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A paint crew gets a rush order to paint 80 houses in a new d

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A paint crew gets a rush order to paint 80 houses in a new d

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A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?

(A) 0.8(80 - y)
(B) 0.8 + 0.0025y
(C) 80/y - 1.25
(D) 80/1.25y
(E) 80 - 0.25y

OA B

Source: Official Guide

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Hi All,

We're told that a paint crew gets a rush order to paint 80 houses in a new development. They paint the first Y houses at a rate of X houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25X houses per week. We're asked to find the total time it takes them to paint all the houses under this scenario as a fraction of the time it would have taken if they had painted all the houses at their original rate of X houses per week. This question can be solved in a number of different ways, including by TESTing VALUES (and the answer choices are written in such a way that you don't have to do too much math overall to answer the question).

To start, we should choose a value for X that will work well with 1.25X. Let's choose X = 4 (so 1.25X = 5). In addition, we should look to choose a value for Y that will leave a remaining number of house that will be a multiple of 5...

Let's TEST...
X = 4
Y = 20

For the first 20 houses, painting 4 houses/week will take 20/4 = 5 weeks.
For the remaining 60 houses, painting 5 houses/week will take 60/5 = 12 weeks.
Total time = 5 + 12 = 17 weeks

At the original rate, the 80 houses would take 80/4 = 20 weeks.

Thus, we're looking for a fraction that equals 17/20 = .85.... notice how that answer is a number that is LESS than 1. Considering how the answer choices are written, and that our Y = 20, you should be able to eliminate all of the wrong answers without doing too much math...

Answer A: (.8)(60) --> greater than 1
Answer B: (.8) + a tiny decimal --> exactly what we're looking for!
Answer C: 80/20 - 1.25 --> a little less than 3
Answer D: (80)/(1.25)(20) = 80/25 --> greater than 1
Answer E: (80) - (.25)(20) --> greater than 1

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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original time = 80/x weeks
new time = y/x + (80-y)/1.25x
ratio=y/x + (80-y)/1.25x : 80/x = 1.25y+80 - y:100 = 0.25y+80:100
ratio = 0.8 0.0025y

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BTGmoderatorDC wrote:
A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?

(A) 0.8(80 - y)
(B) 0.8 + 0.0025y
(C) 80/y - 1.25
(D) 80/1.25y
(E) 80 - 0.25y
Let y=0, implying that NONE of the 80 houses are painted at the original rate of x houses per week, with the result that ALL 80 houses are painted at the greater rate of (5/4)x houses per week.

The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate?
Time and rate have a RECIPROCAL RELATIONSHIP.
Since the rate for painting all 80 houses is 5/4 the original rate, the time for painting all 80 houses is 4/5 of the original time.

The correct answer must yield 4/5 when y=0.
Only B works:
0.8 + 0.0025y = 0.8 = 4/5.

The correct answer is B.

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