Integer notation

Expert replies

fruti_yum: Master | Next Rank: 500 Posts; Posts: 128; Joined: Thu Jul 30, 2009 1:46 pm; Thanked: 1 times

by fruti_yum » Thu Sep 03, 2009 3:25 pm

If 10^50 - 74 is written as an integer in base 10 notation, what is the sum of the digits in that integer?

btw... the two blocks that appear.. it's a negative sign
A. 424
B. 433
C. 440
D. 449
E. 467

How do i even approach this question?

Like this post

Source: Beat The GMAT — Problem Solving | Thu Sep 03, 2009 3:25 pm

Gdieterling: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Thu Aug 06, 2009 8:20 am; Thanked: 2 times

by Gdieterling » Thu Sep 03, 2009 3:46 pm

IMO : D

10^50 = is a number which has 51 digits.

Thus, when you substract 74 you get : 9 followed by 49 "9's" and the number ends with xx99926.

It asks you to add all the digits of that number :

9 * 49 + 2 + 6 = 449

Am I right ?

Like this post

fruti_yum: Master | Next Rank: 500 Posts; Posts: 128; Joined: Thu Jul 30, 2009 1:46 pm; Thanked: 1 times

by fruti_yum » Thu Sep 03, 2009 4:25 pm

Gdieterling wrote:IMO : D

10^50 = is a number which has 51 digits.

Thus, when you substract 74 you get : 9 followed by 49 "9's" and the number ends with xx99926.

It asks you to add all the digits of that number :

9 * 49 + 2 + 6 = 449

Am I right ?

yes OA is D...how do u quickly find out that there are 49 9's?? I had to do an analogy between 10^5 and then I could determine.. it was too time consuming

Like this post

tom4lax: Master | Next Rank: 500 Posts; Posts: 175; Joined: Mon Feb 09, 2009 3:57 pm; Thanked: 4 times

by tom4lax » Thu Sep 03, 2009 6:50 pm

How do you get to 49 9's I am also curious?

As an example, 10^5 is 100,000 - 74 = 99,926 or 3 9's. The way I looked at it was take the number of zeros then subtract by 2, so 10^50 = 48 9's.
However answer is with 49 9's. What gives?

Like this post

Gdieterling: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Thu Aug 06, 2009 8:20 am; Thanked: 2 times

by Gdieterling » Fri Sep 04, 2009 1:28 am

10^5 = 100 000 --> 10 followed with 4 zeros
When substracting one : 9 followed by 4 9's (99999)

10^10 = 10 000 000 000 --> 10 followed with 9 zeros
When susbtrasting one : 9 followed by 9 9's (9 999 999 999)

10^50 = 10 followed with 49 zeros
When substracting 1 : 9 followed by 49 9's

Then, by susbtracting 76 to 10^50 : 9 followed by 48 9's (which is 49 9's) :

49 * 9 = 441 + 2 + 6 = 449

Besides, I just thought of an interesting way to guess :
You know that the answer will be a multiple of 9 to which we add : 8.

We know that 9 has a dual cyclicality :

9^1 : 9
9^2 : 81
9^3 : 729
9^4 : XXX1

Thus, the solution we are looking for ends either with 7 (9 + 8) or with 9 (1 + 8), reducing the solutions to 449 or 467.

467 - 8 = 459 which is 51 * 9 and obviously impossible when 10^50 was containing 51 digits.

Like this post

PussInBoots: Master | Next Rank: 500 Posts; Posts: 157; Joined: Tue Oct 07, 2008 5:47 am; Thanked: 3 times

by PussInBoots » Mon Sep 14, 2009 11:11 pm

10^50 has fifty zeros.

Subtract 1 and we get fifty nines.
Subtract 74 and we get 48 nines, 2 and 6.

48 * 9 + 2 + 6 = 360 + 72 + 8 = 440

Answer is C

https://www.beatthegmat.com/base-10-nota ... 20304.html

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review