Mark and Ann

rsarashi 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

OAA

We are given that Mark and Ann were given n boxes of cookies to sell. Mark sold (n - 10), and Ann sold (n - 2) boxes of cookies; thus, together they sold n - 10 + n - 2 = 2n - 12 boxes of cookies. Since together they sold fewer than n boxes, we can create the following inequality:

2n - 12 < n

n < 12

The only answer that is less than 12 is 11.

Answer: A

rsarashi 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

OAA

Mark sold 10 boxes less than n and Ann sold 2 boxes less than n
So, n - 10 = the number of boxes Mark sold
And n - 2 = the number of boxes Ann sold

Mark and Ann have each sold at least one box of cookies, but together they have sold less than n boxes
TOTAL number of boxes sold = (n - 10) + (n - 2 [/color) = 2n - 12
We can write: 2n - 12 < n
Add 12 to both sides: 2n < n + 12
Subtract n from both sides: n < 12

What is the value of n?
Check the answer choices to see that only one value of n (n = 11) is less than 12.

Answer: A

Cheers,
Brent

Hi All,

We're told that 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... we're asked for the value of N.

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