GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Jul 2018, 08:22

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

If 10^50-74 is written as an integer in base 10 notation

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

Hide Tags

7 KUDOS received
Manager
Manager
User avatar
Joined: 06 Apr 2010
Posts: 134
Reviews Badge
If 10^50-74 is written as an integer in base 10 notation  [#permalink]

Show Tags

New post 26 Aug 2010, 07:42
7
31
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:19) correct 33% (01:43) wrong based on 721 sessions

HideShow timer Statistics

If 10^50-74 is written as an integer in base 10 notation, what is the sum of the digits in that integer?

A. 424
B. 433
C. 440
D. 449
E. 467
Most Helpful Expert Reply
Expert Post
11 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47220
Re: Number System Problem  [#permalink]

Show Tags

New post 26 Aug 2010, 08:25
11
9
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467



\(10^{50}\) has 51 digits (1 followed by 50 zeros). \(10^{50}-74\) has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is \(9*48+2+6=440\).

Answer: C.
_________________

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

General Discussion
Senior Manager
Senior Manager
User avatar
Joined: 25 Feb 2010
Posts: 393
Re: Number System Problem  [#permalink]

Show Tags

New post 26 Aug 2010, 18:58
Bunuel wrote:
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467



\(10^{50}\) has 51 digits (1 followed by 50 zeros). \(10^{50}-74\) has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is \(9*48+2+6=440\).

Answer: C.


:woohoo
_________________

GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...

Manager
Manager
avatar
Joined: 24 Dec 2009
Posts: 194
Re: Number System Problem  [#permalink]

Show Tags

New post 26 Aug 2010, 23:12
C for me too..Excellent expln by Bunnel. Thanks.
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 1897
Re: Sum of digits  [#permalink]

Show Tags

New post 19 Feb 2011, 14:03
The integer is going to have 48 9's.
Last 2 digits will be 26

48*9 + 2 + 6 = 432+8 = 440.

Ans: "C"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 04 Oct 2013
Posts: 4
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

Show Tags

New post 23 Nov 2013, 12:05
I don't understand why in the question it is mentioned "in base 10 notation"

Maybe its because English is not my mother tongue but that instruction really confused me. I thought I was looking for a number like "ten to the power of something".
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47220
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

Show Tags

New post 23 Nov 2013, 13:07
1
1
Lobro wrote:
I don't understand why in the question it is mentioned "in base 10 notation"

Maybe its because English is not my mother tongue but that instruction really confused me. I thought I was looking for a number like "ten to the power of something".


Based 10 notation, or decimal notation, is just a way of writing a number using 10 digits: 1, 2, 3, 4, 5, 6, 7, 8, and 0 (usual way), in contrast, for example, to binary numeral system (base-2 number system) notation.

Similar questions to practice:
the-sum-of-the-digits-of-64-279-what-is-the-141460.html
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html

Hope this helps.
_________________

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

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

Show Tags

New post 04 Apr 2014, 01:26
100 - 74 = 26

The last 2 digits of the term would be 26; all else would be 9

99999999......26

Important rule:

Sum of ANY NUMBER added to 9 would give the SAME value of itself

For example; Consider number = 13

Sum of digits = 1+3 = 4

Adding 9 to 13 = 22 = 2+2 = 4

So the sum would always remain the same;


Back to our problem

99999999......26 = The sum of this number will add up to 2+6 = 8

From the options available, A & B can be discarded

9x1 = 9
9x2= 18
9x3= 27
9x4= 36
9x5= 45
9x6= 54
9x7= 63
9x8= 72 ........................................ 48th time
9x9= 81
9x10=90


99999999......26

\(10^{50}- 74\) means 9 would be repeated 48 times; so last digit would be 2

Now we have 2+2+6 = 10 (Last digit is 0)

Only option C best fits = 440

Answer = C
_________________

Kindly press "+1 Kudos" to appreciate :)

Director
Director
User avatar
G
Joined: 09 Mar 2016
Posts: 666
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

Show Tags

New post 01 Apr 2018, 05:00
Bunuel wrote:
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467



\(10^{50}\) has 51 digits (1 followed by 50 zeros). \(10^{50}-74\) has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is \(9*48+2+6=440\).

Answer: C.


Hello Bunuel why is the same question tagged both as 600 and 700 level question

here the same https://gmatclub.com/forum/if-10-50-74- ... 51062.html

is it 600 and 700 level question ? :?
Director
Director
User avatar
G
Joined: 09 Mar 2016
Posts: 666
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

Show Tags

New post 01 Apr 2018, 05:18
Bunuel wrote:
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467



\(10^{50}\) has 51 digits (1 followed by 50 zeros). \(10^{50}-74\) has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is \(9*48+2+6=440\).

Answer: C.


generis can you please explain ? :-)

i dont understand how after \(10^{50}-74\) we have 50 digits :?

And how we get "last 2 digits are 2 and 6 (26) and first 48 digits are 9's" :?
1 KUDOS received
SVP
SVP
User avatar
P
Joined: 26 Mar 2013
Posts: 1730
Reviews Badge CAT Tests
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

Show Tags

New post 01 Apr 2018, 05:25
1
dave13 wrote:
Bunuel wrote:
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467



\(10^{50}\) has 51 digits (1 followed by 50 zeros). \(10^{50}-74\) has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is \(9*48+2+6=440\).

Answer: C.


Hello Bunuel why is the same question tagged both as 600 and 700 level question

here the same https://gmatclub.com/forum/if-10-50-74- ... 51062.html

is it 600 and 700 level question ? :?


Hi dave13

I'm happy to answer you.

Have you posted question in GMATclub before? When someone posts a question, s/he chooses the level by checking. So it is subjective to the person who solves the question. I can say easy but another considers it hard or medium. Personally, I trust he level of a question when an instructor like Bunuel...etc tags the level.

Hi Bunuel
Can you merge the same question in one post?
https://gmatclub.com/forum/if-10-50-74- ... 51062.html
SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1838
Premium Member CAT Tests
If 10^50-74 is written as an integer in base 10 notation  [#permalink]

Show Tags

New post 01 Apr 2018, 12:57
1
dave13 wrote:
Bunuel wrote:
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467

\(10^{50}\) has 51 digits (1 followed by 50 zeros). \(10^{50}-74\) has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is \(9*48+2+6=440\).

Answer: C.

generis can you please explain ? :-)

i dont understand how after \(10^{50}-74\) we have 50 digits :?

And how we get "last 2 digits are 2 and 6 (26) and first 48 digits are 9's" :?

dave13 , I've seen you use patterns. Good instinct. Use a pattern. (I think you missed the "1,000" pattern above.)

First we have to figure out what the digits ARE. That's just subtraction. Start with 100. (You could start with 1,000, which would be a little more accurate. 1,000 - 74 = 926. There is a 9. But, see below, 26 is always there.)

Given (100-74), what is the sum of the digits?*
100-74 = 26. Sum of the digits? (2+6)=8

How many digits in the answer? TWO. You wrote: "i dont understand how after \(10^{50}-74\) we have 50 digits"

The exponent, 50, gives us a clue. Back to the earlier pattern.
100 = 10\(^2\). How many digits in \(10^2 -74?\) TWO digits in the answer, 26

But we have to be careful. If subtracting a positive integer (less than 100) from 10\(^2\), the possible number of digits in the answer is two OR one.
Two digits: (100-74) = 26
One digit: (100-94) = 6

The exponent is a clue only. Simple subtraction, with a few examples, will tell us how many digits. So let's go higher by powers of 10:
10\(^3\) = 1,000
10\(^4\) = 10,000
10\(^5\) = 100,000

Subtract 74 from each one. (Writing on paper really shows the pattern. Formatting here is hard):
(1,000 - 76) = 926
(10,000-76) = 9,926
100,000-76 = 99,926

\((10^3 - 74)\) has THREE digits. One 9, and 26
\((10^4 - 74)\) has FOUR digits. Two 9s, and 26
\((10^5 - 74)\) has FIVE digits. Three 9s, and 26

1) We are getting the same number of digits as the exponent on 10
2) The last two digits will always be 26
3) We have to borrow to move the initial 1 to the hundreds place. So there are repeated 9s. And only 9s until 26.
4) How many 9s? Exactly TWO fewer than 10's exponent (because 2 and 6 "use up" two of the digits)

Finally, SUM of the digits?
Back to the pattern
(1,000 - 76) = 926
(10,000-76) = 9,926
100,000-76 = 99,926
\(10^3 - 74 = ((1*9)+26)=(9+26)=35\)
\(10^4-74 = ((2*9)+26)) =(18+26)=44\)
\(10^5-74= ((3*9+26))=(27+26)=53\)


Try extrapolating from the pattern above for
What is the sum of the digits of \(10^{50} - 74\)?

*A fancy way to ask that question: If \(10^{2} - 74\) is written as an integer in base 10 notation, what is the sum of the digits in that integer?

Does that help? :-)
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

If 10^50-74 is written as an integer in base 10 notation &nbs [#permalink] 01 Apr 2018, 12:57
Display posts from previous: Sort by

If 10^50-74 is written as an integer in base 10 notation

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.