Last visit was: 24 May 2024, 04:26 It is currently 24 May 2024, 04:26
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Intern
Intern
Joined: 23 Sep 2011
Posts: 10
Own Kudos [?]: 123 [23]
Given Kudos: 26
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 93447
Own Kudos [?]: 626273 [3]
Given Kudos: 81954
Send PM
User avatar
Intern
Intern
Joined: 23 Sep 2011
Posts: 10
Own Kudos [?]: 123 [3]
Given Kudos: 26
Send PM
Senior Manager
Senior Manager
Joined: 30 Jun 2019
Posts: 275
Own Kudos [?]: 90 [1]
Given Kudos: 8
Send PM
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink]
1
Kudos
10^1 = 10
10^2 = 100
..
10^50 = 50 zeroes

1000-57 = 943 -> (3-2)9 + 4 +3
10^50-57 = (50-2)(9) + 4 +3 = 439
Intern
Intern
Joined: 25 Feb 2024
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 9
Send PM
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink]
hello Bunuel,

can you explain this one also. thanks man
Math Expert
Joined: 02 Sep 2009
Posts: 93447
Own Kudos [?]: 626273 [0]
Given Kudos: 81954
Send PM
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink]
Expert Reply
 
Mansouri wrote:
If x = 10^50 - 57, what is the sum of all the digits of x?

(A) 390
(B) 418
(C) 420
(D) 439
(E) 449­

hello Bunuel,

can you explain this one also. thanks man

­
\(10^{50}\) has 51 digits: 1 followed by 50 zeros;
\(10^{50}-57\) has 50 digits: 48 nines and 43 at the end;

So, the sum of the digits of \(10^{50}-74\) equals to 48*9 + 4 + 3 = 439.

Answer: D.

Hope it helps.­­
Director
Director
Joined: 16 Jul 2019
Posts: 540
Own Kudos [?]: 208 [0]
Given Kudos: 150
Send PM
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink]
10^2-57=43
10^3-57=943

10^n-54=999...(n-2) times 43

sum of Digits=9(n-2)+4+3=9(48)+4+3
9(50-2)+7=450-18+7=450-11=439
GMAT Club Bot
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink]
Moderator:
Math Expert
93447 posts