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

It is currently 14 Aug 2018, 18:38

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

M27-16

  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: 47898
M27-16  [#permalink]

Show Tags

New post 16 Sep 2014, 01:27
1
8
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

32% (00:43) correct 68% (01:50) wrong based on 88 sessions

HideShow timer Statistics

A certain fruit stand sold a total of 76 oranges to 19 customers. How many of them bought only one orange?


(1) None of the customers bought more than 4 oranges.

(2) The difference between the number of oranges bought by any two customers is even.

_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47898
Re M27-16  [#permalink]

Show Tags

New post 16 Sep 2014, 01:27
2
2
Official Solution:


(1) None of the customers bought more than 4 oranges. This basically means that all customers bought exactly 4 oranges (\(\frac{76}{19}=4\)), because if even one customer bought less than 4, the sum would be less than 76. Hence, no one bought only one orange. Sufficient.

(2) The difference between the number of oranges bought by any two customers is even. In order for the difference between ANY number of oranges bought to be even, either all customers must have bought an odd number of oranges or all customers must have bought an even number of oranges. But the first case is not possible: the sum of 19 odd numbers is odd and not even like 76. Hence, again no one bought only one (i.e. odd number) orange. Sufficient.


Answer: D
_________________

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

Current Student
User avatar
B
Joined: 03 Jun 2013
Posts: 22
Concentration: Strategy, General Management
GMAT 1: 520 Q38 V32
GMAT 2: 530 Q44 V22
GMAT 3: 670 Q47 V34
WE: Information Technology (Consulting)
Re: M27-16  [#permalink]

Show Tags

New post 01 Dec 2014, 19:08
Bunuel wrote:
Official Solution:


(1) None of the customers bought more than 4 oranges. This basically means that all customers bought exactly 4 oranges (\(\frac{76}{19}=4\)), because if even one customer bought less than 4, the sum would be less than 76. Hence, no one bought only one orange. Sufficient.

(2) The difference between the number of oranges bought by any two customers is even. In order for the difference between ANY number of oranges bought to be even, either all customers must have bought an odd number of oranges or all customers must have bought an even number of oranges. But the first case is not possible: the sum of 19 odd numbers is odd and not even like 76. Hence, again no one bought only one (i.e. odd number) orange. Sufficient.


Answer: D


Hi,

i had a question regarding the 1st statement.
" None of the customers bought more than 4 oranges."
why would this mean everyone bought EXACTLY 4 oranges. What if someone buys 1,2 or 3 oranges (coz it is still less than 4)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47898
Re: M27-16  [#permalink]

Show Tags

New post 02 Dec 2014, 00:44
arunpkumar wrote:
Bunuel wrote:
Official Solution:


(1) None of the customers bought more than 4 oranges. This basically means that all customers bought exactly 4 oranges (\(\frac{76}{19}=4\)), because if even one customer bought less than 4, the sum would be less than 76. Hence, no one bought only one orange. Sufficient.

(2) The difference between the number of oranges bought by any two customers is even. In order for the difference between ANY number of oranges bought to be even, either all customers must have bought an odd number of oranges or all customers must have bought an even number of oranges. But the first case is not possible: the sum of 19 odd numbers is odd and not even like 76. Hence, again no one bought only one (i.e. odd number) orange. Sufficient.


Answer: D


Hi,

i had a question regarding the 1st statement.
" None of the customers bought more than 4 oranges."
why would this mean everyone bought EXACTLY 4 oranges. What if someone buys 1,2 or 3 oranges (coz it is still less than 4)


There are 19 customers who bought total of 76 oranges and none of the customers bought more than 4 oranges. Could any of them bought less than 4 oranges?
_________________

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

Current Student
avatar
Joined: 29 Apr 2014
Posts: 122
Location: Viet Nam
Concentration: Finance, Technology
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q51 V27
GMAT 3: 680 Q50 V31
GMAT 4: 710 Q50 V35
GMAT 5: 760 Q50 V42
Reviews Badge
Re: M27-16  [#permalink]

Show Tags

New post 17 Nov 2015, 16:56
The explanation for (2) is great Bunnel. I was frustrated with trying pairs of (1,5), (1,7)....
Retired Moderator
avatar
B
Joined: 23 Sep 2015
Posts: 386
Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)
Premium Member Reviews Badge
Re: M27-16  [#permalink]

Show Tags

New post 25 Nov 2015, 04:13
Statement two was a hard one. Great explanation!
_________________

New Application Tracker : update your school profiles instantly!

Intern
Intern
User avatar
Joined: 04 Sep 2015
Posts: 13
WE: Asset Management (Investment Banking)
GMAT ToolKit User
Re: M27-16  [#permalink]

Show Tags

New post 25 Dec 2015, 23:01
1
I thought that 0 is an even number? If it's so then in case 2, two or more people can buy the same odd amount of fruit ( 1, 3, 3 etc or 3, 5, 5 etc.) as long as the sum is 76. Therefore, one may or may not buy exactly 1 orange
--> option 2 is insufficient

Please help
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6512
Re: M27-16  [#permalink]

Show Tags

New post 26 Dec 2015, 00:04
3
1
notMD wrote:
I thought that 0 is an even number? If it's so then in case 2, two or more people can buy the same odd amount of fruit ( 1, 3, 3 etc or 3, 5, 5 etc.) as long as the sum is 76. Therefore, one may or may not buy exactly 1 orange
--> option 2 is insufficient

Please help


Hi,
You rae correct that 0 is an even number..
and you are also correct soeonecan buy 1,1,3 or 3,5,5...
but you have to look at two points
1)the total number of oranges..it is an even number
2) since the difference is even.. either all numbers are even or all numbers will be odd,,..
why? say you have someone with 4 and other with 3.. the difference will be odd...

having seen these two points
we have to ask ourselves " Is it possible to have odd number of people having odd number of oranges and still having total number of oranges as even?"
The answer is NO... Because Sum of odd quantity of numbers having odd values will always be odd
So any odd value gets discarded and along with it goes out the value of '1'..
Thus suff
_________________

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


GMAT online Tutor

Senior Manager
Senior Manager
User avatar
Joined: 31 Mar 2016
Posts: 400
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)
GMAT ToolKit User Premium Member
Re M27-16  [#permalink]

Show Tags

New post 30 Jul 2016, 05:28
I think this is a high-quality question and I agree with explanation.
Intern
Intern
avatar
B
Joined: 23 Jun 2016
Posts: 8
CAT Tests
Re M27-16  [#permalink]

Show Tags

New post 28 Nov 2016, 20:36
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Can you please explain how S2 is sufficient on its own. Did not understand from official solution
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47898
Re: M27-16  [#permalink]

Show Tags

New post 28 Nov 2016, 22:22
pratyushk1 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Can you please explain how S2 is sufficient on its own. Did not understand from official solution


Can you please what part of the following is unclear:

(2) The difference between the number of oranges bought by any two customers is even. In order for the difference between ANY number of oranges bought to be even, either all customers must have bought an odd number of oranges or all customers must have bought an even number of oranges. But the first case is not possible: the sum of 19 odd numbers is odd and not even like 76. Hence, again no one bought only one (i.e. odd number) orange. Sufficient.

Thank you.
_________________

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

Director
Director
User avatar
P
Joined: 18 Aug 2016
Posts: 631
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Premium Member Reviews Badge
Re M27-16  [#permalink]

Show Tags

New post 08 Jun 2017, 06:14
I think this is a high-quality question and I agree with explanation. Great Question +100 Kudos
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

Intern
Intern
avatar
B
Joined: 18 Jan 2017
Posts: 31
Re: M27-16  [#permalink]

Show Tags

New post 08 Jun 2017, 06:42
Hi Bunuel I got the answer alright... but what level question would this be... thanks

Sent from my GT-I9060I using GMAT Club Forum mobile app
Intern
Intern
avatar
B
Joined: 02 Sep 2017
Posts: 20
Location: India
GMAT 1: 710 Q48 V40
GPA: 2
Reviews Badge
Re M27-16  [#permalink]

Show Tags

New post 24 Dec 2017, 06:24
I think this is a high-quality question and I agree with explanation.
Manager
Manager
avatar
B
Status: Turning my handicaps into assets
Joined: 09 Apr 2017
Posts: 120
Re M27-16  [#permalink]

Show Tags

New post 08 May 2018, 03:38
I think this is a high-quality question and I agree with explanation.
_________________

If time was on my side, I'd still have none to waste......

Intern
Intern
avatar
Joined: 29 May 2017
Posts: 4
Re M27-16  [#permalink]

Show Tags

New post 17 May 2018, 00:09
I think this is a high-quality question and I agree with explanation. Statement 2
Best ODD-EVEN Concept so far
Manager
Manager
avatar
S
Joined: 16 May 2016
Posts: 130
Location: India
Concentration: Marketing, Healthcare
GPA: 3
WE: Analyst (Computer Software)
CAT Tests
M27-16  [#permalink]

Show Tags

New post 03 Aug 2018, 04:02
Bunuel wrote:
A certain fruit stand sold a total of 76 oranges to 19 customers. How many of them bought only one orange?


(1) None of the customers bought more than 4 oranges.

(2) The difference between the number of oranges bought by any two customers is even.

Statement 1: None bought < 4- Clearly sufficient since then everyone bought 4 Oranges
Statement 2: Tricky and I got wrong at first However, given a thought
Everyone bought something so there is no customer who has 0 orange
Moving ahead, if 18 customers each bought 1 and 19th customer bought (76-18)= 58 now if I take difference of any 2 numbers from it such as 1-1=0 or 58-1 Not valid
Giving 2 Oranges to each of customers , hence 18 customers have 2 and 18th one has 76-36=40 oranges, now difference of any number in set is even . It means none of them had 1 orange- Sufficient

Ans: D
_________________

Not Giving UP! Kudos if you like the question :)

M27-16 &nbs [#permalink] 03 Aug 2018, 04:02
Display posts from previous: Sort by

M27-16

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

Moderators: chetan2u, Bunuel

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®.