In the year-end clearance sale, a music system is discounted by \(d\%,\) and then it is discounted by another \(3d\%\)

[M7MBA]

In the year-end clearance sale, a music system is discounted by \(d\%,\) and then it is discounted by another \(3d\%\) on the previous discount amount. The original price of the music system is what percent of the final value if the initial discount percent is \(30?\)

A. \(23\%\)
B. \(40\%\)
C. \(143\%\)
D. \(233\%\)
E. \(1429\%\)

[spoiler]OA=D[/spoiler]

Source: e-GMAT

[Jay@ManhattanReview]

In the year-end clearance sale, a music system is discounted by \(d\%,\) and then it is discounted by another \(3d\%\) on the previous discount amount. The original price of the music system is what percent of the final value if the initial discount percent is \(30?\)

A. \(23\%\)
B. \(40\%\)
C. \(143\%\)
D. \(233\%\)
E. \(1429\%\)

[spoiler]OA=D[/spoiler]

Source: e-GMAT

Given that the initial discount percent is \(30,\) we have d = 30% and 3d = 90%

Say the initial price was $100.

So, the price after the first discount = 100 – 30 = $70;

Going by the phrase, "it is discounted by another \(3d\%\) on the previous discount amount,"

The amount of the second discount = 90% of 30 = $27

So, the price after the second discount = 70 – 27 = $43;

The required percent = (100/43)*100% = 233%

Correct answer: D

Hope this helps!

-Jay
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