GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Sep 2018, 06:29

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

A certain bank vault contains 600 safe deposit boxes. A thief possesse

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
A certain bank vault contains 600 safe deposit boxes. A thief possesse  [#permalink]

Show Tags

New post 05 Jul 2018, 04:50
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:43) correct 35% (01:46) wrong based on 79 sessions

HideShow timer Statistics

A certain bank vault contains 600 safe deposit boxes. A thief possesses a sack containing 700 keys, only 300 of which correspond to the safe deposit boxes, with no duplicates. If the thief randomly selects a box and then a key, what is the probability that the thief will be able to open the box?


A. \(\frac{1}{1400}\)

B. \(\frac{1}{600}\)

C. \(\frac{1}{7}\)

D. \(\frac{1}{2}\)

E. \(\frac{6}{7}\)

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3136
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: A certain bank vault contains 600 safe deposit boxes. A thief possesse  [#permalink]

Show Tags

New post 05 Jul 2018, 05:53
Bunuel wrote:
A certain bank vault contains 600 safe deposit boxes. A thief possesses a sack containing 700 keys, only 300 of which correspond to the safe deposit boxes, with no duplicates. If the thief randomly selects a box and then a key, what is the probability that the thief will be able to open the box?


A. \(\frac{1}{1400}\)

B. \(\frac{1}{600}\)

C. \(\frac{1}{7}\)

D. \(\frac{1}{2}\)

E. \(\frac{6}{7}\)


There are \(C_1^{600}\) or 600 ways of choosing a certain safe deposit box.
Similarly, there are \(C_1^{700}\) or 700 ways of choosing a key to open the box.

To open the box, the thief must choose the corresponding 300 boxes for which he has the keys.

Therefore, the probability that the thief will be able to open the box is \(\frac{1*300}{600*700} = \frac{1}{1400}\)(Option A)
_________________

You've got what it takes, but it will take everything you've got

Manager
Manager
User avatar
B
Joined: 13 Feb 2018
Posts: 131
CAT Tests
A certain bank vault contains 600 safe deposit boxes. A thief possesse  [#permalink]

Show Tags

New post 05 Jul 2018, 06:15
1
First we have to choose a box, we need to choose from those 300 boxes for which the thief has the keys, so the probability is \(\frac{300}{600}\)
AND
then we need to choose exactly the right 1 key to open that box \(\frac{1}{700}\).
In probability questions AND means multiplication so we get \(\frac{300}{600}*\frac{1}{700}=\frac{1}{1400}\)

If we had to select first the key and then the box:
\(\frac{300}{700}\) the probability that we choose the key that will definitely open one of the boxes
AND
\(\frac{1}{600}\) the probability that we'll choose exactly the right box for our chosen key
\(\frac{300}{700}*\frac{1}{600}=\frac{1}{1400}\)

In My opinion
Ans: A
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3515
Location: United States (CA)
Re: A certain bank vault contains 600 safe deposit boxes. A thief possesse  [#permalink]

Show Tags

New post 09 Jul 2018, 19:59
Bunuel wrote:
A certain bank vault contains 600 safe deposit boxes. A thief possesses a sack containing 700 keys, only 300 of which correspond to the safe deposit boxes, with no duplicates. If the thief randomly selects a box and then a key, what is the probability that the thief will be able to open the box?


A. \(\frac{1}{1400}\)

B. \(\frac{1}{600}\)

C. \(\frac{1}{7}\)

D. \(\frac{1}{2}\)

E. \(\frac{6}{7}\)


First, he has a 300/700 = 3/7 chance to pick a key that can open any one of the safe deposit boxes. After he picks a key that can open a safe deposit box, he has 1/600 chance to pick the right safe deposit box. Thus, the probability is 3/7 x 1/600 = 1/7 x 1/200 = 1/1400.

Answer: A
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
User avatar
B
Joined: 17 May 2018
Posts: 32
Re: A certain bank vault contains 600 safe deposit boxes. A thief possesse  [#permalink]

Show Tags

New post 10 Jul 2018, 09:13
Let's first find the total number of possible results: we have 700 keys on one side, and 600 boxes on the other, so we have 600*700 possible combinations.

We have 300 desired results, which are the keys that open a box.

The probability is then 300/(600*700) = 1/1400.
_________________

¿Tienes que presentar el GMAT y no sabes por dónde empezar?
¡Visita GMAT para Principiantes y recibe el curso completo gratis!

Re: A certain bank vault contains 600 safe deposit boxes. A thief possesse &nbs [#permalink] 10 Jul 2018, 09:13
Display posts from previous: Sort by

A certain bank vault contains 600 safe deposit boxes. A thief possesse

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.