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Mark and Ann

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rsarashi Master | Next Rank: 500 Posts Default Avatar
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Mark and Ann

Post Sat Feb 11, 2017 10:09 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

OAA

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Matt@VeritasPrep GMAT Instructor
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Post Wed Feb 15, 2017 5:51 pm
Mark = n - 10
Ann = n - 2

(n - 10) + (n - 2) < n

2n - 12 < n

n < 12

Only A fits.

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Post Wed Feb 15, 2017 3:09 pm
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
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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Post Sun Feb 12, 2017 10:29 pm
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
Hi rsarashi,

The number of boxes sold by Mark = n - 10;
And the number of boxes sold by Mark = n - 2

Together they sold (n-10)+(n-2) = 2n-12 boxes

We know that 2n-12 < n

=> n < 12

The only option less than 12 is option A: 11: correct answer.

It would have been interesting had there been at least a couple of options less than 12, for example, 11, 10, 9, ...

Still, the answer would be n=11.

Since Mark's sales = n-10 ≥ 1

=> n ≥ 11

With the two inequalities, we have 12 > n ≥ 11.

The only possible value for n is 11.

Hope this helps!

-Jay

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Post Sun Feb 12, 2017 11:48 am
Hi rsarashi,

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

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Post Sun Feb 12, 2017 4:22 am
Quote:
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 can PLUG IN THE ANSWERS, which represent the value of n.
When the correct answer choice is plugged in, the total sold will be less than n.

D: n=14
Since Mark sold 10 boxes less than n, the number sold by Mark = 14-10 = 4.
Since Ann sold 2 boxes less than n, the number sold by Ann = 14-2 = 12.
Total sold = 4+12 = 16.
Here, the total sold is GREATER THAN n.
Eliminate D.

B: n=12
Since Mark sold 10 boxes less than n, the number sold by Mark = 12-10 = 2.
Since Ann sold 2 boxes less than n, the number sold by Ann = 12-2 = 10.
Total sold = 2+10 = 12.
Here, the total sold is EQUAL TO n.
Eliminate B.

Notice the trend:
n=14 yields a sales volume GREATER THAN n.
n=12 yields a sales volume EQUAL TO n.
Implication:
A smaller value for n is required to yield a sales volume LESS THAN n.

The correct answer is A.

Algebraically:
Mark's sales = n-10.
Ann's sales = n-2.
Since the total sold must be less than n, we get:
(n-10) + (n-2) < n
2n-12 < n
n < 12.

The correct answer is A.

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