1uponGMAT wrote:I have a tough time deciding which variables to choose smart numbers for and also which ones to call x. How do you all decide which variables are the unknowns and which ones you solve for?
An example questions follows:
Is there a good strategy for knowing where to put these variables?
During a trip, Francine traveled x percent of the total
distance at an average speed of 40 miles per hour
and the rest of the distance at an average speed of
60 miles per hour. In terms of x, what was Francine's
average speed for the entire trip?
(A) (180 - x) / 2
(B) (x + 60) / 4
(C) (300 - x) / 5
(D) 600 / (115 - x)
(E) 12,000 / (x + 200)
correct answer is E
The trick is to plug in values that make the math easy.
For the distance traveled at 40mph, plug in a multiple of 40:
d = 80 miles
r = 40 mph
t = d/r = 80/40 = 2 hrs
For the distance traveled at 60 mph, plug in a number that is a multiple not only of 60 but also of 80 (the first distance). Using a multiple of 80 will make it easy later on to determine the value of x:
d = 240 miles
r = 60 mph
t = 240/60 = 4 hrs
First part of the trip = 80 miles.
Total distance = 80+240 = 320 miles.
Since 80 is 25% of 320, x = 25. (See how using a multiple of 80 for the second distance made it easy to determine x?)
Now that we have assigned values to everything, let's get our target:
Total distance = 80+240 = 320 miles
Total time = 2+4 = 6 hrs
Average rate = 320/6 = 160/3. This is our target answer.
Now we plug x=25 into all the answers to see which give us 160/3:
(A) (180 - x) / 2 = (180-25)/2 = 155/2. No.
(B) (x + 60) / 4 = (25+60)/4 = 85/4. No.
(C) (300 - x) / 5 = (300-25)/5 = 275/5 = 55. No.
(D) 600 / (115 - x) = 600/(115-25) = 600/90 = 60/9 = 20/3. No.
The correct answer is E.
(E) 12,000 / (x + 200) = 12000/(25+200) = 12000/225 = 2400/45 = 800/15 = 160/3. This works.
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