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Mark and Ann together were allocated n boxes of cookies to sell for a
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15 Jun 2016, 01:30

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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?

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29 Nov 2016, 15:52

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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:

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

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Re: Mark and Ann together were allocated n boxes of cookies to sell for a
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18 Oct 2017, 05:22

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

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.
_________________

Mark and Ann together were allocated n boxes of cookies to sell for a
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18 Mar 2018, 06:37

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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.
_________________

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.

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

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

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.

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 '-'..
_________________

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

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