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

It is currently 16 Dec 2018, 04:51

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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.
  • Free GMAT Prep Hour

     December 16, 2018

     December 16, 2018

     03:00 PM EST

     04:00 PM EST

    Strategies and techniques for approaching featured GMAT topics

Mark and Ann together were allocated n boxes of cookies to sell for a

  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: 51223
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 15 Jun 2016, 00:30
18
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (01:20) correct 23% (01:32) wrong based on 1218 sessions

HideShow timer Statistics

Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?

A) 11
B) 12
C) 13
D) 14
E) 15

_________________

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

Most Helpful Expert Reply
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4295
Location: United States (CA)
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 29 Nov 2016, 14:52
3
3
Bunuel wrote:
Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?

A) 11
B) 12
C) 13
D) 14
E) 15


We are given that Mark sold 10 boxes less than n and Ann sold 2 boxes less than n, and that together they have sold less than n boxes. We can create the following inequality:

n - 10 + n - 2 < n

2n - 12 < n

n < 12

Answer: A
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Most Helpful Community Reply
Senior Manager
Senior Manager
User avatar
Joined: 18 Jan 2010
Posts: 252
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 15 Jun 2016, 04:23
8
6
Bunuel wrote:
Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?

A) 11
B) 12
C) 13
D) 14
E) 15


Mary sold n-10 boxes.
Ann sold n-2 boxes.

They have each sold at least one box.

so n-10 is more than or equal to 1. Also n-2 is more than or equal to 1
n>= 11 [2nd condition only gives us n>=3. We already have this info when we say n>=11]

Now

Total boxes are n only.

so (n-10+n-2) < n

2n-12 < n
n <12

Only value. n = 11

A is the answer.
General Discussion
Director
Director
User avatar
G
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
Premium Member
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 15 Jun 2016, 03:59
if n =11
mark sold 1 box
and Ann sold 9 boxes
total 10 < 11
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4277
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member CAT Tests
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 10 Oct 2016, 03:49
1
1
Bunuel wrote:
Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?

A) 11
B) 12
C) 13
D) 14
E) 15


Quote:
Mark and Ann together were allocated n boxes of cookies

M + A = n
Quote:
Mark sold 10 boxes less than n

M = n - 10
Quote:
Ann sold 2 boxes less than n.

A = n - 2
Quote:
Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n

M + A = {(n - 10) + (n - 2) } < n
Or, (2n - 12) < n
Or, n < 11

So, Answer will be (A) 11

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Intern
Intern
avatar
Joined: 29 Aug 2016
Posts: 1
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 28 Nov 2016, 04:23
1
Sorry, I ment the part where

"M + A = {(n - 10) + (n - 2) } < n
Or, (2n - 12) < n
Or, n < 11"

I understand how 2n-12<n is received, but n<11? Is it a typo or am I misunderstanding the concept?

As I see it, it should be 2n-12 < n <=> 2n - n < 12 <=> n < 12. Got a little bit confused
Senior Manager
Senior Manager
avatar
Joined: 06 Jun 2016
Posts: 258
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 28 Nov 2016, 05:24
1
MrBarksdale wrote:

Sorry, I ment the part where

"M + A = {(n - 10) + (n - 2) } < n
Or, (2n - 12) < n
Or, n < 11"

I understand how 2n-12<n is received, but n<11? Is it a typo or am I misunderstanding the concept?

As I see it, it should be 2n-12 < n <=> 2n - n < 12 <=> n < 12. Got a little bit confused



Its a typo. n < 12 is right.
only option A suffices the condition
Manager
Manager
User avatar
S
Status: On a 600-long battle
Joined: 21 Apr 2016
Posts: 138
Location: Hungary
Concentration: Accounting, Leadership
Schools: Erasmus '19
GMAT 1: 410 Q18 V27
GMAT 2: 490 Q35 V23
GMAT ToolKit User
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 05 Apr 2017, 20:49
I got it wrong. I think that the catch in this question is to realize that it's an inequality problem.

If you make an equation out of it, you get 12. Else, if you appropriately decode the question, you set up the inequality and you get that \(n<12\).

\(n-10+n-2=n\\ n-10+n-2<n\)
_________________

"When the going gets tough, the tough gets going!"

|Welcoming tips/suggestions/advices (you name it) to help me achieve a 600|

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 681
Premium Member
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 09 Sep 2017, 09:58
Experts please correct me if I have done this wrongly:

Both have sold at least 1 box but together they have sold less than n boxes.

2<=(n-10)+(n-2)<n
2<=2n-12<n
1<=n-6<n/2
7<=n<(n+12)/2

I thought that answer would come from: n< (n+12)/2
From the first part of the inequality, we know that n<=7

2n<n+12
n<12

Only one option fits in. (11)


My query is can we solve only one part of the inequality like I did above or it will impact the answer? Bunuel it would be great if you could give your view about the solution above.
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Intern
Intern
avatar
Joined: 18 Oct 2017
Posts: 1
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 18 Oct 2017, 03:59
Oh my god... it seems that only me don't understand why mark sold n-10 and ann sold n-2... the title says that mark sold 10 boxes less than n. what does that mean? any expert can told me...
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51223
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 18 Oct 2017, 04:22
1
HHXX wrote:
Oh my god... it seems that only me don't understand why mark sold n-10 and ann sold n-2... the title says that mark sold 10 boxes less than n. what does that mean? any expert can told me...


Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?

A) 11
B) 12
C) 13
D) 14
E) 15

Step-by-step:

1. Mark sold 10 boxes less than n --> Mark sold n - 10 boxes;

2. Ann sold 2 boxes less than n --> Ann sold n - 2 boxes;

3. Mark sold at least one box of cookies: \(n - 10 \geq 1\) -->\(n \geq 11\);

4. Together they have sold less than n boxes: \((n - 10) + (n - 2) < n\) -->\(n < 12\).

Answer: A.
_________________

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

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13095
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 17 Jan 2018, 12:13
Hi All,

This question can be solved by TESTing THE ANSWERS. There's a great 'logic shortcut' built into this prompt - but you have to pay careful attention to how the question is specifically phrased to catch the shortcut.

We're told that Mark sold 10 boxes LESS than N and Ann sold 2 boxes LESS than N. The prompt also states that the TOTAL of those two numbers is also LESS than N. Logically-speaking, since that pair of numbers is dependent on the value of N, the way to make the sum of those numbers less than N is to make those two numbers as SMALL as possible. Since we're given 5 possible values for N, we should start with the smallest value and see what happens...

IF.... N = 11 boxes
Mark = 11 - 10 = 1 box sold
Ann = 11 - 2 = 9 boxes sold
Total = 1 + 9 = 10 boxes sold
This matches what we were told, so this MUST be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1269
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 18 Mar 2018, 05:13
niks18 Hatakekakashi
amanvermagmat chetan2u

Quote:
Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?


Can you validate my understanding?

Quote:
n - 10 + n - 2 < n

2n - 12 < n

n < 12


I know n is a positive integer and hence I can subtract n from both sides of inequality without disturbing the inequality.
and also add +12 on both sides giving n < 12. Can I reduce steps in such a manner?
_________________

It's the journey that brings us happiness not the destination.

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7108
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 18 Mar 2018, 05:19
adkikani wrote:
niks18 Hatakekakashi
amanvermagmat chetan2u

Quote:
Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?


Can you validate my understanding?

Quote:
n - 10 + n - 2 < n

2n - 12 < n

n < 12


I know n is a positive integer and hence I can subtract n from both sides of inequality without disturbing the inequality.
and also add +12 on both sides giving n < 12. Can I reduce steps in such a manner?


Hi...

you are correct but the same procedure should be done even when n is negative..

change in INEQUALITY sign is when you multiply both sides by '-'..
_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51223
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 18 Mar 2018, 05:19
1
adkikani wrote:
niks18 Hatakekakashi
amanvermagmat chetan2u

Quote:
Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?


Can you validate my understanding?

Quote:
n - 10 + n - 2 < n

2n - 12 < n

n < 12


I know n is a positive integer and hence I can subtract n from both sides of inequality without disturbing the inequality.
and also add +12 on both sides giving n < 12. Can I reduce steps in such a manner?


This is correct but there is a flaw in your reasoning. We are concerned about the sign of a variable when multiplying/dividing an inequality by it. However we can safely add/subtract a variable from both sides of an inequality regardless of its sign.
_________________

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 Aug 2009
Posts: 7108
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 18 Mar 2018, 05:37
1
Bunuel wrote:

This is correct but there is a flaw in your reasoning. We are concerned about the sign of a variable when multiplying/dividing an inequality by it. However we can safely add/subtract a variable from both sides of an inequality regardless of its sign.


Quote:
you are correct but the same procedure should be done even when n is negative..

change in INEQUALITY sign is when you multiply both sides by '-'..


Hi Bunuel, I thought both the quoted portion meant same but the member asking question must have felt otherwise and seems did not understand my reply..
I am off to taking VERBAL coaching classes. ;)
_________________

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

VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1129
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 18 Mar 2018, 10:59
Bunuel wrote:
Mark and Ann together were allocated n boxes of cookies to sell for a club project. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. If Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes, what is the value of n?

A) 11
B) 12
C) 13
D) 14
E) 15


total sold boxes=2n-12
let unsold boxes=x
n=2n-12+x
→x=12-n
x must=1 because if x>1, then n<11
substituting, 1=12-n
n=11
A
Director
Director
User avatar
V
Joined: 11 Feb 2015
Posts: 617
Premium Member CAT Tests
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

Show Tags

New post 17 Oct 2018, 03:54
n − 10 ≥ 1 and n − 2 ≥ 1, which implies that n ≥ 11.

(n − 10) + (n − 2) < n, which implies that n < 12.

Therefore, n is an integer such that n ≥ 11 and n < 12, which implies that n = 11.
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

GMAT Club Bot
Re: Mark and Ann together were allocated n boxes of cookies to sell for a &nbs [#permalink] 17 Oct 2018, 03:54
Display posts from previous: Sort by

Mark and Ann together were allocated n boxes of cookies to sell for a

  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®.