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) 1.21DThis 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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