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Wrong GMAT answer?

by inactived » Fri Sep 03, 2010 12:08 am
Hello all,

I come across the problem #149, page 173, GMAT 12th Edision Review as the follows:

During a trip, Francine traveled x% of the total distance at an average speed of 40 miles/hour and the rest of the distance at an average speed of 60 miles/hour. In term of x, what was Francine's average speed of the entire trip?

A. (180 - x) / 2
B. (x + 60) / 4
C. (300 - x) / 5
D. 600 / (115 - x)
E. 12000 / (x + 200)

The answer provided in the book assume the traveling distance is 100 miles -> it conclude E is the right answer. However, if you replace the traveling distance to different number, e..g 1000 miles, 200 miles -> you will get a different answer.

Per my solution, if I call the total traveling distance is S, and the total traveling time is T. Then I have the following:

- Time to travel for x% distance = (x% * S) / 40
- Time to travel for the rest distance = [(100 - x%) * S] / 60
- Total time travel (T) = (x% * S) / 40 + [(100 - x%) * S] / 60
- The average velocity is S / T. If you substitute T with the above formula, then you will have an answer like this: (40 + 20x) / [x * [100 - x%]). And it must be true for all distance.

Any thought?

Kind regards

the answer should be (40 + 20 *x ) / [x * [1 - x]).
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by this_time_i_will » Fri Sep 03, 2010 12:33 am
Let total distance traveled = S.
T1 = time for distance traveled with 40mph = xs/400.
T2 = time distance traveled with 60mph = (100-x)s/600
total time = T1+T2.
Avg speed = S/(T1+T2)..solve and u will get E.
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by inactived » Fri Sep 03, 2010 12:48 am
this_time_i_will wrote:Let total distance traveled = S.
T1 = time for distance traveled with 40mph = xs/400.
T2 = time distance traveled with 60mph = (100-x)s/600
total time = T1+T2.
Avg speed = S/(T1+T2)..solve and u will get E.
Idk where you get the formula T1 & T2 though. Do you mean xs/40 & (100-x)s/60? Even with your formula, it doesn't match the E answer.
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by GMATGuruNY » Sat Sep 04, 2010 12:31 pm
inactived wrote:Hello all,

I come across the problem #149, page 173, GMAT 12th Edision Review as the follows:

During a trip, Francine traveled x% of the total distance at an average speed of 40 miles/hour and the rest of the distance at an average speed of 60 miles/hour. In term of x, what was Francine's average speed of the entire trip?

A. (180 - x) / 2
B. (x + 60) / 4
C. (300 - x) / 5
D. 600 / (115 - x)
E. 12000 / (x + 200)

The answer provided in the book assume the traveling distance is 100 miles -> it conclude E is the right answer. However, if you replace the traveling distance to different number, e..g 1000 miles, 200 miles -> you will get a different answer.
Percent means out of 100. x% of the total distance means x out of 100 (the total distance). To solve algebraically, distance = 100, x = first part of the distance, and 100-x = remainder of the distance. If we use a number other than 100 -- say 200 -- then we're saying x out of 200, which is not the definition of percent.

To solve algebraically:

Total distance = 100
Time for the first part of the distance: t = x/40
Time for the remainder of the distance: t = (100-x)/60
Total time = x/40 + (100-x)/60 = (60x + 4000 - 40x)/2400 = (20x + 4000)/2400 = (x+200)/120
Rate for the whole distance = (Total distance)/(Total time) = 100/[(x+200)/120] = 12000/(x+200)

The correct answer is E.

One way to avoid making an algebraic error is to solve by plugging in values:

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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