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

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 \(n<12\).

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

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.

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

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?

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 '-'..

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.

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.

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

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?

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?

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

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.



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.





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.

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

0<m,a<=n
m = n-10
a = n -2
m + a < n
n-10 + n-2 <n
n < 12
n = 11 is only possible solution since n-10>0; n>10 and n<12

IMO A

Video solution from Quant Reasoning:

Answer: Option A

Video solution by GMATinsight



Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub

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!

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.