Work Rate

[sparkle6]

If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

1) Tom makes 20% less per hour than Jim does
2) x + y = $43.75


[spoiler]Answer: B. Can someone explain the best way to solve this?[/spoiler]

[shankar.ashwin]

From question you know

4x=5y

1) Statement one says Tom makes 20% less than Jim

or Y = 80/100 * X

y = 4/5 X (which is what the question says already) INSUFFICIENT

2) X+Y = 43.75

You know 4X=5Y, hence we can find X and Y. [Sufficient]

Hence, B

[Anurag@Gurome]

If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

1) Tom makes 20% less per hour than Jim does
2) x + y = $43.75


[spoiler]Answer: B. Can someone explain the best way to solve this?[/spoiler]

4x = 5y

(1) 0.8x = y
4x = 5y; NOT sufficient.

2) x + y = 43.75 and 4x = 5y. There are 2 equations and two variables; SUFFICIENT.

The correct answer is B.

[Geva@EconomistGMAT]

If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

1) Tom makes 20% less per hour than Jim does
2) x + y = $43.75


[spoiler]Answer: B. Can someone explain the best way to solve this?[/spoiler]

The explanations above are well and good. I would just like to add the right approach to organize the information and set up the problem. The preferred method here would be a Rate | Time | "work" table, where work is the actual money earned. The relation between these three columns is Rate * time = Work

Organize the information given, a row for each of the players. Remember that whenever you have two columns for a certain row, you can find the third using the relation above.

Rate | Time | work
Jim x 4 hrs 4x
Tom y 5 5y

No that you've filled in the table, and extracted as much information as the question stem holds, you can see what's going on. Since the "work" is the same (it's the same jacket), we get that 4x=5y.

Stat. (1) in that case doesn't really tell you anything you don't already know: if 4x=5y, then y=4x/5 - which means that y is four fifths (80%) of x. Stat. (1) reiterates the question stem, and thus is insufficient.

Stat. (2): replace y with 4x/5 and get a singe equation with x:

x + 4x/5 = $43.75

From here you can find x, and then find the price of the jacket 4x. Sufficient.