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OG - Q.137

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neeg: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Feb 26, 2013 8:12 am

by neeg » Tue Mar 05, 2013 5:00 pm

At a regular hourly rate, Don had estimated that labor cost of a repair job as $336 and he was paid that amount. However, the job took 4hrs longer that he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate, What was the time Don had estimated for the job, in hours?

(a)28
(b)24
(c)16
(d)14
(e)12

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by GMATGuruNY » Tue Mar 05, 2013 5:40 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Mar 05, 2013 7:30 pm

neeg wrote:At a regular hourly rate, Don had estimated that labor cost of a repair job as $336 and he was paid that amount. However, the job took 4hrs longer that he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate, What was the time Don had estimated for the job, in hours?

(a)28
(b)24
(c)16
(d)14
(e)12

Algebraic Approach:

Let us assume that the regular hourly rate = R, and the estimated time = T
Then RT = 336 ... Equation (1)
Also, (R - 2)(T + 4) = 336 ... Equation (2)
From Equations (1) and (2), RT = (R - 2)(T + 4)
Solving we get, RT = RT - 2T + 4R - 8
T = 2R - 4
Now we can plug in answer choices for T and get the value of R. The option which gives the product of RT as 336 will be the correct answer.

It can be seen that answer choice B is the correct one, since T = 24, R = 14 implies RT = 14 * 24 = 336

The correct answer is B.

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Tue Mar 05, 2013 11:17 pm

hard to understand why this equation is not good enough

let x be the expected no of hours

336/x-336/(x+4) = 2
x^2+4x-672=0

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Abhishek Doon: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Jul 11, 2012 4:13 am

by Abhishek Doon » Wed Mar 06, 2013 12:21 am

vipulgoyal wrote:hard to understand why this equation is not good enough

let x be the expected no of hours

336/x-336/(x+4) = 2
x^2+4x-672=0

This equaltions is equally good enough.
Factoring the above equation you get: (x+28)(x-24)=0; which clearly gives us x=24.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Mar 06, 2013 12:34 am

vipulgoyal wrote:hard to understand why this equation is not good enough

let x be the expected no of hours

336/x-336/(x+4) = 2
x^2+4x-672=0

As stated by Abhishek this equation is good enough for those who are fairly good at algebra.
If someone feels it is a bit difficult to factorize the expression, here is a trick...

--> (xÂ² + 4x - 672) = 0
--> (xÂ² + 4x + 4) - 676 = 0
--> (x + 2)Â² = 676 = 26Â²
--> (x + 2) = Â±26

Hence, x = 24 or x = -28
As x must be positive, x = 24

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