Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46167

Question Stats:
61% (01:44) correct 39% (01:51) wrong based on 115 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 46167

Re M1014 [#permalink]
Show Tags
16 Sep 2014, 00:42
Official Solution:Set \(S\) consists of all prime integers less than 10. If a number is selected from set \(S\) at random and then another number, not necessarily different, is selected from set \(S\) at random, what is the probability that the sum of these numbers is odd? A. \(\frac{1}{8}\) B. \(\frac{1}{6}\) C. \(\frac{3}{8}\) D. \(\frac{1}{2}\) E. \(\frac{5}{8}\) Set \(S =\{2, 3, 5, 7\}\). The question "what is the probability that the sum of these numbers is odd?" is equivalent to the question "what is the probability that one of these numbers is 2 while the other is not?". \(P(\text{the sum is odd}) = (P(\text{the first number is 2}) * P(\text{the second number is not 2})) +\) \(+ (P(\text{the first number is not 2}) * P(\text{the second number is 2})) =\) \(= \frac{1}{4}*\frac{3}{4} + \frac{3}{4}*\frac{1}{4} = \frac{6}{16} = \frac{3}{8}\). Answer: C
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 30 Jun 2012
Posts: 13

Re: M1014 [#permalink]
Show Tags
05 Dec 2014, 21:54
I quickly listed out the set of numbers (2,2) (2,3) (2,5) (2,7) (3,3) (3,5) (3,7) (5,5) (5,7) and (7,7) and then I counted the only odd pair which left me with a probability of 3/10. Why is this method incorrect?



Math Expert
Joined: 02 Sep 2009
Posts: 46167

Re: M1014 [#permalink]
Show Tags
06 Dec 2014, 06:24
rsamant wrote: I quickly listed out the set of numbers (2,2) (2,3) (2,5) (2,7) (3,3) (3,5) (3,7) (5,5) (5,7) and (7,7) and then I counted the only odd pair which left me with a probability of 3/10. Why is this method incorrect? There are more possibilities when picking two numbers: (2,2) (2,3) (3,2) (2,5) (5,2) (2,7) (7,2) (3,3) (3,5) (5,3) (3,7) (7,3) (5,5) (5,7) (7,5) (7,7) P = 6/16 = 3/8.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Status: One Last Shot !!!
Joined: 04 May 2014
Posts: 246
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35

This question is basically asking If two numbers are randomly selected from the set {2,3,5,7}, what is the probability that EXACTLY one of them is 2?(and suddenly it becomes a sub600 level ) P(Exactly one 2) = [P(2 in first pick) AND P(not 2 in second pick)] OR [P(not 2 in first pick) and P(2 in second pick)]\(=> \frac{1}{4} * \frac{3}{4} + \frac{3}{4} * \frac{1}{4}\) \(=> 2* \frac{3}{16}\) \(=> \frac{3}{8}\) Option C
_________________
One Kudos for an everlasting piece of knowledge is not a bad deal at all...
 Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. Mark Twain



Intern
Joined: 03 Jul 2016
Posts: 1

Re: M1014 [#permalink]
Show Tags
03 Aug 2016, 00:05
I struggle to know when order matters. Why is the answer not simply 1/4*3/4?
Why is picking 2 then 3 or 5 or 7 different from picking picking 3 or 5 or 7 then 2?



Manager
Joined: 17 Aug 2015
Posts: 117

if a number is drawn then remaining numbers are 3 out of 4
total cases  4C2*2 ( first selected 02 numbers out of 4 and again as order matters, multiply by 2)= 12
now favorable cases where 2 is always selected so the combination is (2,3), (2,5), (2,7) again as order matters (3,2), (5,2) (7,2) also possible so total cases = 03+03= 06
probability = 06/12= 1/2
now if you say that if a number is withdrawn and you can draw the same number again for the second chance, hard to understand, until unless it is mentioned that the same number is available in the pool all the time



Intern
Joined: 02 Sep 2016
Posts: 10

Re: M1014 [#permalink]
Show Tags
27 Sep 2016, 14:48
how can i calculate the total outcomes for this questions? i got the p(e)=6 but struggled to calculate the total outcomes through a formula.



Intern
Joined: 25 Jul 2016
Posts: 8

Re: M1014 [#permalink]
Show Tags
13 Jan 2017, 07:24
The sum to be odd, the numbers selected must be either {2,3}, {2,5} or {2,7}.
The probability to drawn the numbers 2 and 3 is 2*\(\frac{1}{4}\)*\(\frac{1}{4}\) (We multiply by 2 because the numbers drawn could be either 2 and 3 OR 3 and 2 => so there are 2 cases AB, BA) The probability is the same for the numbers {2,5} and {2,7}.
So, the probability that the sum of the 4 numbers is odd is: 2*\(\frac{1}{4}\)*\(\frac{1}{4}\)+2*\(\frac{1}{4}\)*\(\frac{1}{4}\)+2*\(\frac{1}{4}\)*\(\frac{1}{4}\)=\(\frac{3}{8}\)



Manager
Joined: 01 Dec 2016
Posts: 118
Concentration: Finance, Entrepreneurship
WE: Investment Banking (Investment Banking)

Re: M1014 [#permalink]
Show Tags
16 Jan 2017, 11:53
I used the below Proba(sum is odd) = 1  Proba(sum is even) The set is made of {2;3;5;7}. Number of all possible events is 4^2, which is 16 The sum is even if and only if you : pick twice an even number : there is only {2;2}, ie. 1 possibility or pick 2 odd numbers out of the 3 in the set: 3^2 ie. 9 possiblities. Therefore, Proba(sum is even)= (1+9)/16 = 10/16 and hence Proba(sum is odd)= 6/16 = 3/8 Done!!!
_________________
What was previously considered impossible is now obvious reality. In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them



Intern
Joined: 28 Apr 2016
Posts: 20

Re: M1014 [#permalink]
Show Tags
26 Mar 2017, 04:56
The question says "not necessarily different". Can we safely assume that the first number will be pot in the box again?



Math Expert
Joined: 02 Sep 2009
Posts: 46167

Re: M1014 [#permalink]
Show Tags
26 Mar 2017, 05:00



Intern
Joined: 28 Apr 2016
Posts: 20

Re: M1014 [#permalink]
Show Tags
26 Mar 2017, 09:46
Bunuel wrote: dyg wrote: The question says "not necessarily different". Can we safely assume that the first number will be pot in the box again? It implies that numbers can be repeated. That's why the denominator in the solution is 4 for the second pick too. Yes I got it but I actually wanted to ask is "is it always OK to repeat numbers/colors etc whenever we see "not necessarily different"? Thanks.



Math Expert
Joined: 02 Sep 2009
Posts: 46167

Re: M1014 [#permalink]
Show Tags
26 Mar 2017, 22:49



Intern
Joined: 10 May 2017
Posts: 27

Re: M1014 [#permalink]
Show Tags
01 Jul 2017, 03:13
I solved in the different way though which I figured after I got it wrong.
Since the order of the selection matters, we should not use combination formula, use permutation.
S = (2,3,5,7)
Picking two numbers from the set is 4P2= 12.
but the stem specifically says that choosing the same number is also possible which is (2,2)(3,3)(5,5)(7,7)
So total number of ways = 12+4 = 16 ways.
The rest is easy. Sum of two numbers is ODD. We know that Odd+Even = Odd (Since 2 is the only even)
(2, 3 or 5 or 7) or (3 or 5 or 7 , 2). We know that OR means addition. So total 6 ways.
6/16 = 3/8



Intern
Joined: 29 Jul 2016
Posts: 9

Re M1014 [#permalink]
Show Tags
03 Jul 2017, 00:39
I think this is a poorquality question and I don't agree with the explanation. i want to understand. what do you mean by "not necessarily different? that means Set 'S' can have repetition of prime numbers. also, what if set S has (2,2,2,2,3,5,5,7,7) or any combinations of prime numbers less than 10? i marked the answer as a guess.
please clarify



Math Expert
Joined: 02 Sep 2009
Posts: 46167

Re: M1014 [#permalink]
Show Tags
03 Jul 2017, 00:46
Sushilait84 wrote: I think this is a poorquality question and I don't agree with the explanation. i want to understand. what do you mean by "not necessarily different? that means Set 'S' can have repetition of prime numbers. also, what if set S has (2,2,2,2,3,5,5,7,7) or any combinations of prime numbers less than 10? i marked the answer as a guess.
please clarify The question is mathematically very precise. It implies that numbers can be repeated. That's why the denominator in the solution is 4 for the second pick too. For example, you can choose 2 and 2 OR 7 and 7. All possible combinations are given here: https://gmatclub.com/forum/m10183859.html#p1452001
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 12 Jun 2016
Posts: 221
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)

Re: M1014 [#permalink]
Show Tags
17 Oct 2017, 23:06
Hello BunuelI think this is a highquality question and I agree with the solution. I have the same conceptual gap as Demba below. Can you please help? Usually, for questions like these, I find the total possibilities first and then the favourable outcomes. To do this, its necessary to know if the order of outcome matters. Clearly, in this question order matters. (2,3) is different from (3,2). How do we understand after reading the question that order matters? Is it because the question says 'not necessarily different' which implies repetition is allowed? I was comparing this solution with this one  https://gmatclub.com/forum/m20184246.html#p1859217. In this solution that I pasted, Order does not matter. So, we wanted to know how to decide after reading a question if order matters or no. I hope I was able to communicate what I intend to say. Thanking you in advance! Demba wrote: I struggle to know when order matters. Why is the answer not simply 1/4*3/4?
Why is picking 2 then 3 or 5 or 7 different from picking picking 3 or 5 or 7 then 2?
_________________
My Best is yet to come!



Manager
Joined: 14 May 2017
Posts: 55

Re: M1014 [#permalink]
Show Tags
31 Dec 2017, 09:17
P (EO) = 1/4 *3/4* 2! = 3/8 If you have any confusion with this method let me know.



Intern
Joined: 08 Aug 2017
Posts: 15

Re: M1014 [#permalink]
Show Tags
11 Mar 2018, 12:51
Hi Bunuel
I solved this way. For denominator I figured out total cases = 4*4=16
For numerator I applied combinatorics: No. of ways digit 2 can be selected= 4C1 No. of ways digit other than 2 can be selected= 3C1 So total ways = 4C1*3C1
P= (4C1*3C1)/16= 3/4.
Please correct my mistake if possible, I suspect I am not considering the order, but how can I incorporate that here? Thanks so much.










