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

Question

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 :-)

PareshGmat · Accepted Answer

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

sunita123 · Answer

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

generis · Answer

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 H

.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.

pkshankar · Answer

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

ScottTargetTestPrep · Answer

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

Answer: D

Zeus_ · Answer

I did the following:

* 7/10

replacing D with 5H

* 7/10

17H/2 * 7/10 = 119H/20 = 5.95H

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