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Before January, the price of a dress was D and the price of a matching

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Magoosh GMAT Instructor
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Before January, the price of a dress was D and the price of a matching  [#permalink]

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New post 31 Dec 2014, 10:53
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  25% (medium)

Question Stats:

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Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 5H, which of the following represents the amount that Roberta paid?
(A) D + 40
(B) D + H – 1
(C) D + 2H
(D) 5.95H
(E) 1.21D


This is an example of a problem with variables in the answer choices. What is the best way to approach these: a fully algebraic approach, or plugging in numbers? For a detailed discussion of these questions, with example solutions, see:
https://magoosh.com/gmat/2014/gmat-prac ... r-choices/

Mike :-)

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Re: Before January, the price of a dress was D and the price of a matching  [#permalink]

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New post 31 Dec 2014, 12:31
Ans Is D : 5.95H

before Discount price was: 1.4D+1.5H
After Discount: 1.4D +1.5H-.42D-.45H
substitute D=5H
final value: 5.95H

mikemcgarry wrote:
Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 5H, which of the following represents the amount that Roberta paid?
(A) D + 40
(B) D + H – 1
(C) D + 2H
(D) 5.95H
(E) 1.21D


This is an example of a problem with variables in the answer choices. What is the best way to approach these: a fully algebraic approach, or plugging in numbers? For a detailed discussion of these questions, with example solutions, see:
https://magoosh.com/gmat/2014/gmat-prac ... r-choices/

Mike :-)

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Re: Before January, the price of a dress was D and the price of a matching  [#permalink]

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New post 31 Dec 2014, 18:22
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Answer = (D) 5.95H

............................. Dress ............... Shoes

Initial Price ............. d ........................... h

January ................. \(\frac{140d}{100}\) ................. \(\frac{150h}{100}\)

Total price \(= 140 * \frac{5h}{100} + \frac{150h}{100} = \frac{850h}{100}\)

30% discount, means purchased at 70% price

\(= \frac{850h}{100} * \frac{70}{100} = 5.95h\)
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Before January, the price of a dress was D and the price of a matching  [#permalink]

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New post 26 Sep 2017, 13:53
mikemcgarry wrote:
Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 5H, which of the following represents the amount that Roberta paid?
(A) D + 40
(B) D + H – 1
(C) D + 2H
(D) 5.95H
(E) 1.21D


This is an example of a problem with variables in the answer choices. What is the best way to approach these: a fully algebraic approach, or plugging in numbers? For a detailed discussion of these questions, with example solutions, see:
https://magoosh.com/gmat/2014/gmat-prac ... r-choices/

Mike :-)

With one variable:
H = price of shoes
D = 5H = price of dress

So we have H and 5H

1) After the price increase

Shoe price increases 50%: 1.5H

Dress price increases 40%:
1.4(5H) = 7H

2) After the discount

She pays .70 of the price for both (30 percent discount)

Price for both:
1.5H + 7H = 8.5H

So with a 30 percent discount, she pays .70 of 8.5H

I broke up the 8.5 and multiplied each part by .7

\(.7 * 8 = 5.6[m]H

[m].7 * .5 = .35\)H

Add: 5.6H + .35H = 5.95H

Answer D

I found out the hard way that this one works better with algebra than it did with plugging in. Two choices matched the numbers I had selected. I switched, used algebra, and it was faster.
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Before January, the price of a dress was D and the price of a matching  [#permalink]

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New post 02 Sep 2018, 00:22
Price before January
Dress - D
Pair of shoes - H

Price in January
Dress - 1.4D
Pair of shoes - 1.5H

Total price = 1.4D + 1.5H

Given that D = 5H

hence, Total price = (1.4*5*H ) + 1.5H

Total price = 8.5H

but this was purchased at 30* discount hence total amount paid = 8.5*0.7 *H = 5.95H
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Before January, the price of a dress was D and the price of a matching &nbs [#permalink] 02 Sep 2018, 00:22
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