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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
Posts: 4485
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
2
6
00:00

Difficulty:

25% (medium)

Question Stats:

79% (02:36) correct 21% (03:03) wrong based on 214 sessions

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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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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
3

............................. 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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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]

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02 Sep 2018, 01:22
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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Re: Before January, the price of a dress was D and the price of a matching  [#permalink]

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27 Feb 2019, 10:20
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

The new price of the dress is 1.4D, and the new price of the shoes is 1.5H. When purchased at a 30% discount, the prices are 0.7 x 1.4D = 0.98D and 0.7 x 1.5H = 1.05H.

Since D = 5H, we have:

0.98(5H) + 1.05H

4.9H + 1.05H = 5.95H

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Re: Before January, the price of a dress was D and the price of a matching   [#permalink] 27 Feb 2019, 10:20
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