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

It is currently 17 Feb 2019, 10:05

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Algebra Webinar

     February 17, 2019

     February 17, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
  • Valentine's day SALE is on! 25% off.

     February 18, 2019

     February 18, 2019

     10:00 PM PST

     11:00 PM PST

    We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

A collection of 36 cards are numbered in two sets. Each card has a uni

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

Hide Tags

 
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2568
A collection of 36 cards are numbered in two sets. Each card has a uni  [#permalink]

Show Tags

New post 12 Nov 2018, 18:40
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

61% (02:15) correct 39% (02:21) wrong based on 103 sessions

HideShow timer Statistics

A collection of 36 cards are numbered in two sets. Each card has a unique number. The cards are numbered in such a way that the first 18 cards are numbered with all odd integers from 1 to 36. The remaining cards are numbered using the even integers from 35 to 72. If two cards are drawn at random, then what is the probability that the sum of the numbers on those two cards will be odd?

    A.\(\frac{18 * 18}{^{36}C_2}\)

    B. \(\frac{18 * 17}{^{36}C_2}\)

    C. \(\frac{18 * 19}{^{36}C_2}\)

    D. \(\frac{19 * 17}{^{36}C_2}\)

    E. \(\frac{18 * 19}{^{37}C_2}\)

Image

_________________








Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Weession:- Key strategy to score 760

Success Stories
Q38 to Q50 | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Question to reach Q51 | Question of the week | Tips From V40+ Scoreres | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
A collection of 36 cards are numbered in two sets. Each card has a uni  [#permalink]

Show Tags

New post 12 Nov 2018, 22:30
A collection of 36 cards are numbered in two sets. Each card has a unique number. The cards are numbered in such a way that the first 18 cards are numbered with all odd integers from 1 to 36. The remaining cards are numbered using the even integers from 35 to 72. If two cards are drawn at random, then what is the probability that the sum of the numbers on those two cards will be odd?

    A.\(\frac{18 * 18}{^{36}C_2}\)

    B. \(\frac{18 * 17}{^{36}C_2}\)

    C. \(\frac{18 * 19}{^{36}C_2}\)

    D. \(\frac{19 * 17}{^{36}C_2}\)

    E. \(\frac{18 * 19}{^{37}C_2}\)

There are \(\frac{36}{2}=18\) odd numbers from 1 to 36 and similarly 18 even numbers in next 36 numbers from 37 to 72
so way two number sum will be odd - one from odd and one from even so 18*18
total - 36
hence \(\frac{18 * 18}{^{36}C_2}\)
A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Manager
Manager
User avatar
S
Joined: 21 Jun 2017
Posts: 234
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
CAT Tests
Re: A collection of 36 cards are numbered in two sets. Each card has a uni  [#permalink]

Show Tags

New post 12 Nov 2018, 23:17
How can 36 to 72 be 18 integers. Still ans maybe (eo + oe)/36*35 = (2*18*18)/(36*35)
A
_________________

Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!!

Intern
Intern
avatar
B
Joined: 09 Nov 2018
Posts: 27
Re: A collection of 36 cards are numbered in two sets. Each card has a uni  [#permalink]

Show Tags

New post 13 Nov 2018, 00:58
Assume set 1 to be 1st 18 cards with unique odd integer values from 1 to 36
Assume set 2 to be remaining 18 cards with unique even integer values from 35 to 72
For sum of 2 numbers to be odd, one number must be odd and other must be even.

Here, if the 1st card drawn is odd and 2nd card drawn is even, then the probability that sum will be odd = (18/36)*(18/35)
(since, there are totally 36 cards, i can choose any 1 of 18 cards from 1st set, and in the remaining 35 cards, i can choose any 1 of 18 cards from 2nd set)

There is one more possibility that, 1st card drawn is even and 2nd card drawn is odd, then the probability that sum will be odd = (18/36)*(18/35)
(same reason as above)

so, total probability that sum will be odd = (18/36)+(18/36)=(18/36)*(18/35)*2
=(18*18)/36C2
NOTE : 36C2= (36*35)/2, since formula for combination is
nCr= (n!)/((r!)*(n-r)!)

OPTION :A
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2568
Re: A collection of 36 cards are numbered in two sets. Each card has a uni  [#permalink]

Show Tags

New post 14 Nov 2018, 04:14

Solution


Given:
    • A collection of 36 cards, numbered in 2 sets
    • Each card has a unique number
    • First 18 cards are numbered with all the odd integers from 1 to 36
    • Remaining 18 cards are numbered using the even integers from 35 to 72

To find:
    • The probability that the sum of the numbers on the two cards chosen at random is odd

Approach and Working:
    • For the sum of two numbers to be odd
      o One of them must be odd and the other must be even

    • Total number of cards with an odd number = 18
    • Total number of cards with an even number = 18

Thus, probability for the sum to be odd = \(\frac{^{18}C_1 * ^{18}C_1}{^{36}C_2}\)

Hence the correct answer is Option A.

Answer: A

Image

_________________








Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Weession:- Key strategy to score 760

Success Stories
Q38 to Q50 | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Question to reach Q51 | Question of the week | Tips From V40+ Scoreres | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

SVP
SVP
User avatar
G
Joined: 18 Aug 2017
Posts: 1775
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: A collection of 36 cards are numbered in two sets. Each card has a uni  [#permalink]

Show Tags

New post 15 Nov 2018, 02:05
EgmatQuantExpert wrote:
A collection of 36 cards are numbered in two sets. Each card has a unique number. The cards are numbered in such a way that the first 18 cards are numbered with all odd integers from 1 to 36. The remaining cards are numbered using the even integers from 35 to 72. If two cards are drawn at random, then what is the probability that the sum of the numbers on those two cards will be odd?

    A.\(\frac{18 * 18}{^{36}C_2}\)

    B. \(\frac{18 * 17}{^{36}C_2}\)

    C. \(\frac{18 * 19}{^{36}C_2}\)

    D. \(\frac{19 * 17}{^{36}C_2}\)

    E. \(\frac{18 * 19}{^{37}C_2}\)

Image



To get an odd sum of number upon drawing two cards one has to be odd and other even..

From given info we know that from no of odd cards 18 and even is 18

so P of getting odd sum : 18*18/36c2= option A
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Manager
Manager
User avatar
S
Joined: 13 Feb 2018
Posts: 154
GMAT 1: 640 Q48 V28
CAT Tests
A collection of 36 cards are numbered in two sets. Each card has a uni  [#permalink]

Show Tags

New post 22 Jan 2019, 06:32
chetan2u sir can you help?

I considered 2 cases:
1) even, odd
2) odd, even

As there are 18 even and 18 odd, total 36

first case: \(\frac{18}{36}*\frac{18}{35}=\frac{9}{35}\)
Second case: \(\frac{18}{36}*\frac{18}{35}=\frac{9}{35}\)

prob to occur first OR second case \(\frac{9}{35}+\frac{9}{35}=\frac{18}{35}\)

Where do I go wrong?

Regards
L
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
Re: A collection of 36 cards are numbered in two sets. Each card has a uni  [#permalink]

Show Tags

New post 22 Jan 2019, 06:43
1
LevanKhukhunashvili wrote:
chetan2u sir can you help?

I considered 2 cases:
1) even, odd
2) odd, even

As there are 18 even and 18 odd, total 36

first case: \(\frac{18}{36}*\frac{18}{35}=\frac{9}{35}\)
Second case: \(\frac{18}{36}*\frac{18}{35}=\frac{9}{35}\)

prob to occur first OR second case \(\frac{9}{35}+\frac{9}{35}=\frac{18}{35}\)

Where do I go wrong?

Regards
L


You have not gone wrong anywhere. It is only that the answer is not in a simified form..
(18*18)/(36C2)=18*18/(36!/2!(36-2)!)=18*18/(36*35/2)=18*18/(18*35)=18/35..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Senior Manager
Senior Manager
User avatar
S
Joined: 08 Aug 2017
Posts: 325
Re: A collection of 36 cards are numbered in two sets. Each card has a uni  [#permalink]

Show Tags

New post 22 Jan 2019, 07:02
Hello Chetan2u Sir,

Here you mentioned that 18 numbers from 37 to 72, but in question stem says 18 numbers from 35 to 72.

Is it a typo error in question?
chetan2u wrote:
A collection of 36 cards are numbered in two sets. Each card has a unique number. The cards are numbered in such a way that the first 18 cards are numbered with all odd integers from 1 to 36. The remaining cards are numbered using the even integers from 35 to 72. If two cards are drawn at random, then what is the probability that the sum of the numbers on those two cards will be odd?

    A.\(\frac{18 * 18}{^{36}C_2}\)

    B. \(\frac{18 * 17}{^{36}C_2}\)

    C. \(\frac{18 * 19}{^{36}C_2}\)

    D. \(\frac{19 * 17}{^{36}C_2}\)

    E. \(\frac{18 * 19}{^{37}C_2}\)

There are \(\frac{36}{2}=18\) odd numbers from 1 to 36 and similarly 18 even numbers in next 36 numbers from 37 to 72
so way two number sum will be odd - one from odd and one from even so 18*18
total - 36
hence \(\frac{18 * 18}{^{36}C_2}\)
A
GMAT Club Bot
Re: A collection of 36 cards are numbered in two sets. Each card has a uni   [#permalink] 22 Jan 2019, 07:02
Display posts from previous: Sort by

A collection of 36 cards are numbered in two sets. Each card has a uni

  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®.