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

 It is currently 07 Dec 2019, 11:38

### 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

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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59588
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

15 Jun 2016, 01:30
1
34
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:46) correct 23% (01:55) wrong based on 1652 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

_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8622
Location: United States (CA)
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

29 Nov 2016, 15:52
12
7
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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 18 Jan 2010
Posts: 238
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

15 Jun 2016, 05:23
8
1
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

##### General Discussion
Director
Joined: 20 Feb 2015
Posts: 737
Concentration: Strategy, General Management
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

15 Jun 2016, 04:59
1
if n =11
mark sold 1 box
and Ann sold 9 boxes
total 10 < 11
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4834
Location: India
GPA: 3.5
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

10 Oct 2016, 04:49
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
Joined: 29 Aug 2016
Posts: 1
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

28 Nov 2016, 05:23
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
Joined: 06 Jun 2016
Posts: 250
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

28 Nov 2016, 06:24
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
Status: On a 600-long battle
Joined: 22 Apr 2016
Posts: 136
Location: Hungary
Schools: Erasmus '19
GMAT 1: 410 Q18 V27
GMAT 2: 490 Q35 V23
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

05 Apr 2017, 21:49
1
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|
Math Expert
Joined: 02 Sep 2009
Posts: 59588
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

18 Oct 2017, 05:22
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: $$(n - 10) + (n - 2) < n$$ -->$$n < 12$$.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 59588
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

18 Mar 2018, 06:19
1
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.
_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8284
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

18 Mar 2018, 06:37
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.
_________________
Director
Joined: 02 Sep 2016
Posts: 641
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

09 Sep 2017, 10:58
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.
Intern
Joined: 18 Oct 2017
Posts: 1
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

18 Oct 2017, 04:59
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...
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15661
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

17 Jan 2018, 13:13
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.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1370
Location: India
WE: Engineering (Other)
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

18 Mar 2018, 06:13
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.

Feeling stressed, you are not alone!!
Math Expert
Joined: 02 Aug 2009
Posts: 8284
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

18 Mar 2018, 06:19
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 '-'..
_________________
VP
Joined: 07 Dec 2014
Posts: 1218
Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

18 Mar 2018, 11:59
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
Joined: 12 Feb 2015
Posts: 959
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

17 Oct 2018, 04:54
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.
_________________
________________
Manish

"Only I can change my life. No one can do it for me"
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4125
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

02 Jan 2019, 13:11
Top Contributor
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

Mark sold 10 boxes less than n and Ann sold 2 boxes less than n
We can write:
n - 10 = number of boxes that Mark sold
n - 2 = number of boxes that Ann sold

Together they (Mark and Ann) have sold less than n boxes
In other words: (# boxes Mark sold) + (# boxes Ann sold) < n
Rewrite as: (n - 10) + (n - 2) < n
Simplify: 2n - 12 < n
Add 12 to both sides: 2n < n + 12
Subtract n from both sides: n < 12

What is the value of n?
We know that n < 12
Check the answer choices . . . only answer choice A (11) is less than 12

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Intern
Joined: 15 Jul 2016
Posts: 12
Re: Mark and Ann together were allocated n boxes of cookies to sell for a  [#permalink]

### Show Tags

17 Apr 2019, 19:52
This question doesn't make sense to me...

From the question I arrived at 2n<n+12, however, this was my approach:

2<M+A<n
2<2n-12<n
14<2n<n+12
7<n<(n+12)/2

Even though the answer n=11 fits this criteria, you cannot have half a box of cookies from (n+12)/2

I don't know anymore
Re: Mark and Ann together were allocated n boxes of cookies to sell for a   [#permalink] 17 Apr 2019, 19:52

Go to page    1   2    Next  [ 24 posts ]

Display posts from previous: Sort by