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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Thurston wrote an important seven-digit phone number on a na [#permalink]

Show Tags

12 Sep 2013, 03:25

3

This post received KUDOS

13

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

48% (03:27) correct
52% (02:03) wrong based on 203 sessions

HideShow timer Statistics

Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 10 phone numbers by using the readable digits followed by 10 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?

Re: Thurston wrote an important seven-digit phone number on a na [#permalink]

Show Tags

12 Sep 2013, 03:33

1

This post received KUDOS

1

This post was BOOKMARKED

The answer is 1/27.

Our first step is determining how many possible three-digit numbers there are with at least one zero and one nonzero. Treat this like a permutations question in which you could have any of the following six sequences, where N = non-zero integer. 0NN, N0N, NN0, N00, 00N, 0N0

There are 9 numbers that could appear in the N-slots and 1 number (zero) that could appear in the zero slots. Each sequence with two nonzero numbers will have 81 possible outcomes (1 * 9 * 9, or 9 * 1 * 9, or 9 * 9 * 1), while each sequence with one nonzero will have 9 possible outcomes (9 * 1 * 1, or 1 * 1 * 9, or 1 * 9 * 1). The total number of possible three-digit numbers here is 81 * 3 + 9 * 3 = 270.

Thurston calls 10 of these numbers, so the odds of dialing the right one are 10/270 = 1/27.

Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 10 phone numbers by using the readable digits followed by 10 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?

A. 1/9 B. 10/243 C. 1/27 D. 10/271 E. 1/1000000

If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).

If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).

Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 10 phone numbers by using the readable digits followed by 10 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?

A. 1/9 B. 10/243 C. 1/27 D. 10/271 E. 1/1000000

If the last three digits have 1 zero (XX0), the total # of numerous possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX). If the last three digits have 2 zeros (X00), the total # of numerous possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).

Re: Thurston wrote an important seven-digit phone number on a na [#permalink]

Show Tags

16 Mar 2014, 21:05

If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).

If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).

P = 10/(9*9*3+9*3) = 1/27.

Answer: C.

Hi Bunuel,

Since I got this question wrong, I need insights on this.

We have two options of using either (1).two zeros and a non-zero or (2). two non-zero and a zero.

In the above solution when you say XX0 can be arranged in 3 ways, since the problem is that you are considering XX as a unique single digit non-zero. However, there can be a case where 450 and 540 can be the numbers in which case the permutation will come out different.

We can consider permutations in

N00 as 3 since 0 is a unique number and we have 9 possibilities for 'N'.So, we have

9 possibilities for N and arrangement of NOO which would be !3/!2 (Divide by !2 since 0 are unique) =27

NN0

9 possibilities for each N and arrangement of NNO which would be !3 (Not divide by !2 since N is not unique) =9*9*6

Please suggest where I am going wrong in this one

Rgds, TGC!
_________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: Thurston wrote an important seven-digit phone number on a na [#permalink]

Show Tags

26 Mar 2014, 10:03

Can someone please explain why we divide 10 to 270. I know that the probability means dividing desired outcome to possible outcomes. Here desired outcome is just one number not ten.
_________________

If my post was helpful, press Kudos. If not, then just press Kudos !!!

Can someone please explain why we divide 10 to 270. I know that the probability means dividing desired outcome to possible outcomes. Here desired outcome is just one number not ten.

But Thurston tries 10 times not just 1:

"If Thurston dials 10 phone numbers by using the readable digits followed by 10 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?"
_________________

Re: Thurston wrote an important seven-digit phone number on a na [#permalink]

Show Tags

30 Mar 2014, 01:38

Hi.

Please explain why after find the total possible number of the telephone numbers, we have 10 divided by 270? I have thought that the chance that there is one correct phone numbers and 9 incorrect phone numbers is:

(1/270)*[(269/270)^9]*10!

The correct answer choice seems to indicate that each pick does not relate to the later picks, but the chance to pick the correct phone numbers increases after each pick, it isn't? That is why I multiply the chance to get correct phone numbers and the chance to get incorrect phone numbers.

Thurston wrote an important seven-digit phone number on a na [#permalink]

Show Tags

21 Jul 2014, 07:16

Bunuel wrote:

If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).

If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).

P = 10/(9*9*3+9*3) = 1/27.

Answer: C.

Hi Bunuel,

I have a Query. In case 1 where there is only one zero, XX0 can also be XY0, in that case should it not be multiplied by 3! (i.e. 6)? For. example 3,2,0 can be written in 6 ways.

If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).

If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).

P = 10/(9*9*3+9*3) = 1/27.

Answer: C.

Hi Bunuel,

I have a Query. In case 1 where there is only one zero, XX0 can also be XY0, in that case should it not be multiplied by 3! (i.e. 6)? For. example 3,2,0 can be written in 6 ways.

Thanks in advance for your clarification.

The point is that 9*9 gives all possible ordered pairs of the remaining two digits:

11 12 13 14 15 16 17 18 19 21 ... 99

Now, 0, in three digits can take either first, second or third place, hence multiplying by 3: XX0, X0X, 0XX.

Thurston wrote an important seven-digit phone number on a na [#permalink]

Show Tags

15 Oct 2014, 10:01

Bunuel wrote:

arichinna wrote:

Bunuel wrote:

If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).

If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).

P = 10/(9*9*3+9*3) = 1/27.

Answer: C.

Hi Bunuel,

I have a Query. In case 1 where there is only one zero, XX0 can also be XY0, in that case should it not be multiplied by 3! (i.e. 6)? For. example 3,2,0 can be written in 6 ways.

Thanks in advance for your clarification.

The point is that 9*9 gives all possible ordered pairs of the remaining two digits:

11 12 13 14 15 16 17 18 19 21 ... 99

Now, 0, in three digits can take either first, second or third place, hence multiplying by 3: XX0, X0X, 0XX.

I have a Query. In case 1 where there is only one zero, XX0 can also be XY0, in that case should it not be multiplied by 3! (i.e. 6)? For. example 3,2,0 can be written in 6 ways.

Thanks in advance for your clarification.

The point is that 9*9 gives all possible ordered pairs of the remaining two digits:

11 12 13 14 15 16 17 18 19 21 ... 99

Now, 0, in three digits can take either first, second or third place, hence multiplying by 3: XX0, X0X, 0XX.

I didn't get this explanation. Why are we taking XX0 and not XY0, because the non-zero numbers can also be different. Such as

120 102 210 201 012 021

Which should lead to 6 combinations - \(3*2*1 = 6\)

Thanks

12 and 21 in your example are treated as two different numbers in my explanation. So, when I multiply by 3 I get the same result as you when you multiply by 6.

Sorry, cannot explain any better than this: 11 12 13 14 15 16 17 18 19 21 ... 99

Total of 81 numbers. 0 in three digits can take either first, second or third place, hence multiplying by 3: XX0, X0X, 0XX.
_________________

Re: Thurston wrote an important seven-digit phone number on a na [#permalink]

Show Tags

29 Apr 2016, 07:54

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: Thurston wrote an important seven-digit phone number on a na [#permalink]

Show Tags

18 Sep 2016, 07:37

Please help me understand this -

We need to find - If Thurston dials 10 phone numbers by using the readable digits followed by 10 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?.

Please consider this while counting possible outcomes. Remember, logically he will stop trying once he gets the original number. When Thurston starts dialing 10 numbers, he - ->gets the original number in 1st attempt. So he tries just 1 out of 10 number. ->gets the original number in 2nd attempt. So he tries just 2 out of 10 number. .... ... .. gets the original number in 10th attempt. So he tries just 10 out of 10 number.

But all the explanation seems to focus on finding numbers that fit in criteria - at least one 0 and at least one non-zero for counting favorable outcomes, and not on the number that is original and ONLY ONE.

I think probability has to be calculated at two levels -

Choosing 10 numbers from all favorable outcome i.e. from 270 X (original number found at 1st attempt + original number found at 2nd attempt +......+original number found at 10th attempt).

Can somebody help where I am going wrong.

gmatclubot

Re: Thurston wrote an important seven-digit phone number on a na
[#permalink]
18 Sep 2016, 07:37

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...