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The net price of a certain article is $306 after successive discounts

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The net price of a certain article is $306 after successive discounts  [#permalink]

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New post 27 Feb 2018, 23:47
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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

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Re: The net price of a certain article is $306 after successive discounts  [#permalink]

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New post Updated on: 28 Feb 2018, 00:15
Net price given = $306
Discounts
D1= 15% D2= 10%

Marked price be M
M*(1-D1)*(1-D2 )= 306
M = 306/(0.85*0.9)
= 400

Answer should be B

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Originally posted by chandan1988 on 28 Feb 2018, 00:10.
Last edited by chandan1988 on 28 Feb 2018, 00:15, edited 1 time in total.
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The net price of a certain article is $306 after successive discounts  [#permalink]

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New post 02 Mar 2018, 16:11
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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The net price of a certain article is $306 after successive discounts &nbs [#permalink] 02 Mar 2018, 16:11
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