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Last month, the selling price of a certain product was $12.

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Last month, the selling price of a certain product was $12.

by Max@Math Revolution » Thu Aug 08, 2019 11:37 pm
[GMAT math practice question]

Last month, the selling price of a certain product was $12. This month, the product's price was cut by 20%. 165 more units of the product were sold this month than last month, and the total sales of the product this month were $420 higher than last month. How many units of the product were sold last month?

A. 400
B. 445
C. 485
D. 500
E. 520
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by deloitte247 » Sat Aug 10, 2019 10:02 am
Last month's selling price = $12
Let unit sold last month = x
This month's selling price = $12 - (20% of $12)
$$=$12-\left(\frac{20}{100}\cdot12\right)\ =\ $9.6$$
$$Unit\ sold\ this\ month=x+165$$
Sale of this month = this month's selling price * this month's unit
$$=$9.6\cdot\left(x+165\right)$$
This month's sale = last month's sales + $420
$$$9.6\cdot\left(x+165\right)=12x+$420$$
$$9.6x+$1584=12x+$420$$
$$$1584-$420=12x-9.6x$$
$$$1164=2.4x$$
$$x=\frac{1164}{2.4}=$485$$

The correct answer is option C
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by Max@Math Revolution » Sun Aug 11, 2019 11:49 pm
=>

Let n be the number of units of the product sold last month.

Then (n+165)(12)(1-20/100) - n*12 = 420.
Simplifying yields (n+165)(12)(0.8) - 12n = 165*12*(0.8) - 12n*(0.2) = 420. So, 12n*(0.2) = 165*12*(0.8) - 420

We solve this equation to find n = 485.

Therefore, the answer is C.
Answer: C
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