GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 17 Jan 2020, 11:22 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Three boys are ages 4, 6 and 7 respectively. Three girls are

Author Message
TAGS:

### Hide Tags

Manager  Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 117
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Three boys are ages 4, 6 and 7 respectively. Three girls are  [#permalink]

### Show Tags

2
15 00:00

Difficulty:   55% (hard)

Question Stats: 68% (02:52) correct 32% (02:49) wrong based on 236 sessions

### HideShow timer Statistics

Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is z, what is the difference between the probability that z is even and the probability that z is odd?

(A) 1/9
(B) 1/6
(C) 2/9
(D) 1/4
(E) 1/2

Originally posted by mun23 on 09 Dec 2012, 10:05.
Last edited by Bunuel on 09 Dec 2012, 10:09, edited 2 times in total.
Renamed the topic and edited the question.
Manager  Joined: 31 May 2012
Posts: 108
Re: Three boys are ages 4, 6 and 7 respectively. Three girls are  [#permalink]

### Show Tags

11
1
2
Age of Boys:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11

Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14

9 Combinations of sum between sets(10,12,11) & (13,17,14)
=23,27,24- 16,30,17- 24,28,25

Prob(Even)= 5/9
Prob(Odd) =4/9

##### General Discussion
Intern  Joined: 17 Nov 2012
Posts: 17
Re: Three boys are ages 4, 6 and 7 respectively. Three girls are  [#permalink]

### Show Tags

1
I would present another approach.

P(z odd) = P(boys odd)* P(girls even) + P(boys even)* P(girls odd)
= 2/C2,3 * 1/C2,3 + 1/C2,3 * 2/C2,3
= 4/9

P(z even) = 1 - P(z odd) = 5/9

|P(z even)-P(z odd)| = 1/9
Senior Manager  B
Joined: 02 Dec 2014
Posts: 352
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
Re: Three boys are ages 4, 6 and 7 respectively. Three girls are  [#permalink]

### Show Tags

1
umeshpatil wrote:
Age of Boys:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11

Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14

9 Combinations of sum between sets(10,12,11) & (13,17,14)
=23,27,24- 16,30,17- 24,28,25

Prob(Even)= 5/9
Prob(Odd) =4/9

I think 13 should be here not 12. And i don't understand second bolded fragment. May be this should be (26,30,27)?
_________________
"Are you gangsters?" - "No we are Russians!"
Manager  Joined: 04 May 2015
Posts: 69
Concentration: Strategy, Operations
WE: Operations (Military & Defense)
Re: Three boys are ages 4, 6 and 7 respectively. Three girls are  [#permalink]

### Show Tags

1
Please feel free to critique me here but this is how I solved.

Boys: 4, 6, 7
Girls: 5, 8, 9
Number of possible combinations of boys or girls = 3!/2! = 3
i.e. there is 3 possible combinations of girls and 3 of boys

Probability that sum of 2 boys ages is even = 1/3 [a]
Probability that sum of 2 boys ages is odd = 2/3 [b]
Probability that sum of 2 girls ages is even = 1/3 [c]
Probability that sum of 2 girls ages is odd = 2/3 [d]

probability that sum of 2 girls and 2 boys is even = [a]*[c] + [b]*[d] = 5/9 [e]
probability that sum of 2 girls and 2 boys is odd = [a]*[b] + [c]*[d] = 4/9 [f]

Therefore the differences in the probabilities is [e] - [f] = 1/9

No idea if this is correct or if it was dumb luck. I am struggling daily with this GMAT journey so would appreciate the feedback. Director  G
Joined: 26 Oct 2016
Posts: 599
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: Three boys are ages 4, 6 and 7 respectively. Three girls are  [#permalink]

### Show Tags

1
Total ways to choose the 4 children:
Number of pairs of boys that can be formed from 3 options = 3C2 = 3.
Number of pairs of girls that can be formed from 3 options = 3C2 = 3.
To combine these options, we multiply:
3*3 = 9.

We could list all the ways to pick four children—two boys and two girls. We could also take the opposite approach: list all the ways to leave out two children—one boy and one girl. There are fewer scenarios to list with the left-out children, so let's take that approach. The sum of the ages of all six children is (4 + 6 + 7) + (5 + 8 + 9) = 39, an odd number. We can then list all 9 scenarios, subtracting out the ages of the left-out children.

Of the 9 scenarios listed, 5 yield an even z and 4 yield an odd z. Each outcome is equally likely.
The difference between the probability that z is even and the probability that z is odd is therefore 5/9 – 4/9 = 1/9.

Table pasted below to represent all 9 scenarios.
Attachments table.PNG [ 263.31 KiB | Viewed 2661 times ]

_________________
Thanks & Regards,
Anaira Mitch
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9032
Location: United States (CA)
Re: Three boys are ages 4, 6 and 7 respectively. Three girls are  [#permalink]

### Show Tags

1
1
mun23 wrote:
Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is z, what is the difference between the probability that z is even and the probability that z is odd?

(A) 1/9
(B) 1/6
(C) 2/9
(D) 1/4
(E) 1/2

The sum of the two selected boys can be either 4 + 6 = 10, 4 + 7 = 11 or 6 + 7 = 13. Thus, there is a 1/3 probability that the sum of the ages of the two boys will be even and 2/3 probability that the sum of the ages of the two boys will be odd.

Similarly, the sum of the two selected girls can be either 5 + 8 = 13, 5 + 9 = 14 or 8 + 9 = 17. Thus, there is a 1/3 probability that the sum of the ages of the two girls will be even and 2/3 probability that the sum of the ages of the two girls will be odd.

Now, let’s first find the probability that z is even. Since z is the sum of ages of the selected boys and girls, z can be even if the sum of both the selected boys and selected girls ages are even or if sum of both the selected boys and selected girls ages are odd. The probability that both sums are even is 1/3 x 1/3 = 1/9 and the probability that both sums are odd is 2/3 x 2/3 = 4/9. Thus, there is a 1/9 + 4/9 = 5/9 probability that z is even.

Similarly, let’s find the probability that z is odd. z can only be odd of one of the sums is even and the other is odd. Probability that the boys sum is even and girls sum is odd is 1/3 x 2/3 = 2/9. Probability that the boys sum is odd and the girls sum is even is 2/3 x 1/3 = 2/9. Thus, there is a 2/9 + 2/9 = 4/9 probability that z is odd.

Finally, the difference between the probabilities that z is even and z is odd is 5/9 - 4/9 = 1/9.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User Joined: 09 Sep 2013
Posts: 13963
Re: Three boys are ages 4, 6 and 7 respectively. Three girls are  [#permalink]

### Show Tags

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: Three boys are ages 4, 6 and 7 respectively. Three girls are   [#permalink] 08 Dec 2019, 10:32
Display posts from previous: Sort by

# Three boys are ages 4, 6 and 7 respectively. Three girls are  