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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?

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

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15 Jun 2016, 05:23

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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]

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

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10 Oct 2016, 04:49

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This post was BOOKMARKED

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

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

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.

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

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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...

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: \((n - 10) + (n - 2) < n\) -->\(n < 12\).