A box contains red and blue balls only. If there are 8 balls

Expert replies

Previous Topic Next Topic

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Feb 06, 2019 5:40 am

Timer

00:00

Answers

Stats

Difficulty—

A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

OA A

Source: Magoosh

Like this post

Source: Beat The GMAT — Data Sufficiency | Wed Feb 06, 2019 5:40 am

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Wed Feb 06, 2019 10:27 pm

BTGmoderatorDC wrote:A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

OA A

Source: Magoosh

We have to determine the number of red balls.

Say the number of red balls is r; thus, the number of blue balls = 8 - r.

Let's take each statement one by one.

(1) If two balls are randomly selected without replacement, the probability that both balls are red is 5/14

=> rC2 / 8C2 = r*(r - 1)/8.7 = 5/14 => r*(r - 1) = 20 => r*(r - 1) = 5*4 => r = 5. Sufficient.

(2) If two balls are randomly selected without replacement, the probability is 15/56 that the first ball is red and the second ball is blue.

Probability of drawing the first ball being red = r/8;
Probability of drawing the second ball being blue = (8 - r) / 7; there would be only 7 balls left after the drawing the first ball.

Thus, the required probability = r/8 * (8 - r) / 7 = 5/14

=> r*(8 - r) = 15
r*(8 - r) = 3*5

r = 3 or 5. No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Classes DC | GMAT Tutoring Seattle | GRE Prep Boston | TOEFL Prep Classes Houston | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

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