When David drove from his home to his parents' home, was his average

Question

When David drove from his home to his parents' home, was his average speed between 35 miles per hour and 50 miles per hour?

(1) To the nearest 100 miles, the distance that David drove from his home to his parents' home was 300 miles.

(2) To the nearest hour, it took David 8 hours to drive from his home to his parents' home.

Bunuel · Accepted Answer

When David drove from his home to his parents' home, was his average speed between 35 miles per hour and 50 miles per hour?

(1) To the nearest 100 miles, the distance that David drove from his home to his parents' home was 300 miles.

The above implies that the distance is between 250 and 350 miles, which is not sufficient to get the speed.

(2) To the nearest hour, it took David 8 hours to drive from his home to his parents' home.

The above implies that the time is between 7.5 and 8.5 hours, which is also not sufficient to get the speed.

(1)+(2) The speed could be anywhere between 250/8.5 ≈ 30 to 350/7.5 ≈ 45 miles per hour. Therefore, the speed may or may not be between 35 miles per hour and 50 miles per hour. Not sufficient.

Answer: E.

Kinshook · Answer

@LaracboAsked: When David drove from his home to his parents' home, was his average speed between 35 miles per hour and 50 miles per hour?

Average speed = Total distance travelled / Total time taken

(1) To the nearest 100 miles, the distance that David drove from his home to his parents' home was 300 miles.
Since time taken for the trip is unknown
NOT SUFFICIENT

(2) To the nearest hour, it took David 8 hours to drive from his home to his parents' home.Since total distance travelled is unknown
NOT SUFFICIENT

(1) + (2) 
(1) To the nearest 100 miles, the distance that David drove from his home to his parents' home was 300 miles.
(2) To the nearest hour, it took David 8 hours to drive from his home to his parents' home.
251/8.49 = 500/17 = 29.56 miles per hour  < Average speed < 349/7.5 = 46.53 miles per hour
With the information, it can not ascertained whether average speed was between 35 miles per hour and 50 miles per hour.
NOT SUFFICIENT

IMO E

Laracbo · Answer

Hi   MartyMurray   KarishmaB   Sajjad1994   GMATCoachBen   JeffTargetTestPrep   chetan2u   Bunuel 
I would greatly appreciate if someone could tell me where I went wrong. I guess many people would be inclined to make the same mistake:

D= R * T therefore R= D/T

(1) D= 300 miles. I do not know anything about Time & Rate so insufficient on its own.
(2) T= 8 hours. I do not know anything about Distance & Rate so insufficient on its own.

BUT then I thought when I combine them I get: D=300 and T=8 therefore R= 300/8 = 37.5 --> So yes, average speed was between 35 mph and 50 mph.

Why can I not solve it this way?

Ps. This is a GMAT (Focus) Offical Question from my pracice exam 3

vishwathols · Answer

try to calculate the minimum and maximum average speeds based on the limits on travel time and distance. Then the range would fall out of the given avg. speed range. hence, not deterministic

av722 · Answer

MartyMurray   KarishmaB   Bunuel

how does "To the nearest 100 miles" equate to between 250 and 350 mi? i thought it was between 200 and 400 mi since it would be 300 ± 100.

MartyMurray · Answer

Notice that it's the "NEAREST 100 miles."

The nearest 100 miles to 200 miles is 200. The nearest hundred miles to 400 is 400.

300 is nearest to numbers between 250 and 349.999999. Numbers below 250 or above 349.999999 are closer to 200 or 400 respectively.

So, that's why "To the nearest 100 miles, the distance that David drove from his home to his parents' home was 300 miles," means, basically, that he drove between 250 and 350 miles. If there were a close call at the high end, we could say that he didn't drive quite 350 miles since 350 would normally be rounded up to 400, but as the question is written, 350 works.

KarishmaB · Answer

We use rounding rules in this question.

To get the speed, we need both distance and time. Hence either statement alone is not sufficient.

Using both together, distance was 250 <= d < 350 and time taken was 7.5 <= t < 8.5.

If the distance covered were 300 miles and time taken was 8 hrs, speed would be 300/8 = 37.5 mph. It is very close to the lower limit of the speed we are considering, 35 mph.
 
Hence, check - if the distance were 250 miles and time was 8.5 hrs (it could easily be 8.499999 hrs), the speed would be much lower. 
Speed = 250/8.5 = 500/17 = 2something (because 17*3 = 51) some the speed is not even in 30s. Even if time taken was a tiny bit less than 8.5 hrs, the speed is much less than 35 mph. 
Hence speed less than 35 mph is possible and between 35 to 50 is possible.

Answer (E)

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=81412 (1) essentially means 250<=distance<350. With no idea about time taken, (1) is insufficient. (2) essentially means 7.5 speed = distance/time. To find the possible values speed can take, we need to find the range of speed values. This means finding the min and max of speed values. To minimize speed -> min (distance - numerator) & max (time - denominator). To maximize speed -> max (distance - numerator) & min (time - denominator). In effect, (1) and (2) give us the info needed to determine the range of speed. 250/8.4 < speed < 350/7.4 -> approx 29.something < s < 46.something. We can see that speed can be <35 (say 30) or between 35 to 50 (say 40). Thus, even with (1) and (2), the data is not sufficient. So, choice E. Hope this helps! Harsha GMAT-Club-Forum-t1a9gnha.png

lawyeroffduty · Answer

i got my answer right, but basis on the wording ie, to the nearest 100 miles and to the nearest hour, i straightly jumped to answer e because we don't know the exact value and i can't find the average speed, is my way of approach right?

Bunuel · Answer

No, that wouldn’t be correct, because “to the nearest 100 miles” and “to the nearest hour” could have been such numbers that an average speed would turn out to be between 35 and 50.

For example, if we were told that “to the nearest 100 miles, the distance that David drove from his home to his parents' home was 900 miles” and “to the nearest hour, it took David 19 hours to drive from his home to his parents' home,” then the average speed would have been between 850/18.5 ≈ 46 and 950/19.5 ≈ 49. So in this case the answer would be C, because in any way the speed is between 35 miles per hour and 50 miles per hour.

When David drove from his home to his parents' home, was his average

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