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

 It is currently 19 Oct 2018, 10:45

### 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

# What is the sum of the digits of integer k, if k = (10^40- 46)

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50002
What is the sum of the digits of integer k, if k = (10^40- 46)  [#permalink]

### Show Tags

22 Sep 2015, 02:50
3
8
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:52) correct 30% (02:12) wrong based on 207 sessions

### HideShow timer Statistics

What is the sum of the digits of integer k, if k = (10^40- 46)

(A) 351
(B) 360
(C) 363
(D) 369
(E) 378

Kudos for a correct solution.

_________________
Manager
Joined: 29 Jul 2015
Posts: 159
Re: What is the sum of the digits of integer k, if k = (10^40- 46)  [#permalink]

### Show Tags

22 Sep 2015, 04:41
1
1
Bunuel wrote:
What is the sum of the digits of integer k, if k = (10^40- 46)

(A) 351
(B) 360
(C) 363
(D) 369
(E) 378

Kudos for a correct solution.

There are 41 digits in 10^4
When we subtract 46 from it, there will be 40 digits left.
10^4 can be written as 9999999....(40 times) + 1
So,
10^40 - 46 = 9999999....(40 times) + 1 - 46 = 9999999....(40 times) -45
Consider the last 2 digits,
99-45 = 54
The last 2 digits will be 54.
And our number would be 99999......99954 with 2 less 9s after subtraction.
Nuber of 9s left are 38 and the last two digits are 54
The sum of the digits will be
(38*9) + 5 + 4 =351

Intern
Joined: 19 Dec 2014
Posts: 35
Re: What is the sum of the digits of integer k, if k = (10^40- 46)  [#permalink]

### Show Tags

22 Sep 2015, 11:51
2
(10^40- 46) is nothing but 999... (38 of them) followed by 54

so that adds to (9*38)+5+4 = 351

Math Expert
Joined: 02 Sep 2009
Posts: 50002
Re: What is the sum of the digits of integer k, if k = (10^40- 46)  [#permalink]

### Show Tags

27 Sep 2015, 11:11
Bunuel wrote:
What is the sum of the digits of integer k, if k = (10^40- 46)

(A) 351
(B) 360
(C) 363
(D) 369
(E) 378

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

While this may look like a monster problem, it’s really just one of arithmetic. 10^40 is an insanely large number, but conceptually it’s not much different from 10^3 (i.e. 1000). If you test this relationship with a few small numbers, you can get a good look at what k will look like. For example:

$$10^2 -46 = 100-46 = 54$$
$$10^3 -46 = 1000-46 = 954$$
$$10^4 -46 = 10000-46 = 9954$$

Do you see the pattern? Every time we add one to the exponent, we add another 9 to the solution. And the number of digits in the solution is always the same as the exponent itself. So for this problem, where the exponent is 40, k will have 40 digits: a 5, a 4, and the other 38 are 9s. And since 5 + 4 is 9, then really we’re just adding up 39 9s. And 39*9 is 351 (or you can just see that it will end in a 1, and only A matches).
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 8461
Re: What is the sum of the digits of integer k, if k = (10^40- 46)  [#permalink]

### Show Tags

22 Sep 2018, 05:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: What is the sum of the digits of integer k, if k = (10^40- 46) &nbs [#permalink] 22 Sep 2018, 05:14
Display posts from previous: Sort by