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

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by AAPL » Sat May 16, 2020 9:36 am

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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?

A. 11
B. 12
C. 13
D. 14
E. 15

OA A

Source: Beat The GMAT — Problem Solving | Sat May 16, 2020 9:36 am

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

by Brent@GMATPrepNow » Sat May 16, 2020 2:16 pm

AAPL wrote: ↑
Sat May 16, 2020 9:36 am
Official Guide

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

OA A

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

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