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

 It is currently 17 Jan 2019, 03:51

### 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
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# How many trailing zeros will 11^50 - 1 will have ?

Author Message
Intern
Joined: 28 Mar 2015
Posts: 3
How many trailing zeros will 11^50 - 1 will have ?  [#permalink]

### Show Tags

28 Mar 2015, 21:39
1
6
00:00

Difficulty:

75% (hard)

Question Stats:

47% (01:04) correct 53% (01:48) wrong based on 51 sessions

### HideShow timer Statistics

How many trailing zeros will 11^50 - 1 will have ?

A) 3
B) 4
C) 5
D) 6
E) 7
Director
Joined: 07 Aug 2011
Posts: 535
GMAT 1: 630 Q49 V27
Re: How many trailing zeros will 11^50 - 1 will have ?  [#permalink]

### Show Tags

29 Mar 2015, 03:25
CrazyIvan wrote:
How many trailing zeros will $$11^5^0 - 1$$ will have ?

A) 3
B) 4
C) 5
D) 6
E) 7

i doubt this is a GMAT standard question , but let try to give it a shot .

$$11^5^0 - 1= (1+10)^50 -1 = 1+ ^5^0C_1 *10 + ^5^0C_2 *10^2 + ^5^0C_3 *10^3 + .... +^5^0C_50 *10^5^0 -1$$

$$50*10 (1+ \frac{49}{2*1}*10 + \frac{49*48}{3*2*1} * 10^2 + ..... + \frac{49*48...*2}{50!} 10^4^9)$$

taking LCM 50!

$$50*10 *( 50!+ \frac{49}{2*1}*10 *\frac{50!}{2!} + \frac{49*48}{3*2*1} * 10^2 *\frac{50!}{3!} + .....)/50!$$

we can take out 50 from the inner brackets and the remaining quantity will still be > 1

so answer should be 3 .

but i am not very sure .
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Intern
Joined: 20 Mar 2015
Posts: 18
Location: Italy
GMAT 1: 670 Q48 V34
GPA: 3.7
Re: How many trailing zeros will 11^50 - 1 will have ?  [#permalink]

### Show Tags

29 Mar 2015, 09:28
It took me a lot of time to solve it, not only 2 minutes... so I wouldn't have been able to solve it in a test

I noticed that the powers of 11 can be calculated as
$$11^0=1 \\11^1=11 \\ 11^2=121 \\11^3=1331 \\11^4=14641$$

It reminds me of the Pascal's triangle, and the powers of 11 can be written as $$11^n=\sum_{i=0}^{n} (10^{i} \cdot \frac{n!}{i!(n-i)!})$$

I consider the last 4 digits, so I calculate $$1000\cdot \frac{50!}{47!3!}+100\cdot \frac{50!}{48!2!}+10 \cdot \frac{50!}{49!1!} +1=39200000+1225+500+1=39223001$$

If we subtract 1, there are three zeroes, so A is the correct answer.

Unfortunately I cannot explain it in a simpler way
Non-Human User
Joined: 09 Sep 2013
Posts: 9419
Re: How many trailing zeros will 11^50 - 1 will have ?  [#permalink]

### Show Tags

12 Jul 2018, 06:05
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: How many trailing zeros will 11^50 - 1 will have ? &nbs [#permalink] 12 Jul 2018, 06:05
Display posts from previous: Sort by