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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
Joined: 28 Dec 2011
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Before January, the price of a dress was D and the price of a matching [#permalink]

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31 Dec 2014, 11:53
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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
[Reveal] Spoiler: OA

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Mike McGarry
Magoosh Test Prep

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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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31 Dec 2014, 13:31
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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31 Dec 2014, 19:22
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............................. 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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Re: Before January, the price of a dress was D and the price of a matching [#permalink]

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24 Jan 2016, 18:55
Hello from the GMAT Club BumpBot!

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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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26 Sep 2017, 02:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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26 Sep 2017, 14:53
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

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] 26 Sep 2017, 14:53
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