Find all School-related info fast with the new School-Specific MBA Forum

It is currently 12 Feb 2016, 06:57
GMAT Club Tests

Close

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
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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A lottery is played by selecting X distinct single digit

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 11 Aug 2012
Posts: 128
Schools: HBS '16, Stanford '16
Followers: 0

Kudos [?]: 67 [0], given: 16

A lottery is played by selecting X distinct single digit [#permalink] New post 05 Feb 2013, 07:40
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

63% (01:53) correct 37% (00:50) wrong based on 447 sessions
A lottery is played by selecting X distinct single digit numbers from 0 to 9 at once such that order does not matter. What is the probability that a player will win playing the lottery?

1) Players must match at least two numbers with machine to win.

(2) X = 4
[Reveal] Spoiler: OA
Expert Post
4 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2790
Followers: 947

Kudos [?]: 3974 [4] , given: 44

Re: A lottery is played by selecting X distinct single digit [#permalink] New post 05 Feb 2013, 10:12
4
This post received
KUDOS
Expert's post
danzig wrote:
A lottery is played by selecting X distinct single digit numbers from 0 to 9 at once such that order does not matter. What is the probability that a player will win playing the lottery?
(1) Players must match at least two numbers to win.
(2) X = 4

I'm happy to help. :-)

This is a somewhat offbeat question, but then again, that's just what the GMAT will throw at you.

So, from the prompt, we know we are picking X different single digit numbers: X must be greater than two and less than 9 (or 10, if we are counting zero as a "single digit number" ----- let's ignore that complication). Order doesn't matter. We know nothing about what constitutes winning.

Statement #1: Players must match at least two numbers to win.
Now, at least we know what constitutes winning. The trouble is --- we don't know the how many digits are picked. If X = 9 ---- the lottery picks all the digits from 1-9, then I also pick all the digits from 1-9 --- then I have 100% chance of matching at least two digits and winning. That wouldn't be much of a lottery. If X = 3 --- the lottery picks three, and then I pick three --- well, that's harder. Clearly the probability of winning depends on the value of X, and we don't know that in Statement #1. This statement, alone and by itself, is insufficient.

Statement #2: X = 4
Now, we know how many digits are picked ---- lottery picks 4, then I pick 4 --- but now I have no idea what constitutes "winning". (This is an example of a DS question in which it's crucially important to forget all about Statement #1 when we are analyzing Statement #2 on its own.) In Statement #2, we know how many digits are picked, but we have absolutely no idea what constitutes winning. This statement, alone and by itself, is insufficient.

Combined statements:
Now, we know --- the lottery picks 4 digits, then I pick 4 digits, and if at least two of my digits match two of the lottery's cards, I win. This is now a well defined math problem, and if we wanted, we could calculate the numerical value of the probability. Of course, since this is DS, it would be a big mistake to waste time with that calculation. We have enough information now. Combined, the statements are sufficient.

Answer = C

Does all this make sense?

Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Expert Post
1 KUDOS received
Manager
Manager
User avatar
Joined: 27 Jan 2013
Posts: 199
GMAT 1: 780 Q49 V51
Followers: 40

Kudos [?]: 165 [1] , given: 20

Re: A lottery is played by selecting X distinct single digit [#permalink] New post 05 Feb 2013, 11:49
1
This post received
KUDOS
Expert's post
Hi,

I think that Mike's explanation is great. I'm just wondering where this question came from? The wording seems strange to the point that the question may not be solvable. Here is the potentially problematic wording: distinct single digit numbers from 0 to 9

What does that mean? Does that mean single digit INTEGERS between 0 and 9 or just single digit numbers. My assumption is that single digit numbers between 0 and 9 are not just "the digits" but could include the single digit decimals .1,.2,.3.... Anyone?

I guess that if you assume that the question includes the extra decimals then Mike's solution still works although I'm curious about whether this is an official question.

HG.
_________________

"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land

GMAT vs GRE Comparison

If you found my post useful KUDOS are much appreciated.

IMPROVE YOUR READING COMPREHENSION with the ECONOMIST READING COMPREHENSION CHALLENGE:

Here is the first set along with some strategies for approaching this work: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-151479.html

Intern
Intern
avatar
Joined: 09 Oct 2012
Posts: 7
Location: United States
Concentration: Strategy, Finance
GMAT 1: 590 Q34 V38
GPA: 3.56
WE: Analyst (Consumer Products)
Followers: 0

Kudos [?]: 5 [0], given: 8

Re: A lottery is played by selecting X distinct single digit [#permalink] New post 07 Feb 2013, 08:22
HerrGrau wrote:
Hi,

I think that Mike's explanation is great. I'm just wondering where this question came from? The wording seems strange to the point that the question may not be solvable. Here is the potentially problematic wording: distinct single digit numbers from 0 to 9

What does that mean? Does that mean single digit INTEGERS between 0 and 9 or just single digit numbers. My assumption is that single digit numbers between 0 and 9 are not just "the digits" but could include the single digit decimals .1,.2,.3.... Anyone?

I guess that if you assume that the question includes the extra decimals then Mike's solution still works although I'm curious about whether this is an official question.

HG.


It's tagged as a grockit problem, so I would guess that this is not an official question. It is also tagged as a 600-700 lvl question, which seems high to me for this question...I don't have any experience with Grockit, but MGMAT questions that are in the 600-700 range tend to be more difficult for me to solve.
Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2790
Followers: 947

Kudos [?]: 3974 [0], given: 44

Re: A lottery is played by selecting X distinct single digit [#permalink] New post 07 Feb 2013, 10:09
Expert's post
HerrGrau wrote:
Hi,
The wording seems strange to the point that the question may not be solvable. Here is the potentially problematic wording: distinct single digit numbers from 0 to 9 What does that mean? Does that mean single digit INTEGERS between 0 and 9 or just single digit numbers. My assumption is that single digit numbers between 0 and 9 are not just "the digits" but could include the single digit decimals .1,.2,.3.... Anyone?

Dear HerrGrau
Thank you for your kind words. :-)

In my experience, I have never heard "single digit numbers" apply to anything other than non-negative integers. I have never seen any book or hear anyone ever refer to, say, -5 or 0.008 or 3 x 10^8 as a "single digit number. Yes, technically, each of these is written with a single non-zero digit, but I have never heard the term "single digit number" used for them. (We could say that each of these has "one significant figure", but that carries us far afield into measurement theory, well beyond GMAT territory.)

In my mind, the only ambiguity in this question is whether zero is included --- I guess I was assuming, whatever their understanding of the term, this understanding would be fixed and wouldn't change as we moved through the statements of the DS ---- therefore, with both statements, and with whatever convention they are following, the question can be definitely answered.

I agree with you ---- this question is not written with the tight precision so characteristic of official GMAT questions. The very fact that there's any ambiguity at all makes this a woefully substandard question.

Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Expert Post
Manager
Manager
User avatar
Joined: 27 Jan 2013
Posts: 199
GMAT 1: 780 Q49 V51
Followers: 40

Kudos [?]: 165 [0], given: 20

Re: A lottery is played by selecting X distinct single digit [#permalink] New post 07 Feb 2013, 14:47
Expert's post
Hi Mike,

In general I agree with everything that you're saying. Just to clarify, I think that .008 is a three digit number with 2 unique digits and so would be excluded. The numbers in question are .1, .2, .3, .4, .5, .6, .7, .8, and .9. They are numbers that have only one digit and hence are "single digit numbers". I have never seen this distinction be an actual issue on a GMAT question but am curious as to what the general consensus is.

HG.
_________________

"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land

GMAT vs GRE Comparison

If you found my post useful KUDOS are much appreciated.

IMPROVE YOUR READING COMPREHENSION with the ECONOMIST READING COMPREHENSION CHALLENGE:

Here is the first set along with some strategies for approaching this work: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-151479.html

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8222
Followers: 419

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: A lottery is played by selecting X distinct single digit [#permalink] New post 26 Jul 2014, 01:46
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
avatar
Joined: 30 Mar 2013
Posts: 137
Followers: 0

Kudos [?]: 33 [0], given: 196

GMAT ToolKit User
Re: A lottery is played by selecting X distinct single digit [#permalink] New post 16 Oct 2014, 11:04
just for the sake of understanding, how would we solve this question?
1- probability of matching none - prob of matching 1?
none= (5/9)*4/9*3/9*2/9

probability of matching one: 1*5/9*4/9*3/9

is this the way?

Thank you!
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8222
Followers: 419

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: A lottery is played by selecting X distinct single digit [#permalink] New post 02 Dec 2015, 07:31
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
1 KUDOS received
Math Revolution GMAT Instructor
User avatar
Joined: 16 Aug 2015
Posts: 673
GPA: 3.82
Followers: 34

Kudos [?]: 258 [1] , given: 0

Re: A lottery is played by selecting X distinct single digit [#permalink] New post 05 Dec 2015, 11:47
1
This post received
KUDOS
Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A lottery is played by selecting X distinct single digit numbers from 0 to 9 at once such that order does not matter. What is the probability that a player will win playing the lottery?

1) Players must match at least two numbers to win.

(2) X = 4

There are 2 variables (x and how many to be win) and 2 equations are given, so there is high chance (C) will be the answer.
Looking at the conditions together,
the probability to win is 1-(10C4/10^4), which is unique and makes the condition sufficient,
and the answer becomes (C).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 20% off coupon code for GMAT Club members.
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Re: A lottery is played by selecting X distinct single digit   [#permalink] 05 Dec 2015, 11:47
    Similar topics Author Replies Last post
Similar
Topics:
13 Experts publish their posts in the topic If x is a positive, single-digit integer, is x prime? Bunuel 9 28 Aug 2015, 01:44
3 Experts publish their posts in the topic If X and Y are single-digit positive integers, is X + Y goodyear2013 2 11 Jan 2014, 05:19
41 Experts publish their posts in the topic The average of 5 distinct single digit integers is 5. If qweert 18 02 Sep 2012, 20:20
2 Experts publish their posts in the topic If each of the two digits X and Y is distinct ConnectTheDots 6 28 Aug 2012, 05:56
12 Experts publish their posts in the topic In the decimal above, ♣ and x represent single digits. What perseverant 20 28 May 2010, 14:32
Display posts from previous: Sort by

A lottery is played by selecting X distinct single digit

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.