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In a village of 100 households, 75 have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:

(A) 65
(B) 55
(C) 45
(D) 35
(E) 25

Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.

(A) 1/3
(B) 1/2
(C) 1/4
(D) 1
(E) 5/6

This is a cooperative rate question so I would recommend using the T's to organize the information. It's a word problem so take your time reading and taking inventory of the question. Initially don't worry too much about the numbers. Pay attention to the structure and the question itself which you should define before doing any calculations. My first move is to splash out three T's to represent the three rates that were given, A + B, A + B, and B + C. We know that the rates need to be added because the pumps are operating simultaneously to fill the tank. What do we want to calculate: How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank? So we want to solve for the cooperative rate A + B + C  and then with that calculate the time it takes to get the tank filled. So, go ahead and add up the three sets of cooperative rates (5/6, 2/3, 1/2) and set them equal to the three cooperative rates they represent (A + B, A + C, B + C). Then group like terms and get common denominators for the fractions. You should end up with 2(A + B + C) = 2 or A + B + C = 1. The rate of 1 tank per hour means that the time it takes to fill the tank is, you guessed it: 1 hour.

Here are more Official GMAT distance, work, and rate question for which we use the T method:

Circular gears P and Q start rotating at the same time at constant speeds

A boat traveled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream

Here are another bunch of cooperative work and rate questions to practice on:

Work and Rate 1

Work and Rate 2

Work and Rate 3

Work and Rate 4

Work and Rate 5

For more distance, work, and rate examples you can also check out our GMAT Question of the Day page

Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. At these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.

(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

When a certain tree was first planted, it was 4 feet tall and the height of the tree increased by a constant amount each year for the next 6 years. At the end of 6 year the tree was 1/5 taller than it was at the end of 4 year. By how many feet did the height of the tree increase each year

(A) 3/10
(B) 2/5
(C) 1/2
(D) 2/3
(E) 6/5

The "tree" questions comes up about 50% of the time in GMAT tutoring sessions. There's nothing crazy going on here but you do need to focus on the question and then stay organized in the follow through. I'd go ahead and draw a little chart to make sense of the information. When the tree was first planted it was 4 feet tall so that's the start of the number line and then it grew by a constant amount each year so assign a variable for that, say x. Then you can define the 6th year in terms of the 4th year (the 6th year is 5/4ths the 4th year). That's it. Solve for x.

Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6

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