An auto dealer sells each car at either $20,000 or $30,000. Some cars are marked up at 20% of the cost price and the remaining are marked up at 30% of the cost price. If the dealer sells 50 cars in total, what is the total profit of the dealer?
(1) 20 cars were sold for $20,000
(2) 30 cars were marked up 30%
The OA is E.
Source: e-GMAT
An auto dealer sells each car at either $20,000 or $30,000.
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- Jay@ManhattanReview
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Note that some cars with cost price $20,000 may be sold with 20% markup, while some cars may be sold with 30% markup. The same goes for the cars with the cost price of $30,000.swerve wrote:An auto dealer sells each car at either $20,000 or $30,000. Some cars are marked up at 20% of the cost price and the remaining are marked up at 30% of the cost price. If the dealer sells 50 cars in total, what is the total profit of the dealer?
(1) 20 cars were sold for $20,000
(2) 30 cars were marked up 30%
The OA is E.
Source: e-GMAT
Let's take each statement one by one.
(1) 20 cars were sold for $20,000.
Certainly insufficient. No idea about other cars.
(2) 30 cars were marked up 30%.
Certainly insufficient. No idea about other cars.
(1) and (2) together
From Statement 1, we do not know how many of the 20 cars sold for $20,000 were sold with a markup of 20%.
From Statement 2, we do not know, of the 30 cars sold for 30% markup, how many were sold costing $20,000 and how many were sold costing $30,000.
Insufficient.
The correct answer: E
Hope this helps!
-Jay
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- fskilnik@GMATH
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Both "grids" (double-matrix) below are viable (check that!) and each one gives a different total profit (our FOCUS) to the dealer.swerve wrote:An auto dealer sells each car at either $20,000 or $30,000. Some cars are marked up at 20% of the cost price and the remaining are marked up at 30% of the cost price. If the dealer sells 50 cars in total, what is the total profit of the dealer?
(1) 20 cars were sold for $20,000
(2) 30 cars were marked up 30%
Source: e-GMAT
(No need to calculate explicitly: in the second scenario the dealer sells a larger quantity of cars with lower cost and larger markup...)
\[\left( {1 + 2} \right)\,\,\,{\text{BIFURCATES}}:\]
\[\begin{array}{*{20}{c}}
{}&{{\text{markup}}\,\,{\text{20\% }}}&{{\text{markup}}\,\,{\text{30\% }}}&{{\text{total}}} \\
{{\text{\$ }}\,{\text{20,000}}}&{20}&0&{20} \\
{{\text{\$ }}\,{\text{30,000}}}&0&{30}&{30} \\
{{\text{total}}}&{20}&{30}&{50}
\end{array}\]
\[\begin{array}{*{20}{c}}
{}&{{\text{markup}}\,\,{\text{20\% }}}&{{\text{markup}}\,\,{\text{30\% }}}&{{\text{total}}} \\
{{\text{\$ }}\,{\text{20,000}}}&0&{20}&{20} \\
{{\text{\$ }}\,{\text{30,000}}}&{20}&{10}&{30} \\
{{\text{total}}}&{20}&{30}&{50}
\end{array}\]
We are done!
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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