Apr 20 10:00 PM PDT  11:00 PM PDT The Easter Bunny brings … the first day of school?? Yes! Now is the time to start studying for the GMAT if you’re planning to apply to Round 1 of fall MBA programs. Get a special discount with the Easter sale! Apr 21 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Apr 20 07:00 AM PDT  09:00 AM PDT Christina scored 760 by having clear (ability) milestones and a trackable plan to achieve the same. Attend this webinar to learn how to build trackable milestones that leverage your strengths to help you get to your target GMAT score. Apr 21 10:00 PM PDT  11:00 PM PDT $84 + an extra $10 off for the first month of EMPOWERgmat access. Train to be ready for Round 3 Deadlines with EMPOWERgmat's Score Booster. Ends April 21st Code: GCENHANCED Apr 22 08:00 AM PDT  09:00 AM PDT What people who reach the high 700's do differently? We're going to share insights, tips, and strategies from data we collected on over 50,000 students who used examPAL. Save your spot today! Apr 23 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, April 23rd at 8 pm ET Apr 24 08:00 PM EDT  09:00 PM EDT Maximize Your Potential: 5 Steps to Getting Your Dream MBA Part 3 of 5: Key TestTaking Strategies for GMAT. Wednesday, April 24th at 8 pm ET Apr 27 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 29 Aug 2013
Posts: 74
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q41 V29 GMAT 2: 540 Q44 V20
GPA: 3.5
WE: Programming (Computer Software)

Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
Updated on: 12 Sep 2013, 04:31
Question Stats:
46% (02:43) correct 54% (02:42) wrong based on 232 sessions
HideShow timer Statistics
Thurston wrote an important sevendigit 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 nonzero 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 nonzero 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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by shameekv on 12 Sep 2013, 04:25.
Last edited by Bunuel on 12 Sep 2013, 04:31, edited 1 time in total.
Renamed the topic and edited the question.



Intern
Joined: 03 Sep 2013
Posts: 1

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
12 Sep 2013, 04:33
The answer is 1/27.
Our first step is determining how many possible threedigit 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 = nonzero integer. 0NN, N0N, NN0, N00, 00N, 0N0
There are 9 numbers that could appear in the Nslots 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 threedigit 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.



Math Expert
Joined: 02 Sep 2009
Posts: 54376

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
12 Sep 2013, 04:36
shameekv wrote: Thurston wrote an important sevendigit 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 nonzero 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 nonzero 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). P = 10/(9*9*3+9*3) = 1/27. Answer: C. P.S. Please read carefully and follow: rulesforpostingpleasereadthisbeforeposting133935.html Pay attention to the rule #3. Thank you.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 54376

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
12 Sep 2013, 04:39
Bunuel wrote: shameekv wrote: Thurston wrote an important sevendigit 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 nonzero 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 nonzero 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). P=10/(9*9*3+9*3)=1/27. Answer: C. P.S. Please read carefully and follow: rulesforpostingpleasereadthisbeforeposting133935.html Pay attention to the rule #3. Thank you. Similar question to practice: johnwroteaphonenumberonanotethatwaslaterlost94787.html
_________________



Intern
Joined: 21 Mar 2013
Posts: 38
GMAT Date: 03202014

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
11 Mar 2014, 21:09
We know that atleast one digit is Zero and atleast one digit is nonzero. The third digit can be any single digit integer (zero or nonzero).
Total # of combinations should be [One zero] * [One Nonzero] * [Any single digit integer] * \(\frac{3!}{2!}\)
= 1*9*10*3 = 270
P=10/270 = 1/27
Hence C



Director
Joined: 03 Aug 2012
Posts: 695
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
16 Mar 2014, 22:05
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 nonzero or (2). two nonzero 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 nonzero. 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!



Director
Joined: 19 Apr 2013
Posts: 567
Concentration: Strategy, Healthcare
GPA: 4

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
26 Mar 2014, 11:03
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 !!!



Math Expert
Joined: 02 Sep 2009
Posts: 54376

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
26 Mar 2014, 11:15
Ergenekon wrote: 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 nonzero integer, what is the probability that he will dial the original number correctly?"
_________________



Intern
Joined: 06 May 2013
Posts: 11
Location: United States

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
30 Mar 2014, 02:38
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.
What is wrong with my answer?



Intern
Joined: 24 Jun 2013
Posts: 32

Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
21 Jul 2014, 08:16
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. Thanks in advance for your clarification.



Math Expert
Joined: 02 Sep 2009
Posts: 54376

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
21 Jul 2014, 10:20
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. Hope it's clear.
_________________



Manager
Joined: 02 Jul 2012
Posts: 186
Location: India
GPA: 2.6
WE: Information Technology (Consulting)

Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
15 Oct 2014, 11:01
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. Hope it's clear. Dear Bunuel, I didn't get this explanation. Why are we taking XX0 and not XY0, because the nonzero numbers can also be different. Such as 120 102 210 201 012 021 Which should lead to 6 combinations  \(3*2*1 = 6\) Thanks
_________________
Give KUDOS if the post helps you...



Math Expert
Joined: 02 Sep 2009
Posts: 54376

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
15 Oct 2014, 11:16
Thoughtosphere wrote: Bunuel wrote: arichinna wrote: [
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. Hope it's clear. Dear Bunuel, I didn't get this explanation. Why are we taking XX0 and not XY0, because the nonzero 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.
_________________



Intern
Joined: 01 Sep 2015
Posts: 3

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
18 Sep 2016, 08:37
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 nonzero 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 nonzero 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.



Senior Manager
Joined: 03 Apr 2013
Posts: 274
Location: India
Concentration: Marketing, Finance
GPA: 3

Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
Show Tags
16 Jul 2017, 23:25
Bunuel wrote: shameekv wrote: Thurston wrote an important sevendigit 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 nonzero 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 nonzero 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). P = 10/(9*9*3+9*3) = 1/27. Answer: C. P.S. Please read carefully and follow: http://gmatclub.com/forum/rulesforpos ... 33935.html Pay attention to the rule #3. Thank you. How did you simply write 10/270? This is how I did it. Total possibilities for the numbers = 270 (found this one exactly how you did) Of these only 1 is correct and the other 269 are incorrect. Final probability = Probability of selecting 1 correct and 9 incorrect / probability of selecting any 10 out of 270 This will also give the same answer. I just want to know your "exact mathematical logic" why you wrote 10/270. Thank you for your help
_________________
Spread some love..Like = +1 Kudos




Re: Thurston wrote an important sevendigit phone number on a na
[#permalink]
16 Jul 2017, 23:25






