum of all unit digits= 11(1+2+3+....+9)=11*45=495
sum of all ten's digits=10(1+2+3+...+9)+1=451 (+1 is in 110)
sum of all hundred's digits=11
Hence, sum of all digits = 495+451+11=957

Kudos [?]: 30 [0], given: 0

Senior Manager
Senior Manager
User avatar
S
Joined: 03 Apr 2013
Posts: 276

Kudos [?]: 44 [0], given: 854

GMAT ToolKit User
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 25 Jun 2016, 11:44
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


Okay..here's a quick approach that worked for me..

I solved this problem using the digit sum principle..Let me first elucidate what we will be doing with a simple example..

Consider numbers chosen at random(and you can check this by picking any number of random numbers)

15,45,67,89

The actual total sum of these numbers is 216..is this number divisible by 3? Yes..9? Yes.

We could check the same by individually adding all the digits of all these numbers

1+5+4+5+6+7+8+9 = 45..is this number divisible by 3? Yes..9? Yes.

Even if these two sums left a remainder with 3 and 9, it would be the same in both the cases.

Now lets come to the problem at hand..

Sum of the numbers from 1 to 110 inclusive is calculated by the formula

\(\frac{n(n+1)}{2}\) , here..n=110

= \(\frac{110*111}{2}\)

= \(55*111\)

The remainder that this number will leave when divided by 3 or 9, will be the same if we added the individual digits of every number in this range.

Is this number divisible by 3?..Yes..9? No.

Now check options..only (D) satisfies these conditions. :)

_________________

Spread some love..Like = +1 Kudos :)

Kudos [?]: 44 [0], given: 854

Manager
Manager
User avatar
B
Joined: 24 Jun 2016
Posts: 247

Kudos [?]: 43 [0], given: 13

Location: Viet Nam
Schools: Booth '19
GMAT 1: 770 Q60 V60
GPA: 4
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 26 Jun 2016, 00:33
Bunuel wrote:
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


We need to find the sum of all digits used in the following expression: 1 + 2 + 3 + 4 + ... + 109 + 110.

Look at the sum from 1 to 99, inclusive:
01
02
03
...
98
99

Each digit above is used 10 times for units digits and 10 times for tens digits, so 20 times in total. Therefore the sum of the digits used to write the sum of the integers from 1 to 99, inclusive is 20(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = (something with 0 as units digit).

Now, the sum of the digits used to write the sum of the integers from 100 to 110, inclusive (100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110) is 11 + 1 + (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 57.

Total: (something with 0 as units digit) + 57 = (something with 7 as units digit).

Answer: D.

Hope it's clear.


This is the credited response.

I think the question was made unnecessarily complicated by including the numbers from 101 to 110. Solving the same problem of numbers from 1 to 100 is plenty challenging IMO.
_________________

Offering top quality online and offline GMAT tutoring service in Vietnam, Southeast Asia, and worldwide.

$60/hour as of November 2017.


http://www.facebook.com/HanoiGMATtutor
HanoiGMATTutor@gmail.com

Kudos [?]: 43 [0], given: 13

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1846

Kudos [?]: 2608 [1], given: 362

Location: Canada
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 28 Jul 2016, 12:19
1
This post received
KUDOS
Expert's post
Top Contributor
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


IMPORTANT: Always check the answer choices before beginning any solution. The answer choices may hint at an approach and/or suggest that you can skip tedious calculations.

Here, the units digits in the answer choices are all different, which suggests that I may be able to avoid some "grunt" work.

First, let's examine the numbers from 00 to 99 inclusive (i.e., 00, 01, 02, .... 97, 98, 99) [note: adding 00 to the mix doesn't change the final answer]
Notice that there are 100 digits from 00 to 99 inclusive.
Also notice that the digits in the tens and units position are equally distributed

So, in the UNITS position, there will be ten 0's, ten 1's, ten 2's . . . ten 8's and ten 9's
In the TENS position, there will be ten 0's, ten 1's, ten 2's . . . ten 8's and ten 9's
So, the sum of ALL DIGITS from 00 to 99 will equal 20(1+2+3+...7+8+9)

IMPORTANT: We don't need to calculate 20(1+2+3+...7+8+9). We need only recognize that the units digit will equal 0. That is 20(1+2+3+...7+8+9) = ??0

From here, we need to add the digits in 100 to 110 inclusive.
To do so, we can use Rich's approach, or we might even list the values and add them in our head, since there aren't many to add here.
When we add the digits in 100 to 110 inclusive, we get 57

So, the sum of the digits from 00 to 110 inclusive = ??0 + 57 = ??7

Since only D has a 7 in the units position, this is the correct answer.

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2608 [1], given: 362

VP
VP
avatar
P
Joined: 26 Mar 2013
Posts: 1284

Kudos [?]: 296 [0], given: 165

Reviews Badge CAT Tests
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 29 Jul 2016, 08:33
GMATPrepNow wrote:
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


IMPORTANT: Always check the answer choices before beginning any solution. The answer choices may hint at an approach and/or suggest that you can skip tedious calculations.

Here, the units digits in the answer choices are all different, which suggests that I may be able to avoid some "grunt" work.

First, let's examine the numbers from 00 to 99 inclusive (i.e., 00, 01, 02, .... 97, 98, 99) [note: adding 00 to the mix doesn't change the final answer]
Notice that there are 100 digits from 00 to 99 inclusive.
Also notice that the digits in the tens and units position are equally distributed

So, in the UNITS position, there will be ten 0's, ten 1's, ten 2's . . . ten 8's and ten 9's
In the TENS position, there will be ten 0's, ten 1's, ten 2's . . . ten 8's and ten 9's
So, the sum of ALL DIGITS from 00 to 99 will equal 20(1+2+3+...7+8+9)

IMPORTANT: We don't need to calculate 20(1+2+3+...7+8+9). We need only recognize that the units digit will equal 0. That is 20(1+2+3+...7+8+9) = ??0

From here, we need to add the digits in 100 to 110 inclusive.
To do so, we can use Rich's approach, or we might even list the values and add them in our head, since there aren't many to add here.
When we add the digits in 100 to 110 inclusive, we get 57

So, the sum of the digits from 00 to 110 inclusive = ??0 + 57 = ??7

Since only D has a 7 in the units position, this is the correct answer.

Cheers,
Brent


Hi Brent,

I have a question. I have used the formula for sum from 1 to 110.

n(n+1)/2 =110*111/2=55 * 111=6105. Then sum of digits 6+1+0+5=12.

I did the above base don example provided in the beginning of the stem.

10+11+12+13=46. Sumf of digits =6+4= 10.

Where did I go wrong?

I'm totally confused

Kudos [?]: 296 [0], given: 165

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1846

Kudos [?]: 2608 [1], given: 362

Location: Canada
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 29 Jul 2016, 10:37
1
This post received
KUDOS
Expert's post
Top Contributor
Mo2men wrote:

Hi Brent,

I have a question. I have used the formula for sum from 1 to 110.

n(n+1)/2 =110*111/2=55 * 111=6105. Then sum of digits 6+1+0+5=12.

I did the above base don example provided in the beginning of the stem.

10+11+12+13=46. Sumf of digits =6+4= 10.

Where did I go wrong?

I'm totally confused


I think you're answering a different question.
You're first finding the SUM of the integers from 1 to 110, inclusive, and then you're finding the sum of the digits in that SUM
This is not what the question is asking.

Unfortunately, the person who wrote the question didn't realize that the sum of ten applies to the sum of all integers AND the sum of the digits in the sum of the integers.
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10
In other words, 1 + 0 + 1 + 1 + 1 + 2 + 1 + 3 = 10

Here's what the question asking: Let's say you write the list of all integers from 1 to 110, inclusive. Then, you start adding every individual digit. What is the sum of all of those individual digits?

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2608 [1], given: 362

Current Student
User avatar
S
Joined: 28 Nov 2014
Posts: 915

Kudos [?]: 211 [0], given: 79

Concentration: Strategy
Schools: Fisher '19 (M)
GPA: 3.71
Reviews Badge
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 26 Oct 2016, 02:26
Bunuel wrote:
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


We need to find the sum of all digits used in the following expression: 1 + 2 + 3 + 4 + ... + 109 + 110.

Look at the sum from 1 to 99, inclusive:
01
02
03
...
98
99

Each digit above is used 10 times for units digits and 10 times for tens digits, so 20 times in total. Therefore the sum of the digits used to write the sum of the integers from 1 to 99, inclusive is 20(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = (something with 0 as units digit).

Now, the sum of the digits used to write the sum of the integers from 100 to 110, inclusive (100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110) is 11 + 1 + (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 57.

Total: (something with 0 as units digit) + 57 = (something with 7 as units digit).

Answer: D.

Hope it's clear.


Bunuel
Won't there be 9 0's from 1 to 99? I am not sure what I am missing! Although that won't affect the answer, I am asking just for clarity!

Kudos [?]: 211 [0], given: 79

Manager
Manager
avatar
Joined: 29 Aug 2008
Posts: 111

Kudos [?]: 48 [0], given: 284

The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 26 Oct 2016, 04:59
GMATPrepNow wrote:
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


IMPORTANT: Always check the answer choices before beginning any solution. The answer choices may hint at an approach and/or suggest that you can skip tedious calculations.

Here, the units digits in the answer choices are all different, which suggests that I may be able to avoid some "grunt" work.
First, let's examine the numbers from 00 to 99 inclusive (i.e., 00, 01, 02, .... 97, 98, 99) [note: adding 00 to the mix doesn't change the final answer]
Notice that there are 100 digits from 00 to 99 inclusive.
Also notice that the digits in the tens and units position are equally distributed


So, in the UNITS position, there will be ten 0's, ten 1's, ten 2's . . . ten 8's and ten 9's
In the TENS position, there will be ten 0's, ten 1's, ten 2's . . . ten 8's and ten 9's
So, the sum of ALL DIGITS from 00 to 99 will equal 20(1+2+3+...7+8+9)

IMPORTANT: We don't need to calculate 20(1+2+3+...7+8+9). We need only recognize that the units digit will equal 0. That is 20(1+2+3+...7+8+9) = ??0

From here, we need to add the digits in 100 to 110 inclusive.
To do so, we can use Rich's approach, or we might even list the values and add them in our head, since there aren't many to add here.
When we add the digits in 100 to 110 inclusive, we get 57

So, the sum of the digits from 00 to 110 inclusive = ??0 + 57 = ??7

Since only D has a 7 in the units position, this is the correct answer.

Cheers,
Brent


Keats wrote:
Bunuel wrote:
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


We need to find the sum of all digits used in the following expression: 1 + 2 + 3 + 4 + ... + 109 + 110.

Look at the sum from 1 to 99, inclusive:
01
02
03
...
98
99

Each digit above is used 10 times for units digits and 10 times for tens digits, so 20 times in total. Therefore the sum of the digits used to write the sum of the integers from 1 to 99, inclusive is 20(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = (something with 0 as units digit).

Now, the sum of the digits used to write the sum of the integers from 100 to 110, inclusive (100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110) is 11 + 1 + (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 57.

Total: (something with 0 as units digit) + 57 = (something with 7 as units digit).

Answer: D.

Hope it's clear.


Bunuel
Won't there be 9 0's from 1 to 99? I am not sure what I am missing! Although that won't affect the answer, I am asking just for clarity!


Refer to the highlighted text in quote from Brent, I hope that answers your question.

HTH

Kudos [?]: 48 [0], given: 284

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7738

Kudos [?]: 17817 [0], given: 235

Location: Pune, India
Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 26 Oct 2016, 08:11
Expert's post
1
This post was
BOOKMARKED
Keats wrote:
Bunuel wrote:
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


We need to find the sum of all digits used in the following expression: 1 + 2 + 3 + 4 + ... + 109 + 110.

Look at the sum from 1 to 99, inclusive:
01
02
03
...
98
99

Each digit above is used 10 times for units digits and 10 times for tens digits, so 20 times in total. Therefore the sum of the digits used to write the sum of the integers from 1 to 99, inclusive is 20(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = (something with 0 as units digit).

Now, the sum of the digits used to write the sum of the integers from 100 to 110, inclusive (100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110) is 11 + 1 + (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 57.

Total: (something with 0 as units digit) + 57 = (something with 7 as units digit).

Answer: D.

Hope it's clear.


Bunuel
Won't there be 9 0's from 1 to 99? I am not sure what I am missing! Although that won't affect the answer, I am asking just for clarity!


Think of the first 100 numbers as:

00, 01, 02, 03, 04, ... 10, 11, 12, ... 97, 98, 99

This brings in complete uniformity. Each digit is used 10 times in each place (tens as well as units place).
So the sum of all digits will be
2*10*(0 + 1 + 2 + 3 + ...9) = 900

Now we have to worry about numbers from 100 to 110 only.
Again, I would like to consider 10 numbers at a time only. From 100 to 109.
10 1s in hundreds place give us a sum of 10. All tens places are 0. The sum of all units digits is 0 + 1 + 2 + 3 + ...9 = 45

Now only 1 number left to consider 110.

Total sum = 900 + 10 + 45 + 2 = 957

Answer (D)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17817 [0], given: 235

Manager
Manager
avatar
B
Joined: 31 Dec 2016
Posts: 91

Kudos [?]: 11 [0], given: 22

Re: The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 01 Aug 2017, 21:23
HanoiGMATtutor wrote:
Bunuel wrote:
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


We need to find the sum of all digits used in the following expression: 1 + 2 + 3 + 4 + ... + 109 + 110.

Look at the sum from 1 to 99, inclusive:
01
02
03
...
98
99

Each digit above is used 10 times for units digits and 10 times for tens digits, so 20 times in total. Therefore the sum of the digits used to write the sum of the integers from 1 to 99, inclusive is 20(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = (something with 0 as units digit).

Now, the sum of the digits used to write the sum of the integers from 100 to 110, inclusive (100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110) is 11 + 1 + (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 57.

Total: (something with 0 as units digit) + 57 = (something with 7 as units digit).

Answer: D.

Hope it's clear.


This is the credited response.

I think the question was made unnecessarily complicated by including the numbers from 101 to 110. Solving the same problem of numbers from 1 to 100 is plenty challenging IMO.


Agreed. I don't even get the point of the question. I knew how to do it but all the solutions above are too slow.

Kudos [?]: 11 [0], given: 22

Manager
Manager
avatar
B
Joined: 31 Dec 2016
Posts: 91

Kudos [?]: 11 [0], given: 22

The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 01 Aug 2017, 21:31
I really dislike Karishma's solution.

This solution doesn't even make sense. The first 100 numbers sum to 910 not 900. Buy maybe you just made a typo.

Anyways, here is how I did it. I don't think we can think of how you did it on the spot since that isn't a trick at all. That would be something thought of in the spur of the moment and clearly you wouldn't have enough time to notice your pattern on the spot. And even if you did, you still have a lot of math work ahead of you.

1) You may notice the first Bar adds up to 46
2) The second bar adds up to 56.

Therefore, you can assume that each bar is 10 higher and there are 10 bars.

We can use the counting formula
An= N1+d(n-1) D=10 as it goes up by 10 on each rung
AN= 46+10(9) = 136

So we can now use the summing formula of 10(46+136)/2. which is 182/2 or 91 X 10 which is 910.

3) Now all we need to do is sum the final row which is 46 if you remember + 1 extra one.


I agree with the above, this problem is excessively mean and it doesn't test ability.
Attachments

hard math one.png
hard math one.png [ 198.18 KiB | Viewed 1183 times ]

Kudos [?]: 11 [0], given: 22

Senior SC Moderator
User avatar
D
Joined: 14 Nov 2016
Posts: 1239

Kudos [?]: 1296 [0], given: 434

Location: Malaysia
GMAT ToolKit User Premium Member CAT Tests
The sum of the digits used to write the sum 10 + 11 + 12 + 1 [#permalink]

Show Tags

New post 09 Sep 2017, 20:17
Bunuel wrote:
honchos wrote:
The sum of the digits used to write the sum 10 + 11 + 12 + 13 is 10. What is the sum of the digits used to write the sum of the integers from 1 to 110, inclusive?

A. 900
B. 911
C. 955
D. 957
E. 1001


We need to find the sum of all digits used in the following expression: 1 + 2 + 3 + 4 + ... + 109 + 110.

Look at the sum from 1 to 99, inclusive:
01
02
03
...
98
99

Each digit above is used 10 times for units digits and 10 times for tens digits, so 20 times in total. Therefore the sum of the digits used to write the sum of the integers from 1 to 99, inclusive is 20(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = (something with 0 as units digit).

Now, the sum of the digits used to write the sum of the integers from 100 to 110, inclusive (100 + 101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110) is 11 + 1 + (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 57.

Total: (something with 0 as units digit) + 57 = (something with 7 as units digit).

Answer: D.

Hope it's clear.


Hi Bunuel,

100 = 1
101 = 2
102 = 3
103 = 4
104 = 5
105 = 6
106 = 7
107 = 8
108 = 9
109 = 10
110 = 11

If I sum 1+2+3+4+5+6+7+8+9+10+11 = 66. How to get 57?

If 10 = 1, 11= 2, 45 + 1 + 2 = 48?
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Kudos [?]: 1296 [0], given: 434

The sum of the digits used to write the sum 10 + 11 + 12 + 1   [#permalink] 09 Sep 2017, 20:17

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

The sum of the digits used to write the sum 10 + 11 + 12 + 1

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.