Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49915

Question Stats:
34% (01:23) correct 66% (01:50) wrong based on 196 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 49915

Re M2716
[#permalink]
Show Tags
16 Sep 2014, 01:27
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? Extrahard Quant Tests with Brilliant Analytics



Current Student
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: M2716
[#permalink]
Show Tags
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
Joined: 02 Sep 2009
Posts: 49915

Re: M2716
[#permalink]
Show Tags
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? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 29 Apr 2014
Posts: 120
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

Re: M2716
[#permalink]
Show Tags
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
Joined: 23 Sep 2015
Posts: 383
Location: France
GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

Re: M2716
[#permalink]
Show Tags
25 Nov 2015, 04:13
Statement two was a hard one. Great explanation!
_________________
New Application Tracker : update your school profiles instantly!



Intern
Joined: 04 Sep 2015
Posts: 13
WE: Asset Management (Investment Banking)

Re: M2716
[#permalink]
Show Tags
25 Dec 2015, 23:01
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
Joined: 02 Aug 2009
Posts: 6956

Re: M2716
[#permalink]
Show Tags
26 Dec 2015, 00:04
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 oddSo any odd value gets discarded and along with it goes out the value of '1'.. Thus suff
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Senior Manager
Joined: 31 Mar 2016
Posts: 390
Location: India
Concentration: Operations, Finance
GPA: 3.8
WE: Operations (Commercial Banking)

Re M2716
[#permalink]
Show Tags
30 Jul 2016, 05:28
I think this is a highquality question and I agree with explanation.



Intern
Joined: 23 Jun 2016
Posts: 8

Re M2716
[#permalink]
Show Tags
28 Nov 2016, 20:36
I think this is a highquality 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
Joined: 02 Sep 2009
Posts: 49915

Re: M2716
[#permalink]
Show Tags
28 Nov 2016, 22:22
pratyushk1 wrote: I think this is a highquality 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? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 18 Aug 2016
Posts: 625
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38

Re M2716
[#permalink]
Show Tags
08 Jun 2017, 06:14
I think this is a highquality question and I agree with explanation. Great Question +100 Kudos
_________________
We must try to achieve the best within us
Thanks Luckisnoexcuse



Intern
Joined: 18 Jan 2017
Posts: 28

Re: M2716
[#permalink]
Show Tags
08 Jun 2017, 06:42
Hi Bunuel I got the answer alright... but what level question would this be... thanks Sent from my GTI9060I using GMAT Club Forum mobile app



Intern
Joined: 02 Sep 2017
Posts: 20
Location: India
GPA: 2

Re M2716
[#permalink]
Show Tags
24 Dec 2017, 06:24
I think this is a highquality question and I agree with explanation.



Manager
Status: Turning my handicaps into assets
Joined: 09 Apr 2017
Posts: 125

Re M2716
[#permalink]
Show Tags
08 May 2018, 03:38
I think this is a highquality question and I agree with explanation.
_________________
If time was on my side, I'd still have none to waste......



Intern
Joined: 29 May 2017
Posts: 6
Concentration: Strategy, Technology
WE: Analyst (Consulting)

Re M2716
[#permalink]
Show Tags
17 May 2018, 00:09
I think this is a highquality question and I agree with explanation. Statement 2 Best ODDEVEN Concept so far



Manager
Joined: 16 May 2016
Posts: 152
Location: India
Concentration: Marketing, Healthcare
GPA: 3.5
WE: Analyst (Consulting)

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 (7618)= 58 now if I take difference of any 2 numbers from it such as 11=0 or 581 Not valid Giving 2 Oranges to each of customers , hence 18 customers have 2 and 18th one has 7636=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










