Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 19 Aug 2007
Posts: 17

If 10^50  74 is written as an integer in base 10 notation
[#permalink]
Show Tags
24 Aug 2007, 08:04
Question Stats:
64% (01:49) correct 36% (02:04) wrong based on 863 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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 49438

Re: If (10^50) 74 is written as an integer in base 10 notation,
[#permalink]
Show Tags
25 Jan 2012, 10:41
Baten80 wrote: What does "in base 10 notation" mean? 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 (base2 number system) notation. 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: 48 9's and 26 in the end; So, the sum of the digits of \(10^{50}74\) equals to 48*9+2+6=440. Answer: C. Similar questions: valueofn126388.html10126300.htmlHope it 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? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Joined: 19 Nov 2009
Posts: 261

Re: 10^50  74
[#permalink]
Show Tags
18 May 2010, 23:38
C. 440 10^x  74 > last 2 digits are always 2, 6. 10^2  74 = 26 10^3  74 = 926 10^4  74 = 9926 and so on.... If x > 1, the sum of the digits > (x2) * 9 + 2 + 6. hence, (502) * 9 + 8 > 440.
_________________
"Success is going from failure to failure without a loss of enthusiam."  Winston Churchill
As vs Like  Check this link : http://www.grammarquizzes.com/likeas.html.




Director
Joined: 03 May 2007
Posts: 823
Schools: University of Chicago, Wharton School

Re: PS 10 notation
[#permalink]
Show Tags
24 Aug 2007, 08:33
minnu 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
Thanks guys, I am not sure what this question asks...
the question is little confusing:
= (48x9) + 2 + 6
= 432+2+6
= 440



VP
Joined: 08 Jun 2005
Posts: 1136

solving for easier numbers > 10^3 and 74
(10^4)  74 =
(10^4)  10*7.4 =
10*[(10^3)  7.4] =
10*[10^3  7.4] = 992.6*10 = 9926 = 9*2+2+6 = 26
Note that 10^4 will yield two nines a six and a two.
so solving for 10^50 and 74 will give 48 nines a six and a two:
10*[10^49  7.4] = 9*48+2+6 = 440
the answer is (C)



VP
Joined: 10 Jun 2007
Posts: 1386

Re: PS 10 notation
[#permalink]
Show Tags
24 Aug 2007, 13:29
minnu 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
Thanks guys, I am not sure what this question asks...
C.
I am not sure if the GMAT test "base" concept, but basically, base 10 is just regular number.
Find out some numbers:
(10^3)74 = 926
(10^4)74 = 9926
(10^5)74 = 99926
Look at the pattern, the sum of the digits = 9*(502) + 2 + 6 = 440



Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 308

10^50  74
[#permalink]
Show Tags
18 May 2010, 23:08
If 10^50  74 is written as an integer in a base 10 notation.What is the sum of the digits in that integer?
a. 424 b. 433 c. 440 d. 449 e. 467



Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 308

Re: 10^50  74
[#permalink]
Show Tags
19 May 2010, 00:41
nsp007 wrote: C. 440
10^x  74 > last 2 digits are always 2, 6.
10^2  74 = 26
10^3  74 = 926
10^4  74 = 9926 and so on....
If x > 1, the sum of the digits > (x2) * 9 + 2 + 6. hence, (502) * 9 + 8 > 440. great approach but why are you using x here ? as you used ..."If x > 1," ..



VP
Status: mission completed!
Joined: 02 Jul 2009
Posts: 1312
GPA: 3.77

Re: 10^50  74
[#permalink]
Show Tags
19 May 2010, 01:06
dimitri92 wrote: If 10^50  74 is written as an integer in a base 10 notation.What is the sum of the digits in that integer?
a. 424 b. 433 c. 440 d. 449 e. 467 C. 440 another approach is: We know that 10^50 is ending 00, so 10^5074=9....9926 total number of digits in 10^5074 is 50, or 48 digits of 9 and two digits 2 and 6. answer choice is 48*9+8=440 plugging numbers: let represent the sum of the digits in that integer as Y, with the reminder 8, we can represent it in form Y=X*9+8, where X number of digits in 10^5074 and 8=2+6. Start with C and than move to B or D. B. 433=X*9+1, X=48 C. 440=X*9+8, X=48  correct as we have the reminder 8 and 48 number of digits (502), 2 digits are 26. D. 449=X*9+8, X=49 Personally, I like NSP007's approach. My approaches are easy to comprehend.
_________________
Audaces fortuna juvat!
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 19 Nov 2009
Posts: 261

Re: 10^50  74
[#permalink]
Show Tags
19 May 2010, 11:00
great approach but why are you using x here ? as you used ..."If x > 1," .. I meant to say that only when x > 1, for 10^x  74.. the last 2 digits are 2, 6.
_________________
"Success is going from failure to failure without a loss of enthusiam."  Winston Churchill
As vs Like  Check this link : http://www.grammarquizzes.com/likeas.html.



Manager
Joined: 14 Apr 2010
Posts: 184

Re: 10^50  74
[#permalink]
Show Tags
09 Jun 2010, 01:03
Hey Pkit, Please explain your approach. How do you know "total number of digits in 10^5074 is 50, or 48 digits of 9 and two digits 2 and 6"?



VP
Status: mission completed!
Joined: 02 Jul 2009
Posts: 1312
GPA: 3.77

Re: 10^50  74
[#permalink]
Show Tags
09 Jun 2010, 06:38
bibha wrote: Hey Pkit, Please explain your approach. How do you know "total number of digits in 10^5074 is 50, or 48 digits of 9 and two digits 2 and 6"? Approach is easy Just look at the following example, what is the sum of digits of 10^35 ? you know that 10^3=1000 (thus 10^50 is a figure that begins with 1 anf has 50 zeros) and 10005=995, so I have two "9" and one "5". the sum is 9+9+5=23 kudos!
_________________
Audaces fortuna juvat!
GMAT Club Premium Membership  big benefits and savings



Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 542

Re: If (10^50) 74 is written as an integer in base 10 notation,
[#permalink]
Show Tags
25 Jan 2012, 09:09



Manager
Joined: 07 Apr 2012
Posts: 104
Location: United States
Concentration: Entrepreneurship, Operations
GPA: 3.9
WE: Operations (Manufacturing)

Re: If 10^50  74 is written as an integer in base 10 notation
[#permalink]
Show Tags
02 Sep 2013, 20:05
10^1 = 10 10^2  74 = 026 10^3  74 = 926 10^4  74 = 9926
Basically for 10^n , its 9999....(n2)26.
So for 10^5074, it is 99999....4826
48times9 + 2+6 = 440.



Manager
Joined: 03 Jan 2017
Posts: 171

Re: If 10^50  74 is written as an integer in base 10 notation
[#permalink]
Show Tags
23 Mar 2017, 07:51
great question!
so, we have 10^5074 In base 10 notation means in usual system as 10^50 is too big number, let's take sth simple, e.g. 10^3=1000 100074=926 this means that 10^3 gets us one 9, hence 503=47+1(because including the numbers)=48 48*9+2+6=440 Answer is C



Intern
Joined: 06 Sep 2018
Posts: 39

Re: If 10^50  74 is written as an integer in base 10 notation
[#permalink]
Show Tags
07 Sep 2018, 19:45
base 10 notation means in decimal form. by expanding \(10^5^0\), there are 50 zeros in that number and by subtracting 74, there are 48 '9' digits and 2 remaining digits are 2 & 6. e.g. if we subtract 74 from \(10^4\) (10000) then we would get 9926 (2 '9' digits with one 2 and one 6 digit) So sum of all digits would be \(48*9+2+6=440\) Answer C
_________________
Eric Thomas, "When you want to succeed as bad as you want to breathe, then you'll be successful."




Re: If 10^50  74 is written as an integer in base 10 notation &nbs
[#permalink]
07 Sep 2018, 19:45






