The cost of delivery for an order of desk chairs was $10.00 for the first chair, and $1.00 for each additional chair in the order. If an office manager placed an order for n desk chairs, is n > 24 ?
(1) The delivery cost for the order totalled more than $30.00.
(2) The average (arithmetic mean) delivery cost of the n chairs was $1.36.
OA B
Source: GMAT Prep
The cost of delivery for an order of desk chairs was $10.00
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Target question: Is n > 24?BTGmoderatorDC wrote:The cost of delivery for an order of desk chairs was $10.00 for the first chair, and $1.00 for each additional chair in the order. If an office manager placed an order for n desk chairs, is n > 24 ?
(1) The delivery cost for the order totalled more than $30.00.
(2) The average (arithmetic mean) delivery cost of the n chairs was $1.36.
OA B
Source: GMAT Prep
Given: The cost of delivery for an order of desk chairs was $10.00 for the 1st chair, and $1 for each additional chair in the order. The office manager placed an order for n desk chairs.
Statement 1: The delivery cost for the order totaled more than $30.00
There are several scenarios that meet this condition. Here are two:
Case a: n = 25, in which case the total cost is $34 (which is more than $30). Here, n is greater than 24.
Case b: n = 23, in which case the total cost is $32 (which is more than $30). Here, n is not greater than 24.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The average (arithmetic mean) delivery cost per chair of the n chairs was $1.36
The average cost of n chairs = (total cost of n chairs)/n
The total cost = $10 for the first chair plus $1 for each of the remaining n-1 chairs
Algebraically, we can say that the total cost = 10 + 1(n-1)
So, the average cost of n chairs = [10 + 1(n-1)]/n
Statement 2 says the average cost is $1.36, so we can write:
[10 + 1(n-1)]/n = 1.36
IMPORTANT: We could solve this equation for n (but we won't), which means we could definitively determine whether or not n > 24.
Since we could answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
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$10 - first chair
$1 - additional
Order \(n\)
Is \(n>24\)? i.e. cost should be least \(10(1)+1(23)=33\)$ for \(24\) chairs.
(A) delivery cost \(> 30\). Not sufficient.
(B)
\(\begin{align}
S&=An \\
10+(n-1) &= 1.36n \\
9 + n&= 1.36n \\
9 &= 0.36n \\
\frac{9}{0.36} &= n \\
25 &= n
\end{align}\)
Sufficient. Hence, the correct answer is B
$1 - additional
Order \(n\)
Is \(n>24\)? i.e. cost should be least \(10(1)+1(23)=33\)$ for \(24\) chairs.
(A) delivery cost \(> 30\). Not sufficient.
(B)
\(\begin{align}
S&=An \\
10+(n-1) &= 1.36n \\
9 + n&= 1.36n \\
9 &= 0.36n \\
\frac{9}{0.36} &= n \\
25 &= n
\end{align}\)
Sufficient. Hence, the correct answer is B