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

 It is currently 26 Nov 2015, 17:41

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# 10^50 - 74

Author Message
TAGS:
Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 326
Followers: 13

Kudos [?]: 476 [0], given: 20

10^50 - 74 [#permalink]  18 May 2010, 22:08
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

75% (02:22) correct 25% (01:13) wrong based on 9 sessions
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
Joined: 19 Nov 2009
Posts: 326
Followers: 5

Kudos [?]: 76 [2] , given: 44

Re: 10^50 - 74 [#permalink]  18 May 2010, 22:38
2
KUDOS
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 --> (x-2) * 9 + 2 + 6. hence, (50-2) * 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.grammar-quizzes.com/like-as.html.

Forum Moderator
Status: mission completed!
Joined: 02 Jul 2009
Posts: 1426
GPA: 3.77
Followers: 174

Kudos [?]: 690 [1] , given: 620

Re: 10^50 - 74 [#permalink]  19 May 2010, 00:06
1
KUDOS
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 10^50-74=9....9926
total number of digits in 10^50-74 is 50, or 48 digits of 9 and two digits 2 and 6.

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 10^50-74 and 8=2+6.

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 (50-2), 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
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 326
Followers: 13

Kudos [?]: 476 [0], given: 20

Re: 10^50 - 74 [#permalink]  18 May 2010, 23:41
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 --> (x-2) * 9 + 2 + 6. hence, (50-2) * 9 + 8 --> 440.

great approach but why are you using x here ? as you used ..."If x > 1," ..
Senior Manager
Joined: 19 Nov 2009
Posts: 326
Followers: 5

Kudos [?]: 76 [0], given: 44

Re: 10^50 - 74 [#permalink]  19 May 2010, 10:00
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.grammar-quizzes.com/like-as.html.

Manager
Joined: 14 Apr 2010
Posts: 229
Followers: 2

Kudos [?]: 80 [0], given: 1

Re: 10^50 - 74 [#permalink]  09 Jun 2010, 00:03
Hey Pkit,
Please explain your approach. How do you know "total number of digits in 10^50-74 is 50, or 48 digits of 9 and two digits 2 and 6"?
Forum Moderator
Status: mission completed!
Joined: 02 Jul 2009
Posts: 1426
GPA: 3.77
Followers: 174

Kudos [?]: 690 [0], given: 620

Re: 10^50 - 74 [#permalink]  09 Jun 2010, 05:38
bibha wrote:
Hey Pkit,
Please explain your approach. How do you know "total number of digits in 10^50-74 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 10^3-5 ?
you know that 10^3=1000 (thus 10^50 is a figure that begins with 1 anf has 50 zeros) and 1000-5=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

Intern
Joined: 02 Sep 2009
Posts: 18
Followers: 0

Kudos [?]: 1 [0], given: 13

Re: 10^50 - 74 [#permalink]  09 Jun 2010, 09:10
Great explanation. Thanks
Re: 10^50 - 74   [#permalink] 09 Jun 2010, 09:10
Similar topics Replies Last post
Similar
Topics:
18 If 10^50-74 is written as an integer in base 10 notation 10 26 Aug 2010, 06:42
6 What is the remainder when 7^74 - 5^74 is divided by 24? 10 03 Jul 2008, 12:19
19 If x is a positive integer and 10^x – 74 in decimal notation 12 09 Mar 2008, 01:09
15 If 10^50 - 74 is written as an integer in base 10 notation 8 24 Aug 2007, 07:04
34 What is the remainder when 1044*1047*1050*1053 is divided by 26 20 May 2007, 16:19
Display posts from previous: Sort by