GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Jan 2019, 18:23

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
• ### Free GMAT Number Properties Webinar

January 27, 2019

January 27, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

# If 10^50-74 is written as an integer in base 10 notation

Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Apr 2010
Posts: 117
If 10^50-74 is written as an integer in base 10 notation  [#permalink]

### Show Tags

26 Aug 2010, 06:42
8
39
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:51) correct 33% (02:05) wrong based on 801 sessions

### HideShow timer Statistics

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

A. 424
B. 433
C. 440
D. 449
E. 467
Math Expert
Joined: 02 Sep 2009
Posts: 52431

### Show Tags

26 Aug 2010, 07:25
13
9
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467

$$10^{50}$$ has 51 digits (1 followed by 50 zeros). $$10^{50}-74$$ has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is $$9*48+2+6=440$$.

_________________
##### General Discussion
Manager
Joined: 24 Dec 2009
Posts: 174

### Show Tags

26 Aug 2010, 22:12
C for me too..Excellent expln by Bunnel. Thanks.
Retired Moderator
Joined: 20 Dec 2010
Posts: 1810

### Show Tags

19 Feb 2011, 13:03
The integer is going to have 48 9's.
Last 2 digits will be 26

48*9 + 2 + 6 = 432+8 = 440.

Ans: "C"
_________________
Intern
Joined: 04 Oct 2013
Posts: 4
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

### Show Tags

23 Nov 2013, 11:05
I don't understand why in the question it is mentioned "in base 10 notation"

Maybe its because English is not my mother tongue but that instruction really confused me. I thought I was looking for a number like "ten to the power of something".
Math Expert
Joined: 02 Sep 2009
Posts: 52431
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

### Show Tags

23 Nov 2013, 12:07
1
1
Lobro wrote:
I don't understand why in the question it is mentioned "in base 10 notation"

Maybe its because English is not my mother tongue but that instruction really confused me. I thought I was looking for a number like "ten to the power of something".

Based 10 notation, or decimal notation, is just a way of writing a number using 10 digits: 1, 2, 3, 4, 5, 6, 7, 8, and 0 (usual way), in contrast, for example, to binary numeral system (base-2 number system) notation.

Similar questions to practice:
the-sum-of-the-digits-of-64-279-what-is-the-141460.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-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html

Hope this helps.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1823
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

### Show Tags

04 Apr 2014, 00:26
100 - 74 = 26

The last 2 digits of the term would be 26; all else would be 9

99999999......26

Important rule:

Sum of ANY NUMBER added to 9 would give the SAME value of itself

For example; Consider number = 13

Sum of digits = 1+3 = 4

Adding 9 to 13 = 22 = 2+2 = 4

So the sum would always remain the same;

Back to our problem

99999999......26 = The sum of this number will add up to 2+6 = 8

From the options available, A & B can be discarded

9x1 = 9
9x2= 18
9x3= 27
9x4= 36
9x5= 45
9x6= 54
9x7= 63
9x8= 72 ........................................ 48th time
9x9= 81
9x10=90

99999999......26

$$10^{50}- 74$$ means 9 would be repeated 48 times; so last digit would be 2

Now we have 2+2+6 = 10 (Last digit is 0)

Only option C best fits = 440

_________________

Kindly press "+1 Kudos" to appreciate

VP
Joined: 09 Mar 2016
Posts: 1287
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

### Show Tags

01 Apr 2018, 04:00
Bunuel wrote:
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467

$$10^{50}$$ has 51 digits (1 followed by 50 zeros). $$10^{50}-74$$ has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is $$9*48+2+6=440$$.

Hello Bunuel why is the same question tagged both as 600 and 700 level question

here the same https://gmatclub.com/forum/if-10-50-74- ... 51062.html

is it 600 and 700 level question ?
VP
Joined: 09 Mar 2016
Posts: 1287
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

### Show Tags

01 Apr 2018, 04:18
Bunuel wrote:
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467

$$10^{50}$$ has 51 digits (1 followed by 50 zeros). $$10^{50}-74$$ has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is $$9*48+2+6=440$$.

generis can you please explain ?

i dont understand how after $$10^{50}-74$$ we have 50 digits

And how we get "last 2 digits are 2 and 6 (26) and first 48 digits are 9's"
SVP
Joined: 26 Mar 2013
Posts: 2010
Re: If 10^50-74 is written as an integer in base 10 notation  [#permalink]

### Show Tags

01 Apr 2018, 04:25
1
dave13 wrote:
Bunuel wrote:
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467

$$10^{50}$$ has 51 digits (1 followed by 50 zeros). $$10^{50}-74$$ has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is $$9*48+2+6=440$$.

Hello Bunuel why is the same question tagged both as 600 and 700 level question

here the same https://gmatclub.com/forum/if-10-50-74- ... 51062.html

is it 600 and 700 level question ?

Hi dave13

Have you posted question in GMATclub before? When someone posts a question, s/he chooses the level by checking. So it is subjective to the person who solves the question. I can say easy but another considers it hard or medium. Personally, I trust he level of a question when an instructor like Bunuel...etc tags the level.

Hi Bunuel
Can you merge the same question in one post?
https://gmatclub.com/forum/if-10-50-74- ... 51062.html
Senior SC Moderator
Joined: 22 May 2016
Posts: 2375
If 10^50-74 is written as an integer in base 10 notation  [#permalink]

### Show Tags

01 Apr 2018, 11:57
dave13 wrote:
Bunuel wrote:
udaymathapati wrote:
If 10^{50}-74 is written as an integer in base 10 notation, what is the sum of the digits in
that integer?
A. 424
B. 433
C. 440
D. 449
E. 467

$$10^{50}$$ has 51 digits (1 followed by 50 zeros). $$10^{50}-74$$ has 50 digits: last 2 digits are 2 and 6 (26) and first 48 digits are 9's.

Like 1,000-74=926.

So the sum of the digits is $$9*48+2+6=440$$.

generis can you please explain ?

i dont understand how after $$10^{50}-74$$ we have 50 digits

And how we get "last 2 digits are 2 and 6 (26) and first 48 digits are 9's"

dave13 , I've seen you use patterns. Good instinct. Use a pattern. (I think you missed the "1,000" pattern above.)

First we have to figure out what the digits ARE. That's just subtraction. Start with 100. (You could start with 1,000, which would be a little more accurate. 1,000 - 74 = 926. There is a 9. But, see below, 26 is always there.)

Given (100-74), what is the sum of the digits?*
100-74 = 26. Sum of the digits? (2+6)=8

How many digits in the answer? TWO. You wrote: "i dont understand how after $$10^{50}-74$$ we have 50 digits"

The exponent, 50, gives us a clue. Back to the earlier pattern.
100 = 10$$^2$$. How many digits in $$10^2 -74?$$ TWO digits in the answer, 26

But we have to be careful. If subtracting a positive integer (less than 100) from 10$$^2$$, the possible number of digits in the answer is two OR one.
Two digits: (100-74) = 26
One digit: (100-94) = 6

The exponent is a clue only. Simple subtraction, with a few examples, will tell us how many digits. So let's go higher by powers of 10:
10$$^3$$ = 1,000
10$$^4$$ = 10,000
10$$^5$$ = 100,000

Subtract 74 from each one. (Writing on paper really shows the pattern. Formatting here is hard):
(1,000 - 76) = 926
(10,000-76) = 9,926
100,000-76 = 99,926

$$(10^3 - 74)$$ has THREE digits. One 9, and 26
$$(10^4 - 74)$$ has FOUR digits. Two 9s, and 26
$$(10^5 - 74)$$ has FIVE digits. Three 9s, and 26

1) We are getting the same number of digits as the exponent on 10
2) The last two digits will always be 26
3) We have to borrow to move the initial 1 to the hundreds place. So there are repeated 9s. And only 9s until 26.
4) How many 9s? Exactly TWO fewer than 10's exponent (because 2 and 6 "use up" two of the digits)

Finally, SUM of the digits?
Back to the pattern
(1,000 - 76) = 926
(10,000-76) = 9,926
100,000-76 = 99,926
$$10^3 - 74 = ((1*9)+26)=(9+26)=35$$
$$10^4-74 = ((2*9)+26)) =(18+26)=44$$
$$10^5-74= ((3*9+26))=(27+26)=53$$

Try extrapolating from the pattern above for
What is the sum of the digits of $$10^{50} - 74$$?

*A fancy way to ask that question: If $$10^{2} - 74$$ is written as an integer in base 10 notation, what is the sum of the digits in that integer?

Does that help?
_________________

Sometimes at night I would sleep open-eyed underneath a sky dripping with stars.
I was alive then.

—Albert Camus

If 10^50-74 is written as an integer in base 10 notation &nbs [#permalink] 01 Apr 2018, 11:57
Display posts from previous: Sort by