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

Question

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

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

ScottTargetTestPrep · Accepted Answer

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

adiagr · Answer

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

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.

diegocml · Answer

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

HHXX · Answer

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...

Bunuel · Answer

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

Show Answer

Official Answer

A

If this question felt shaky, try an adaptive mini quiz of similar problems in GMAT Club Forum Quiz →. Free plan gives 5 questions per day.

EMPOWERgmatRichC · Answer

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:  A

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

adkikani · Answer

niks18   Hatakekakashi 
 amanvermagmat   chetan2u

Can you validate my understanding?

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?

chetan2u · Answer

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 '-'..

Bunuel · Answer

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.

chetan2u · Answer

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.

BrentGMATPrepNow · Answer

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

Answer: A

RELATED VIDEO 
 https://www.youtube.com/watch?v=Od98BOicIq4

NandishSS · Answer

HI  GMATPrepNow ,  GMATGuruNY ,  IanStewart

Here I got confused by   If Mark and Ann have each sold at least one box of cookies  .

Can you help to elaborate on how this statement affects as whole?

BrentGMATPrepNow · Answer

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

That part of the question is just letting us know that n does not equal zero

GMATGuruNY · Answer

We can PLUG IN THE ANSWERS, which represent the value of n. 
When the correct answer choice is plugged in, the total sold will be less than n.

D: n=14 
Since Mark sold 10 boxes less than n, the number sold by Mark = 14-10 = 4. 
Since Ann sold 2 boxes less than n, the number sold by Ann = 14-2 = 12. 
Total sold = 4+12 = 16. 
Here, the total sold is GREATER THAN n. 
Eliminate D.

B: n=12 
Since Mark sold 10 boxes less than n, the number sold by Mark = 12-10 = 2. 
Since Ann sold 2 boxes less than n, the number sold by Ann = 12-2 = 10. 
Total sold = 2+10 = 12. 
Here, the total sold is EQUAL TO n. 
Eliminate B.

Notice the trend: 
n=14 yields a sales volume GREATER THAN n. 
n=12 yields a sales volume EQUAL TO n. 
Implication: 
A smaller value for n is required to yield a sales volume LESS THAN n.

A

Algebraically: 
Mark's sales = n-10. 
Ann's sales = n-2. 
Since the total sold must be less than n, we get: 
(n-10) + (n-2) < n 
2n-12 < n 
n < 12.

A

As shown in my solution, n<12.
Without the statement above, a test-taker might deduce two possible answers: n=10 or n=11.
The statement above renders n=10 inviable.
If n=10, then the number of boxes sold by Mark = n-10 = 10-10 = 0.
Not possible, given the condition that Mark sells at least one box.
Thus -- because of the condition that Mark sells at least one box -- the only viable solution is n=11.

Kinshook · Answer

Given: 1. Mark and Ann together were allocated n boxes of cookies to sell for a club project. 2. Mark sold 10 boxes less than n and Ann sold 2 boxes less than n. 3. Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes Asked: What is the value of n? Let Mark and Ann sold m & a boxes respectively 00; n>10 and n<12 IMO A

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=PQokfsVzjws

GMATinsight · Answer

Answer: Option A

Video solution by  GMATinsight

https://www.youtube.com/watch?v=54Wr3Tg3H_s

Russ19 · Answer

BrentGMATPrepNow ,  EMPOWERgmatRichC

When I attempted the problem in 2 minutes time frame, the bolded part below taken from the question left me confused on how to go ahead.

''If Mark and Ann have each sold at least one box of cookies''

Is the bolded text above helpful at all to resolve the problem or is it a part of tricky wording? Can one ignore this part?

Thanks a lot!

chetan2u · Answer

Mark sold 10 less than n, so minimum value of n is 10, where Mark sold 0. If n is 10, Ann sold 8. together they have sold less than n boxes => 0+8<10…..Valid. Thus, if one of the options is 10 and there were no more restrictions, then 10 would be correct. But, we have a restriction. But, now the portion of AT LEAST comes in play. Mark sold 10 less than n, but sold at least ONE, so minimum value of n is 10+1 or 11, where Mark sold 1. If n is 11, Ann sold 9. together they have sold less than n boxes => 1+9<11…..Valid. Now, 10 will not be a valid solution as 1+9<10, and this makes 11 as valid A sjuniv32 , If these words ‘at least’ were missing, the answer will be 10, and not 11. Hope it clarifies the doubt.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards