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

It is currently 15 Oct 2018, 20:45

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

If four integers, a, b, c, and d are chosen at random with replacement

  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: 49858
If four integers, a, b, c, and d are chosen at random with replacement  [#permalink]

Show Tags

New post 11 Apr 2018, 21:31
10
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

20% (02:42) correct 80% (02:04) wrong based on 82 sessions

HideShow timer Statistics

If four integers, a, b, c, and d are chosen at random, with replacement, what is the probability that ab + cd is even?

A. 1/4

B. 3/8

C. 1/2

D. 5/8

E. 3/4

_________________

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

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3181
Location: India
GPA: 3.12
Premium Member CAT Tests
If four integers, a, b, c, and d are chosen at random with replacement  [#permalink]

Show Tags

New post 12 Apr 2018, 00:05
1
Bunuel wrote:
If four integers, a, b, c, and d are chosen at random, with replacement, what is the probability that ab + cd is even?

A. 1/4

B. 3/8

C. 1/2

D. 5/8

E. 3/4


We need to know the following rules in order to solve this problem:
Even*Odd = Odd*Even = Even*Even = Even | Odd*Odd = Odd
Even + Odd = Odd + Even = Odd | Odd + Odd = Even + Even = Even


---a-----b-----c-----d------ab+cd--
---E-----E-----E-----E---------E-----
---E-----E-----E-----O---------E-----
---E-----E-----O-----E---------E-----
---E-----E-----O-----O--------O-----
---E-----O-----E-----E---------E-----
---E-----O-----E-----O---------E-----
---E-----O-----O-----E---------E-----
---E-----O-----O-----O---------O-----
---O-----E-----E-----E----------E-----
---O-----E-----E-----O----------E-----
---O-----E-----O-----E----------E-----
---O-----E-----O-----O----------O-----
---O-----O-----E-----E----------O-----
---O-----O-----E-----O----------O-----
---O-----O-----O-----E----------O-----
---O-----O-----O-----O----------E-----


There are a total of 16 possibilities, of which the sum of ab and cd is even in 10 possibilities

Therefore, there are \(\frac{10}{16} = \frac{5}{8}\) possibilities(Option D) when ab+cd is even
_________________

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

Intern
Intern
avatar
B
Joined: 16 Mar 2018
Posts: 46
Location: United Kingdom
GMAT 1: 650 Q45 V35
Re: If four integers, a, b, c, and d are chosen at random with replacement  [#permalink]

Show Tags

New post 12 Apr 2018, 07:11
Oh wow I could not have thought of 16 possibilities like that...
My mind went like this
X=ab and Y=cd
For Sum of x and Y to be even it's possible in 2 cases
ODD +Odd is Even
Even + Even is Even
And other possibilities are
Even+Odd= Odd
Odd+ Even= Odd
So of Total 4 possibilities irrespective of what ab and cd could be the possibility fortheir summation to be even is 2/4 =1/2


Sent from my iPhone using GMAT Club Forum
Manager
Manager
avatar
B
Joined: 24 Mar 2018
Posts: 89
If four integers, a, b, c, and d are chosen at random with replacement  [#permalink]

Show Tags

New post 25 Apr 2018, 07:41
pushpitkc Bunuel
What's wrong in my thinking ?
A number can be either odd or even so the probabiblity is half i.e. 1/2
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3181
Location: India
GPA: 3.12
Premium Member CAT Tests
If four integers, a, b, c, and d are chosen at random with replacement  [#permalink]

Show Tags

New post 25 Apr 2018, 09:29
teaserbae wrote:
pushpitkc Bunuel
What's wrong in my thinking ?
A number can be either odd or even so the probabiblity is half i.e. 1/2


teaserbae

As you have clearly mentioned, the probabilty of a number being odd/even is \(\frac{1}{2}\)

Here we are concerned about the probabilities of 4 numbers.
Therefore, the overall probability will have \(2^4\) or \(16\) possibilities

Hope this helps you!
_________________

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

GMAT Club Bot
If four integers, a, b, c, and d are chosen at random with replacement &nbs [#permalink] 25 Apr 2018, 09:29
Display posts from previous: Sort by

If four integers, a, b, c, and d are chosen at random with replacement

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


Copyright

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®.