Last visit was: 26 Jul 2024, 23:29 It is currently 26 Jul 2024, 23:29
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If x = 10^50 - 57, what is the sum of all the digits of x?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
interceptor77
Intern
Intern
Joined: 23 Sep 2011
Posts: 10
Own Kudos [?]: 126 [23]
Given Kudos: 26
Send PM
GMAT ToolKit User Reviews Badge
If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink] If x = 10^50 - 57, what is the sum of all the digits of x?   01 Nov 2016, 03:33
1
Kudos
22
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

81% (01:56) correct 19% (02:12) wrong based on 206 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
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
ShowHide Answer
Official Answer
D
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 94619
Own Kudos [?]: 644215 [4]
Given Kudos: 86770
Send PM
CAT Tests Forum Quiz Mode
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink] If x = 10^50 - 57, what is the sum of all the digits of x?   01 Nov 2016, 04:02
2
Kudos
2
Bookmarks
Expert Reply
interceptor77 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


Similar questions to practice:
what-is-the-sum-of-digits-of-number-108962.html
if-10-50-74-is-written-as-an-integer-in-base-10-notation-99824.html
if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.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-x-is-a-positive-integer-and-10-x-74-in-decimal-notation-61013.html
what-is-the-sum-of-all-digits-for-the-number-147057.html
if-x-is-a-positive-integer-and-10-x-74-in-decimal-notation-61013.html
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
the-sum-of-the-digits-of-64-279-what-is-the-141460.html
User avatar
interceptor77
Intern
Intern
Joined: 23 Sep 2011
Posts: 10
Own Kudos [?]: 126 [3]
Given Kudos: 26
Send PM
GMAT ToolKit User Reviews Badge
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink] If x = 10^50 - 57, what is the sum of all the digits of x?   01 Nov 2016, 05:12
1
Kudos
2
Bookmarks
Thanks for the links. For this problem I used the following reasoning. 10^50 is an eleven digit number and can be defined as 1 followed by 50 zeros, when we start to perform the subtraction of this giant number from 47 we notice the following pattern:

10^2 100-57=43 (result of two digits number)
10^3 1000-57=943 (result of three digits number)
10^4 10000-57=9943 (result of four digits number)
and so on... until 10^50

The result of the subtraction becomes a 50 digits number composed by 48 pairs of 9 followed by a 4 and 5. Therefore 48*9=432 and 432+(4+5)=439

The correct answer is D.
avatar
G
fireagablast
Senior Manager
Senior Manager
Joined: 30 Jun 2019
Posts: 271
Own Kudos [?]: 93 [1]
Given Kudos: 8
Send PM
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink] If x = 10^50 - 57, what is the sum of all the digits of x?   01 Mar 2020, 17:05
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
User avatar
B
Mansouri
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] If x = 10^50 - 57, what is the sum of all the digits of x?   26 Feb 2024, 17:49
hello Bunuel,

can you explain this one also. thanks man
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 94619
Own Kudos [?]: 644215 [0]
Given Kudos: 86770
Send PM
CAT Tests Forum Quiz Mode
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink] If x = 10^50 - 57, what is the sum of all the digits of x?   27 Feb 2024, 01:22
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.­­
User avatar
D
Oppenheimer1945
Director
Director
Joined: 16 Jul 2019
Posts: 644
Own Kudos [?]: 304 [0]
Given Kudos: 166
Send PM
CAT Tests
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink] If x = 10^50 - 57, what is the sum of all the digits of x?   27 Feb 2024, 11:43
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
gmatclubot
Re: If x = 10^50 - 57, what is the sum of all the digits of x? [#permalink]
27 Feb 2024, 11:43
Moderator:
Bunuel
Math Expert
94619 posts