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Mark and Ann together were allocated n boxes of cookies

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by BTGModeratorVI » Fri Mar 06, 2020 5:46 pm

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Difficulty—

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

Answer: A
Source: Official Guide
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Re: Mark and Ann together were allocated n boxes of cookies

by deloitte247 » Sun Mar 08, 2020 1:10 am
What is the value of n?
Given that ;
Mark sold 10 boxes less than n
Mark sold (n-10)boxes
Ann sold 2 boxes less than n
Ann sold (n-2)boxes.
Mark and Ann sold at least one boxes of cookies but together, they sold less than n boxes
(Mark's sales) +(Ann's sales)<n
(n-10)+(n-2)<n
2n-n <12
n<12
The only option that is less than 12 is
$$Option\ A$$
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Re: Mark and Ann together were allocated n boxes of cookies

by Brent@GMATPrepNow » Sun Mar 08, 2020 5:38 am
BTGModeratorVI wrote: ↑
Fri Mar 06, 2020 5:46 pm
 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

Answer: A
Source: Official Guide
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: Mark and Ann together were allocated n boxes of cookies

by Scott@TargetTestPrep » Sun Mar 15, 2020 4:18 am
BTGModeratorVI wrote: ↑
Fri Mar 06, 2020 5:46 pm
 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

Answer: A
Source: Official Guide
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

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