Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Aug 2014, 21:31

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

m16#36

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
1 KUDOS received
Manager
Manager
avatar
Joined: 07 Jan 2008
Posts: 87
Followers: 2

Kudos [?]: 27 [1] , given: 1

m16#36 [#permalink] New post 05 Feb 2009, 04:42
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (01:40) correct 32% (02:52) wrong based on 299 sessions
What is the sum of digits in decimal notation of number 10^{20} - 16 ?

(A) 158
(B) 162
(C) 165
(D) 174
(E) 183

Source: GMAT Club Tests - hardest GMAT questions
[Reveal] Spoiler: OA
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesManhattan GMAT Discount Codes
SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1580
Followers: 12

Kudos [?]: 180 [0], given: 0

GMAT Tests User
Re: m16#36 [#permalink] New post 05 Feb 2009, 04:49
10^20 will have one 1 and twenty 0's.

10^20 - 16 will have one 4, one 8 and seventeen 9's

Hence, sum of digits = 4 + 8 + 17*9
= 12 + 153 = 165
9 KUDOS received
Manager
Manager
User avatar
Joined: 22 Jul 2009
Posts: 192
Followers: 4

Kudos [?]: 188 [9] , given: 18

GMAT Tests User
Re: m16#36 [#permalink] New post 06 Oct 2009, 21:11
9
This post received
KUDOS
The above answer is wrong.

Right answer (taken from the test) is:

10^{20} - 16 = 10...(20 \text{ zeros})...0 - 16 = 9...(18 \text{ nines})...984 . The sum of digits = 18*9 + 8 + 4 = 174 .
The correct answer is D.
_________________

Please kudos if my post helps.

Manager
Manager
avatar
Joined: 16 Mar 2010
Posts: 191
Followers: 2

Kudos [?]: 38 [0], given: 9

GMAT Tests User
Re: m16#36 [#permalink] New post 27 Apr 2010, 05:43
Yes D is correct answer. If you subtract 1 from 10^20 it will be 999(20 times) if you subtract 15 more from that, you will get last digit 4 second last 8 and all others 9. So answer is D.
4 KUDOS received
Manager
Manager
User avatar
Joined: 27 Feb 2010
Posts: 106
Location: Denver
Followers: 1

Kudos [?]: 107 [4] , given: 14

Re: m16#36 [#permalink] New post 27 Apr 2010, 07:35
4
This post received
KUDOS
10-6 always gives 4 in the units place ..the only answer choice that has 4 in the units place is D.
3 KUDOS received
Intern
Intern
User avatar
Joined: 05 Jan 2010
Posts: 22
Followers: 0

Kudos [?]: 11 [3] , given: 4

Re: m16#36 [#permalink] New post 27 Apr 2010, 11:58
3
This post received
KUDOS
I did it the dinosaur way which still didn't take too long.

100000000000000000000
- 16
99999999999999999984

(9 * 18) + 8 + 4 = 174
Manager
Manager
avatar
Joined: 18 Mar 2010
Posts: 90
Location: United States
GMAT 1: Q V
Followers: 2

Kudos [?]: 26 [0], given: 5

Re: m16#36 [#permalink] New post 29 Apr 2010, 11:24
amitjash wrote:
Yes D is correct answer. If you subtract 1 from 10^20 it will be 999(20 times) if you subtract 15 more from that, you will get last digit 4 second last 8 and all others 9. So answer is D.


I did it the same way. Subtracting 1 first seemed to help me visualize it.
1 KUDOS received
Intern
Intern
User avatar
Joined: 23 Dec 2009
Posts: 49
Schools: HBS 2+2
WE 1: Consulting
WE 2: Investment Management
Followers: 0

Kudos [?]: 14 [1] , given: 7

Re: m16#36 [#permalink] New post 12 May 2010, 16:55
1
This post received
KUDOS
Well, 10^2-16=84 and 10^3-16 = 984. So, we see the exponent tells us the number of digits involved in our answer (2 in the former case, 3 in the latter).

10^2^0-16=999...984; two numbers are the 8 and the 4, whereas the other eighteen are 9s!

(18*9)+8+4=174
_________________

My GMAT quest...

...over!

Manager
Manager
User avatar
Status: On my way !!!
Joined: 11 Apr 2011
Posts: 115
Location: France
Concentration: Operations, Strategy
GMAT 1: 760 Q50 V44
GPA: 3.1
WE: Manufacturing and Production (Energy and Utilities)
Followers: 2

Kudos [?]: 14 [0], given: 4

Re: m16#36 [#permalink] New post 29 Apr 2011, 04:21
10^2^0 would be a 21 digit number ... subtract 16 and you are left with a 20 digit number with 2 digits as 4 and 8 and the rest 9s. The total is 8+4+18*9 = 174 therefore (D)
_________________

http://pyarapopat.wordpress.com

SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1691
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 30

Kudos [?]: 285 [0], given: 36

GMAT Tests User Premium Member Reviews Badge
Re: m16#36 [#permalink] New post 29 Apr 2011, 04:39
Last two digits = 84 and there are 18 9s

8 + 4 + 9 * 18

= 12 + 162

= 174

Answer - D
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 26 Mar 2012
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 3

GMAT ToolKit User
Re: m16#36 [#permalink] New post 03 May 2012, 17:36
zz0vlb wrote:
10-6 always gives 4 in the units place ..the only answer choice that has 4 in the units place is D.


If it was 10^2-16=100-16=84, the sum of the digits would be 8+4=12. So I don't think we can use the shortcut suggested.
Manager
Manager
avatar
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 235
Schools: Johnson '15
Followers: 2

Kudos [?]: 22 [0], given: 16

GMAT Tests User
Re: m16#36 [#permalink] New post 05 May 2012, 09:37
zz0vlb wrote:
10-6 always gives 4 in the units place ..the only answer choice that has 4 in the units place is D.



i liked the way u have answered mate....no need of calculation, but just keen observation.. +1 to u
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat ;)

Satyameva Jayate - Truth alone triumphs

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3372

Kudos [?]: 24540 [0], given: 2680

Re: m16#36 [#permalink] New post 06 May 2013, 05:26
Expert's post
topmbaseeker wrote:
What is the sum of digits in decimal notation of number 10^{20} - 16 ?

(A) 158
(B) 162
(C) 165
(D) 174
(E) 183

Source: GMAT Club Tests - hardest GMAT questions


What is the sum of the digits in decimal notation of number 10^{20}-16?

A. 158
B. 162
C. 165
D. 174
E. 183


10^{20} has 21 digits: 1 followed by 20 zeros;
10^{20}-16 has 20 digits: 18 9's and 84 in the end;

So, the sum of the digits of 10^{20}-16 equals to 18*9+8+4=174.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 04 May 2013
Posts: 1
Followers: 0

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

Re: m16#36 [#permalink] New post 06 May 2013, 21:59
I don't see the need of subtracting the entire number and finding out the number of 9's .

1000 - 16 = 984
10000 -16 = 9984
So, the number of 9's would be the power of 10 minus 2.
So, answer = (20-2)*9 + (8+4) = 174
Intern
Intern
avatar
Joined: 05 May 2013
Posts: 1
Followers: 0

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

Re: m16#36 [#permalink] New post 07 May 2013, 00:36
18*9+8+4=174
I will go with 'D'
Intern
Intern
User avatar
Joined: 12 Apr 2013
Posts: 9
Location: Germany
Concentration: Finance, Accounting
GMAT Date: 05-28-2013
GPA: 3.6
Followers: 0

Kudos [?]: 11 [0], given: 20

Re: m16#36 [#permalink] New post 07 May 2013, 12:19
zz0vlb wrote:
10-6 always gives 4 in the units place ..the only answer choice that has 4 in the units place is D.


You got one +1 from me in the first place but actually the way you "solved" problem is wrong.

It would only be right, if the sum of the previous numbers is 0.
_________________

........................................................................................
See it big and keep it simple.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3372

Kudos [?]: 24540 [0], given: 2680

Re: m16#36 [#permalink] New post 21 Apr 2014, 04:11
Expert's post
Bunuel wrote:
topmbaseeker wrote:
What is the sum of digits in decimal notation of number 10^{20} - 16 ?

(A) 158
(B) 162
(C) 165
(D) 174
(E) 183

Source: GMAT Club Tests - hardest GMAT questions


What is the sum of the digits in decimal notation of number 10^{20}-16?

A. 158
B. 162
C. 165
D. 174
E. 183


10^{20} has 21 digits: 1 followed by 20 zeros;
10^{20}-16 has 20 digits: 18 9's and 84 in the end;

So, the sum of the digits of 10^{20}-16 equals to 18*9+8+4=174.

Answer: D.


Similar questions to practice:
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
the-sum-of-the-digits-of-64-279-what-is-the-141460.html
what-is-the-sum-of-all-digits-for-the-number-147057.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-x-is-a-positive-integer-and-10-x-74-in-decimal-notation-61013.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 09 Nov 2012
Posts: 13
Location: India
saurav: suman
Concentration: Finance, Technology
GMAT Date: 09-02-2014
GPA: 3.38
WE: Engineering (Energy and Utilities)
Followers: 1

Kudos [?]: 9 [0], given: 27

GMAT ToolKit User
Re: m16#36 [#permalink] New post 04 May 2014, 13:12
Bunuel wrote:
topmbaseeker wrote:
What is the sum of digits in decimal notation of number 10^{20} - 16 ?

(A) 158
(B) 162
(C) 165
(D) 174
(E) 183

Source: GMAT Club Tests - hardest GMAT questions


What is the sum of the digits in decimal notation of number 10^{20}-16?

A. 158
B. 162
C. 165
D. 174
E. 183


10^{20} has 21 digits: 1 followed by 20 zeros;
10^{20}-16 has 20 digits: 18 9's and 84 in the end;

So, the sum of the digits of 10^{20}-16 equals to 18*9+8+4=174.

Answer: D.

D can't be the answer. once we subtract 16 from 10^20 we have only 19 numbers left. among 19 numbers 17 are nine and last two are 8 and 4.
therefor sum is 17*9+8+4=165
Intern
Intern
avatar
Joined: 09 Nov 2012
Posts: 13
Location: India
saurav: suman
Concentration: Finance, Technology
GMAT Date: 09-02-2014
GPA: 3.38
WE: Engineering (Energy and Utilities)
Followers: 1

Kudos [?]: 9 [0], given: 27

GMAT ToolKit User
Re: m16#36 [#permalink] New post 04 May 2014, 13:15
OA is wrong
C is the right ans
because on subtracting 16 from 10^20, we have only 19 nos left.
17 are 9 and last two are 8 and 4.
so sum= 17*9+8+4=165
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3372

Kudos [?]: 24540 [0], given: 2680

Re: m16#36 [#permalink] New post 05 May 2014, 00:59
Expert's post
daboo343 wrote:
Bunuel wrote:
topmbaseeker wrote:
What is the sum of digits in decimal notation of number 10^{20} - 16 ?

(A) 158
(B) 162
(C) 165
(D) 174
(E) 183

Source: GMAT Club Tests - hardest GMAT questions


What is the sum of the digits in decimal notation of number 10^{20}-16?

A. 158
B. 162
C. 165
D. 174
E. 183


10^{20} has 21 digits: 1 followed by 20 zeros;
10^{20}-16 has 20 digits: 18 9's and 84 in the end;

So, the sum of the digits of 10^{20}-16 equals to 18*9+8+4=174.

Answer: D.

D can't be the answer. once we subtract 16 from 10^20 we have only 19 numbers left. among 19 numbers 17 are nine and last two are 8 and 4.
therefor sum is 17*9+8+4=165


Nope.

10^{20} has 21 digits: 1 followed by 20 zeros: 100,000,000,000,000,000,000

10^{20}-16 has 20 digits: 18 9's and 84 in the end: 99,999,999,999,999,999,984.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: m16#36   [#permalink] 05 May 2014, 00:59
Display posts from previous: Sort by

m16#36

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 22 posts ] 

Moderators: Bunuel, WoundedTiger



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

Powered by phpBB © phpBB Group and phpBB SEO

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®.