• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Most awarded test prep in the world
Now free for 30 days

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

## For a trade show, two different cars are selected

tagged by: VJesus12

This topic has 1 expert reply and 0 member replies

### Top Member

VJesus12 Master | Next Rank: 500 Posts
Joined
14 Oct 2017
Posted:
211 messages

#### For a trade show, two different cars are selected

Wed Nov 08, 2017 7:59 am
For a trade show, two different cars are selected randomly from a lot of 20 cars. If all the cars on the lot are either sedans or convertibles, is the probability that both cars selected will be sedans greater than 3/4?

1) At least three-fourths of the cars are sedans.
2) The probability that both of the cars selected will be convertibles is less than 1/20.

The OA is E .

Experts, can you help me. I don't have it clear.

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
Posted:
9182 messages
Followed by:
472 members
2867
GMAT Score:
800
Wed Nov 08, 2017 6:27 pm
Hi VJesus12,

We're told that two different cars are selected randomly from a lot of 20 cars (and that all of the cars are either sedans or convertibles). We're asked if the probability that BOTH cars selected will be sedans is greater than 3/4. This is a YES/NO question. We can solve it by TESTing VALUES.

1) At least three-fourths of the cars are sedans.

IF... there are 15 sedans and 5 convertibles, then the probability of selecting 2 sedans is....
(15/20)(14/19) = (3/4)(14/19)
You don't have to actually calculate this value, since we're multiplying 3/4 by a positive fraction, the answer will be LESS then 3/4 and the answer to the question is NO.

IF... there are 19 sedans and 1 convertible, then the probability of selecting 2 sedans is....
(19/20)(18/19) = 18/20 = 90% and the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) The probability that both of the cars selected will be convertibles is less than 1/20.

IF... there are 15 sedans and 5 convertibles, then the probability of selecting 2 convertibles is....
(5/20)(4/19) = 1/19.... This is NOT a match for the information in Fact 2 though, so there MUST BE FEWER than 5 convertibles.

IF... there are 16 sedans and 4 convertibles, then the probability of selecting 2 convertibles is....
(4/20)(3/19) = 3/95
The probability of selecting 2 sedans under these circumstances is...
(16/20)(15/19) = (15/20)(16/19) - since we're multiplying 3/4 by a positive fraction, the answer will be LESS then 3/4 and the answer to the question is NO.

IF... there are 19 sedans and 1 convertible, then the probability of selecting 2 sedans is....
(19/20)(18/19) = 18/20 = 90% and the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know that there must be FEWER than 5 convertibles. From the work that we did in Fact 2 (above), we have proof that the answer could be NO (if there are 4 convertibles) and YES (if there is just 1 convertible).
Combined, INSUFFICIENT

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

_________________
Contact Rich at Rich.C@empowergmat.com

### Best Conversation Starters

1 lheiannie07 112 topics
2 ardz24 71 topics
3 Roland2rule 69 topics
4 LUANDATO 53 topics
5 swerve 45 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

154 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

107 posts
3 Jeff@TargetTestPrep

Target Test Prep

106 posts
4 Scott@TargetTestPrep

Target Test Prep

98 posts
5 EconomistGMATTutor

The Economist GMAT Tutor

91 posts
See More Top Beat The GMAT Experts