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What is the selling price (in dollars) of the HK11B-connecto

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by fskilnik@GMATH » Thu Mar 14, 2019 6:09 am

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GMATH practice exercise (Quant Class 14)

What is the selling price (in dollars) of the HK11B-connector (a specific electronic widget) in Mrs. Tao´s store?

(1) In Mrs. Tao´s store, the difference between the selling price of the HK11B-connector and the cost of this electronic widget is 500 dollars.
(2) If Mrs. Tao agrees on a 10% discount over the selling price of the HK11B-connector, her profit would be 20% over the cost of this electronic widget.

Answer: [spoiler]_____(C)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Source: — Data Sufficiency |
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by fskilnik@GMATH » Thu Mar 14, 2019 12:32 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 14)

What is the selling price (in dollars) of the HK11B-connector (a specific electronic widget) in Mrs. Tao´s store?

(1) In Mrs. Tao´s store, the difference between the selling price of the HK11B-connector and the cost of this electronic widget is 500 dollars.
(2) If Mrs. Tao agrees on a 10% discount over the selling price of the HK11B-connector, her profit would be 20% over the cost of this electronic widget.
$$s,c\,\,\, \to \,\,\,\,\left[ {{\rm{dollars}}} \right]$$
$$? = s$$
$$\left( 1 \right)\,\,\,s - c = 500\,\,\,::\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {s,c} \right) = \left( {600,100} \right)\,\,\,\, \Rightarrow \,\,\,? = 600\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {s,c} \right) = \left( {700,200} \right)\,\,\,\, \Rightarrow \,\,\,? = 700\,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,{9 \over {10}}s = {{12} \over {10}}c\,\,\,\,\,\mathop \Rightarrow \limits^{c\, \ne \,0} \,\,\,\,\,{s \over c} = {4 \over 3}\,\,\,\,\,\,::\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {s,c} \right) = \left( {4,3} \right)\,\,\,\, \Rightarrow \,\,\,? = 4\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {s,c} \right) = \left( {40,30} \right)\,\,\,\, \Rightarrow \,\,\,? = 40\,\, \hfill \cr} \right.\,\,$$
$$\left( {1 + 2} \right)\,\,\,::\,\,\,\left\{ \matrix{
\,\,s - c = 500\,\,\,\left( {\rm{I}} \right)\,\,\,\, \hfill \cr
\,\left( {s,c} \right) = \left( {4k,3k} \right)\,\,\,\left( {{\rm{II}}} \right)\,\,\,\, \hfill \cr} \right.\left( {k > 0} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {{\rm{II}}} \right)\,\,{\rm{in}}\,\,\left( {\rm{I}} \right)} \,\,\,\,\,\,k\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 4k\,\,\,{\rm{unique}}$$

The correct answer is (C).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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