10^50 - 74 : GMAT Problem Solving (PS)

10^50 - 74

Oldest

Best Reply

Author

Message

TAGS:

Senior Manager

Affiliations: SPG

Joined: 15 Nov 2006

Posts: 327

Followers: 9

Kudos [?]: 180 [0], given: 19

10^50 - 74 [#permalink]

18 May 2010, 23:08

00:00

Question Stats:

50% (04:11) correct

50% (01:13) wrong

based on 0 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: 337

Followers: 2

Kudos [?]: 47 [2] , given: 44

Re: 10^50 - 74 [#permalink]

18 May 2010, 23:38

This post received
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.

Senior Manager

Affiliations: SPG

Joined: 15 Nov 2006

Posts: 327

Followers: 9

Kudos [?]: 180 [0], given: 19

Re: 10^50 - 74 [#permalink]

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 --> (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," ..

Forum Moderator

Status: doing good things...

Joined: 02 Jul 2009

Posts: 1232

Concentration: Entrepreneurship, Finance

Schools: Ross '15 (A), INSEAD Jan '13, IMD '15

GMAT 1: Q V
GMAT 2: 690 Q49 V35

GPA: 3.77

WE: Corporate Finance (Other)

Followers: 125

Kudos [?]: 416 [1] , given: 521

Re: 10^50 - 74 [#permalink]

19 May 2010, 01:06

This post received
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.
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 10^50-74 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 (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.
_________________

Follow me, if you find my explanations useful.

Audaces fortuna juvat!

Find out what's new at GMAT Club - latest features and updates

Senior Manager

Joined: 19 Nov 2009

Posts: 337

Followers: 2

Kudos [?]: 47 [0], given: 44

Re: 10^50 - 74 [#permalink]

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.grammar-quizzes.com/like-as.html.

Manager

Joined: 14 Apr 2010

Posts: 241

Followers: 2

Kudos [?]: 7 [0], given: 1

Re: 10^50 - 74 [#permalink]

09 Jun 2010, 01:03

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: doing good things...

Joined: 02 Jul 2009

Posts: 1232

Concentration: Entrepreneurship, Finance

Schools: Ross '15 (A), INSEAD Jan '13, IMD '15

GMAT 1: Q V
GMAT 2: 690 Q49 V35

GPA: 3.77

WE: Corporate Finance (Other)

Followers: 125

Kudos [?]: 416 [0], given: 521

Re: 10^50 - 74 [#permalink]

09 Jun 2010, 06:38

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! :wink:

_________________

Follow me, if you find my explanations useful.

Audaces fortuna juvat!

Find out what's new at GMAT Club - latest features and updates

Intern

Joined: 02 Sep 2009

Posts: 17

Followers: 0

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

Re: 10^50 - 74 [#permalink]

09 Jun 2010, 10:10

Great explanation. Thanks

Re: 10^50 - 74 [#permalink] 09 Jun 2010, 10:10

	Similar topics	Author	Replies	Last post
Similar Topics:	If 10^50 - 74 is written as an integer in base 10 notation,	rthothad	4	30 Jun 2005, 19:32
	Q14: If 1050 74 is written as an integer in base 10	nakib77	3	13 Oct 2005, 13:56
	What is the sum of all digits for the number (10^50) -74	joemama142000	3	08 Jan 2006, 00:13
	If 10^(50) - 74 is written as an integer in base 10	getzgetzu	5	05 May 2006, 23:18
	If 10^50 74 is written as an integer in base 10 notation,	positive_energy	3	01 Aug 2006, 11:54

10^50 - 74

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

10^50 - 74

10^50 - 74

Main navigation

GMAT Resources

Partners

MBA Resources