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GMAT Practice exam 2 - MIN/MAX

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by GMATGuruNY » Sat Jun 04, 2016 2:25 am
If it took Carlos ½ hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (Note: 1 mile = 5,280 feet)

(1) The average speed at which Carlos cycled from his house to the library yesterday was greater than 16 feet per second.

(2) The average speed at which Carlos cycled from his house to the library yesterday was less than 18 feet per second.
Since the two statements are in terms of FEET PER SECOND, rephrase the question stem in terms of FEET PER SECOND.

1/2 hour = 1800 seconds.
Determine the rate needed to travel 6 miles in 1800 seconds:
(6 miles)/(1800 seconds) * (5280 feet)/(1 mile) = (6*5280)/1800 = 528/30 = 176/10
= 17.6 feet per second.
Note that the units in red CANCEL OUT, leaving the resulting value in terms of feet per second.

Thus, to travel MORE than 6 miles in 1800 seconds, the average speed must be GREATER than 17.6 feet per second.
Question rephrased:
Was the average speed greater than 17.6 feet per second?

The two statements combined indicate only that the average speed was between 16 feet per second and 18 feet per second, implying that the average speed could be less than, equal to, or greater than 17.6 feet per second.
INSUFFICIENT.

The correct answer is E.
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by [email protected] » Sat Jun 04, 2016 9:31 am
Hi lucas211,

This question can be solved in a variety of ways; it's just a matter of how you choose to organize the given information.

We're told that Carlos takes 1/2 hour to cycle to the library. We're asked if the distance was greater than 6 miles. The real question is how fast he was traveling; in essence, was it enough to hit more than 6 miles over the course of 1/2 hour. 6 miles = 6(5280 ft) = 31680 ft., so the question is asking if Carlos traveled more than 31,680 feet.

Fact 1: Carlos' speed was > 16 ft/sec.

Let's convert this...

16 ft/sec x 60 secs x 30 mins = 16 x 1800 = 28,800 feet/half-hour

From this, we know how far Carlos traveled AT THE MINIMUM. But we don't know if he traveled 31,680 feet or not.
Fact 1 is INSUFFICIENT

Fact 2: Carlos' speed was < 18 ft/sec.

Let's convert this...

18 ft/sec x 60 secs x 30 mins = 18 x 1800 = 32,400 feet/half-hour

From this, we know how far Carlos traveled AT THE MAXIMUM. But we don't know if he traveled 31,680 feet or not.
Fact 2 is INSUFFICIENT

Combined, we have the range of distances that Carlos traveled: 28,800 < distance traveled < 32,400. From this, we still don't know if Carlos traveled 31,680 feet or not.
Combined INSUFFICIENT

Final Answer: E

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