ds - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

ds

Expert replies

hemant_rajput: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 22, 2012 7:13 amFollowed by: 13 members; Thanked: 46 times; GMAT Score:700

by hemant_rajput » Sat Aug 23, 2014 11:35 am

A jury pool consists of 6 men and w women. If 2 jurors are selected from the pool at random, is the probability that 2 men will be selected higher than the probability that 1 man and 1 woman will be selected?
(1) wâ‰¥ 3
(2) w < 6

I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

Like this post

Source: Beat The GMAT — Data Sufficiency | Sat Aug 23, 2014 11:35 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Aug 23, 2014 11:52 am

A jury pool consists of 6 men and w women. If 2 jurors are selected from the pool at random, is the probability that 2 men will be selected higher than the probability that 1 man and 1 woman will be selected?

(1) w> 3

(2) w < 6

Target question: Is P(2 men) greater than P(1 man and 1 woman)?

Statement 1: w> 3
Let's see what happens if w = 3 (note: this is the best chance that P(2 men) will be greater than P(1 man and 1 woman)

P(2 men) = P(man selected 1st and man selected 2nd)
= (6/9)(5/8)
= 30/72

P(1 man and 1 woman) = P(man selected 1st and woman selected 2nd OR woman selected 1st and man selected 2nd)
= P(man selected 1st and woman selected 2nd) + P(woman selected 1st and man selected 2nd)
= (6/9)(3/8) + (3/9)(6/8)
= 18/72 + 18/72
= 36/72

So, when w = 3, P(2 men) is not greater than P(1 man and 1 woman)

IMPORTANT: Now that we've shown that P(2 men) is not greater than P(1 man and 1 woman) when w = 3, we can see that, as the value of w increases, the answer to the target question will always remain the same.

As such, statement 1 is SUFFICIENT

Statement 2: w < 6
Consider these two conflicting cases:

Case a: w = 1
P(2 men) = (6/7)(5/6)
= 30/42

P(1 man and 1 woman) = P(man selected 1st and woman selected 2nd OR woman selected 1st and man selected 2nd)
= P(man selected 1st and woman selected 2nd) + P(woman selected 1st and man selected 2nd)
= (6/7)(1/6) + (1/6)(6/7)
= 6/42 + 6/42
= 12/42

So, when w = 1, P(2 men) is greater than P(1 man and 1 woman)

Case b: w = 3
In statement 1, we already showed that, when w = 3, P(2 men) is not greater than P(1 man and 1 woman)

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Aug 23, 2014 11:54 am

Hi hemant_rajput,

This DS question can be solved by TESTing Values. It's also important to remember that Quant questions are almost always "pattern-based", so even if you don't immediately spot a pattern, you should continue to look for one.

We're told that we have 6 men and W women. We're asked if the probability of selected 2 men from the group is greater than the probability of selecting 1 man and 1 woman. This is a YES/NO question.

Fact 1: W â‰¥ 3

IF....
W = 3
M = 6
Total = 9
The probability of selecting 2 men is (6/9)(5/8) = 30/72
The probability of selecting 1 of each can be calculated in a couple of different ways. Here, I'll calculate the following:
1st = male, 2nd = female + 1st = female, 2nd = male.....
The probability is (6/9)(3(8) + (3/9)(6/8) = 18/72 + 18/72 = 36/72
The answer to the question is NO.

W = 4
M = 6
Total = 10
The probability of selecting 2 men is (6/10)(5/9) = 30/90 NOTICE how the numerator DOES NOT CHANGE
The probability of selecting 1 of each....
The probability is (6/10)(4/9) + (4/10)(6/9) = 24/72 + 24/72 = 48/72 NOTICE how the numerator GETS BIGGER
The answer to the question is NO.

We now have the pattern behind Fact 1: adding women makes the probability of selecting 2 men DECREASE and the probability of selecting 1 of each INCREASE. In this scenario, the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT.

Fact 2: W < 6

Here, we can use W = 3 (from Fact 1 above) and the answer to the question is NO.

If W = 0, then the probability of selecting 2 men = 100% and the probability of selecting 1 of each = 0%
The answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Aug 23, 2014 12:12 pm

hemant_rajput wrote:A jury pool consists of 6 men and w women. If 2 jurors are selected from the pool at random, is the probability that 2 men will be selected higher than the probability that 1 man and 1 woman will be selected?
(1) wâ‰¥ 3
(2) w < 6

The number of ways to choose 2 men from 6 options = 6C2 = (6*5)/(2*1) = 15.

Question rephrased:
Is the number of ways to choose 1 woman and 1 man less than 15?

Statement 1:
Case 1: w=3
Number of ways to choose 1 woman from 3 options = 3.
Number of ways to choose 1 man from 6 options = 6.
To combine these options, we multiply:
3*6 = 18.
In this case, the number of ways to choose 1 woman and 1 man is NOT less than 15.

If the value of w INCREASES, then the number of ways to choose 1 woman and 1 man will also INCREASE, since the pool of women will be GREATER.
Thus, the number of ways to choose 1 man and 1 woman CANNOT be less than 15.
SUFFICIENT.

Statement 2:
Case 1 also satisfies statement 2.
In Case 1, the number of ways to choose 1 man and 1 woman is NOT less than 15.

Case 2: w=0.
Here, the number of ways to choose 1 woman and 1 man is 0, since there are no women.
In this case, the number of ways to choose 1 woman and 1 man IS less than 15.

Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

The correct answer is A.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Aug 24, 2014 5:39 am

hemant_rajput wrote:A jury pool consists of 6 men and w women. If 2 jurors are selected from the pool at random, is the probability that 2 men will be selected higher than the probability that 1 man and 1 woman will be selected?
(1) wâ‰¥ 3
(2) w < 6

Given :
Number of Men = 6
Number of Women = w
Number of Individuals to be selected = 2

Question : Is P(2 Men) > P(1 Man and 1 Woman) ?

Statement 1) wâ‰¥ 3
Take extreme cases
i.e. Case 1: w = 3,
P(2 Men)= (6/9)x(5/8) = 30/72, AND P(1 Man and 1 Woman)= (6/9)x(3/8)x2! = 36/72
Inference : P(2 Men) < P(1 Man and 1 Woman)

and Case 2: w = 30,
P(2 Men)= (6/36)x(5/35) = 30/(35x36), AND P(1 Man and 1 Woman)= (6/36)x(30/35)x2! = 360/(35x36)
Inference : P(2 Men) < P(1 Man and 1 Woman)
Consistent answer
SUFFICIENT

Statement 2) w < 6
Take extreme cases
i.e. Case 1: w = 0,
P(2 Men)= 1, AND P(1 Man and 1 Woman)= 0 [No Women]
Inference : P(2 Men) > P(1 Man and 1 Woman)

and Case 2: w = 5,
P(2 Men)= (6/11)x(5/10) = 30/(11x10), AND P(1 Man and 1 Woman)= (6/11)x(5/10)x2! = 60/(10x11)
Inference : P(2 Men) < P(1 Man and 1 Woman)
Inconsistent answer
NOT SUFFICIENT

Answer: Option A

"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review