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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/

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

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

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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.