BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Time for a brand-new quant problem, ladies and gentlemen!

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 426
Joined: Tue Aug 22, 2017 8:48 pm
Followed by:1 members

Time for a brand-new quant problem, ladies and gentlemen!

by BTGmoderatorAT » Sun Nov 12, 2017 2:59 pm
Time for a brand-new quant problem, ladies and gentlemen!

A firm has at least 5 partners, of whom at least 2 are male and at least 2 are female. If four of this firm's partners are to be selected at random for an audit, what is the probability that equal numbers of male and female partners will be selected?

(1) The firm has no more than 3 male partners.
(2) The firm has no more than 3 female partners.

What's the best way to determine which statement is sufficient? Can any experts help?
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Mon Nov 13, 2017 12:20 am
ardz24 wrote:Time for a brand-new quant problem, ladies and gentlemen!

A firm has at least 5 partners, of whom at least 2 are male and at least 2 are female. If four of this firm's partners are to be selected at random for an audit, what is the probability that equal numbers of male and female partners will be selected?

(1) The firm has no more than 3 male partners.
(2) The firm has no more than 3 female partners.

What's the best way to determine which statement is sufficient? Can any experts help?
We have the number of partners ≥ 5.

(1) The firm has no more than 3 male partners.

We do not have any information about the number of partners. Since as per the statement, we have 2 or 3 males, but the number of females can be any number. This way, we cannot determine the required answer. Insufficient.

(2) The firm has no more than 3 female partners.

As with Statement 1, this statement is also not sufficient.

(1) and (2) combined:

From Statement 1, we have the number of males = 2 or 3 and from Statement 2, we have the number of females = 2 or 3.

Since the total number of partners ≥ 5, if the number of males = 2, the number of females = 3 and vice-versa.

Case 1: Say, the number of males = 2 and the number of females = 3, thus, the total number of partners = 5

Probability = (2C2*3C2) / 5C4 = (1*3C1) / 5C1 = 3/5; we know that nCr = nC(n-r)

Case 1: Say, the number of females = 2 and the number of males = 3, thus, the total number of partners = 5

Probability = (2C2*3C2) / 5C4 = (1*3C1) / 5C1 = 3/5. Same answser. Sufficient.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Barcelona | Manila | Melbourne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Post new topic Post Reply
• Page 1 of 1