Bunuel wrote:

The net price of a certain article is $306 after successive discounts of 15% and 10% off the marked price. What is the marked price?

(A) $234.09

(B) $400

(C) $382.50

(D) $408

(E) None of these

With successive discounts on the same item, multiply the multipliers.

P = Original price

$306 = (% decrease)*(% decrease) * P

\($306=(.85)(.9)P\)

\($306 = .765P\)

\(P =\frac{$306}{.765}=\)

\(P = $400\)ANSWER B

The arithmetic with decimals is lengthy.

Alternatives:

1) Try fractions, and reduce them.

$306 = (fraction)*P

15 percent discount =

\(.85=\frac{85}{100}=\frac{17}{20}\) 10 percent discount =

\(.90=\frac{90}{100}=\frac{18}{20}\)

\($306 =(\frac{17}{20}*\frac{18}{20})P=(\frac{306}{400})P\)\($306=\frac{306}{400} P\)

\(P=(\frac{400}{306})*($306)= $400\)ANSWER B

2) Use a shortcut formula* and estimate. With two successive percent changes:

A = first decrease

B = second decrease

We can find total decrease with this shortcut:

\(A + B + \frac{(A*B)}{100}\)

\(-15 +(-10)+\frac{(-15)*(-10)}{100}\)

\(-25 +\frac{150}{100}= -25 + 1.5= -23.5\) %

23.5% is a little less than 25% =

\(\frac{1}{4}\)

\(1 -\frac{1}{4}^{-}=\frac{3}{4}^{+}\)The discounted price will be a little

higher than

\(\frac{3}{4}\) of the original.

Answers: $306

\(\approx{\frac{3}{4}}\) of Answers B and D.

Which one? B) $400, would be

\(\frac{$306}{400}=\frac{300}{400}+\frac{6}{400} >\frac{3}{4}\)-- but not greater by much. Perfect.

ANSWER B

Check D. We do NOT want an exact match:

\(\frac{3}{4}*408=306\). That's exact. INCORRECT.

*See VeritasPrepKarishma , Successive Percent Changes (scroll down). I cannot get the precise link to copy properly.
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