Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 24 Feb 2011
Posts: 27

A cyclist travels the length of a bike path that is 225
[#permalink]
Show Tags
12 Jul 2011, 06:32
Question Stats:
28% (02:17) correct 72% (02:32) wrong based on 425 sessions
HideShow timer Statistics
A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5 hrs, rounded to the nearest hour, then his average speed must be between: A. 38 and 50 mph B. 40 and 50 mph C. 40 and 51 mph D. 41 and 50 mph E. 41 and 51 mph
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 58452

Re: Inequalities word problem
[#permalink]
Show Tags
17 Apr 2012, 06:18
ENAFEX wrote: Isn't the answer supposed to be D?
224.5/5.4 = 41.57 AND 225.5/4.5 = 50.1
41 and 50 mph A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5 hrs, rounded to the nearest hour, then his average speed must be between:A. 38 and 50 mph B. 40 and 50 mph C. 40 and 51 mph D. 41 and 50 mph E. 41 and 51 mph Length of a path is 225 miles long, rounded to the nearest mile > \(224.5\leq{distance}<225.5\); The trip took him 5 hrs, rounded to the nearest hour > \(4.5\leq{time}<5.5\); Lowest average rate is \(\frac{224.5}{5.5}\approx{40.8}\) (take the lowest value of nominator and highest value of denominator); Highest average rate is \(\frac{225.5}{4.5}\approx{50.1}\) (take the highest value of nominator and lowest value of denominator); \(40.8<rate<50.1\). Now, the question is: "the average speed must be between..." hence the range from correct answer choice MUST cover all possible values of rate, so must cover all the range: \(40.8<rate<50.1\). Only C does that: \((40)<40.8<rate<50.1<(51)\). D can not be the answer as if \(rate=40.9\) or if \(rate=50.01\) then these possible values of the average rate are not covered by the range from this answer choice, which is (4150). Answer: C. Alternative approach.It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.A. 38 and 50 mph B. 40 and 50 mph C. 40 and 51 mph D. 41 and 50 mph E. 41 and 51 mph Notice that since the range from A covers entire range from B and D, then B and D are out (if B or D is correct so is A and we cannot have two correct answer, leave the bigger range). Similarly since the range from C covers entire range from E, then E is out too (if E is correct so is C and we cannot have two correct answer, leave the bigger range). Thus we are left only with two answer choices A (38, 50) and C (40, 51). From here it's much easier to get the correct answer. Hope it's clear.
_________________




Intern
Joined: 08 Feb 2010
Posts: 35
Concentration: Leadership, International Business
WE: Project Management (Energy and Utilities)

Re: Inequalities word problem
[#permalink]
Show Tags
12 Jul 2011, 07:49
A bit lenghty method though as below.
225 > 224.5 to 225.4 5 > 4.5 to 5.4
224.5/5.4 apprx 40.09 225.4/4.5 apprx 50.1
Hence C



Intern
Joined: 24 Feb 2011
Posts: 27

Re: Inequalities word problem
[#permalink]
Show Tags
12 Jul 2011, 09:14
IF 225.4/4.5 apprx 50.1 why would you round it up to 51? Isn't rounding from 50.5 and up?



Manager
Joined: 04 Apr 2010
Posts: 117

Re: Inequalities word problem
[#permalink]
Show Tags
12 Jul 2011, 20:12
[Hi Surabhhi Does 50.1 equal to 51? I disagree with ur solution. R u from Univ of Central Missouri? ]A bit lenghty method though as below. 225 > 224.5 to 225.4 5 > 4.5 to 5.4 224.5/5.4 apprx 40.09 225.4/4.5 apprx 50.1 Hence C[/quote]
_________________
Consider me giving KUDOS, if you find my post helpful. If at first you don't succeed, you're running about average. ~Anonymous



Intern
Joined: 14 Mar 2010
Posts: 15

Re: Inequalities word problem
[#permalink]
Show Tags
25 Jul 2011, 08:42
224.5/5.4 = 41.57 . how did u approximate it to 40.09?



Manager
Status: And the Prep starts again...
Joined: 03 Aug 2010
Posts: 100

Re: Inequalities word problem
[#permalink]
Show Tags
17 Apr 2012, 06:11
Isn't the answer supposed to be D? 224.5/5.4 = 41.57 AND 225.5/4.5 = 50.1 41 and 50 mph
_________________
My First Blog on my GMAT JourneyArise, Awake and Stop not till the goal is reached



Manager
Status: And the Prep starts again...
Joined: 03 Aug 2010
Posts: 100

Re: A cyclist travels the length of a bike path that is 225
[#permalink]
Show Tags
17 Apr 2012, 18:02
Bunuel, Thanks for the explanations and the alternative approach. Great as always. I am having a problem in selecting the denominator range. In some problems, I noticed that the lowest denominator value is usually taken as <0.5, i.e. 0.4, e.g. in the above problem I thought it should be 4.4. How do you choose between .4 and .5? Hope my question makes sense. :D
_________________
My First Blog on my GMAT JourneyArise, Awake and Stop not till the goal is reached



Math Expert
Joined: 02 Sep 2009
Posts: 58452

Re: A cyclist travels the length of a bike path that is 225
[#permalink]
Show Tags
18 Apr 2012, 04:25
ENAFEX wrote: Bunuel, Thanks for the explanations and the alternative approach. Great as always. I am having a problem in selecting the denominator range. In some problems, I noticed that the lowest denominator value is usually taken as <0.5, i.e. 0.4, e.g. in the above problem I thought it should be 4.4. How do you choose between .4 and .5? Hope my question makes sense. :D It's because of the rounding rules: mathnumbertheory88376.html (check chapter for Rounding). 4.5 rounded equals to 5, while 4.4 rounded equals to 4. So, "the trip took him 5 hrs, rounded to the nearest hour" means \(4.5\leq{time}<5.5\). Hope it's clear.
_________________



Manager
Status: And the Prep starts again...
Joined: 03 Aug 2010
Posts: 100

Re: A cyclist travels the length of a bike path that is 225
[#permalink]
Show Tags
18 Apr 2012, 07:09
Bunuel, I understand the rounding concept but sometimes it is just confusing to apply it in problems. e.g. On a recent trip Cindy drove her car 290 miles, rounded to the nearest 10 miles and used 12 gallons of gasoline rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between: A) 290/12.5 and 290/11.4 B) 294/12 and 284/11.4 C) 284/12 and 295/12 D) 284/12.5 and 295/11.4 E) 295/12.5 and 284/11.4 In this is the correct choice is D 12 rounded to the nearest gasoline should be 11.5<=Value<12.5. But why is it 11.4 in the correct choice? Also why is it 284? Is it not supposed to be 285? I thought the answer will be 285/12.5 to 295/11.5?
_________________
My First Blog on my GMAT JourneyArise, Awake and Stop not till the goal is reached



Senior Manager
Joined: 01 Apr 2010
Posts: 273
Location: Kuwait
GPA: 3.2
WE: Information Technology (Consulting)

Re: A cyclist travels the length of a bike path that is 225
[#permalink]
Show Tags
18 Apr 2012, 07:43
Have to start working on the basics, the concepts are good just taking me too long to divide the numbers and get an accurate answer.



Math Expert
Joined: 02 Sep 2009
Posts: 58452

Re: A cyclist travels the length of a bike path that is 225
[#permalink]
Show Tags
18 Apr 2012, 08:34
ENAFEX wrote: Bunuel, I understand the rounding concept but sometimes it is just confusing to apply it in problems.
e.g. On a recent trip Cindy drove her car 290 miles, rounded to the nearest 10 miles and used 12 gallons of gasoline rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between:
A) 290/12.5 and 290/11.4 B) 294/12 and 284/11.4 C) 284/12 and 295/12 D) 284/12.5 and 295/11.4 E) 295/12.5 and 284/11.4
In this is the correct choice is D 12 rounded to the nearest gasoline should be 11.5<=Value<12.5. But why is it 11.4 in the correct choice? Also why is it 284? Is it not supposed to be 285? I thought the answer will be 285/12.5 to 295/11.5? Question should read: On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between A. 290/12.5 and 290/11.5 B. 295/12 and 285/11.5 C. 285/12 and 295/12 D. 285/12.5 and 295/11.5 E. 295/12.5 and 285/11.5 Cindy drove her car 290 miles, rounded to the nearest 10 miles > \(285\leq{m}<295\); Used 12 gallons of gasoline, rounded to the nearest gallon > \(11.5\leq{g}<12.5\); Minimum Miles per gallon, m/g > \(\frac{285}{12.5}<\frac{m}{g}<\frac{295}{11.5}\) (to get lower limit take min possible for nominator and max possible for denominator, and for upper limit take max possible for nominator and min possible for denominator). Answer: D. See more here: onarecenttripcindydrovehercar290milesroundedto99378.htmlHope it helps.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 58452

Re: A cyclist travels the length of a bike path that is 225
[#permalink]
Show Tags
14 Jun 2013, 05:27
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
_________________



Director
Joined: 25 Apr 2012
Posts: 660
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: Inequalities word problem
[#permalink]
Show Tags
24 Jul 2013, 22:00
Bunuel wrote: ENAFEX wrote: Isn't the answer supposed to be D?
224.5/5.4 = 41.57 AND 225.5/4.5 = 50.1
41 and 50 mph A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5 hrs, rounded to the nearest hour, then his average speed must be between:A. 38 and 50 mph B. 40 and 50 mph C. 40 and 51 mph D. 41 and 50 mph E. 41 and 51 mph Length of a path is 225 miles long, rounded to the nearest mile > \(224.5\leq{distance}<225.5\); The trip took him 5 hrs, rounded to the nearest hour > \(4.5\leq{time}<5.5\); Lowest average rate is \(\frac{224.5}{5.5}\approx{40.8}\) (take the lowest value of nominator and highest value of denominator); Highest average rate is \(\frac{225.5}{4.5}\approx{50.1}\) (take the highest value of nominator and lowest value of denominator); \(40.8<rate<50.1\). Now, the question is: "the average speed must be between..." hence the range from correct answer choice MUST cover all possible values of rate, so must cover all the range: \(40.8<rate<50.1\). Only C does that: \((40)<40.8<rate<50.1<(51)\). D can not be the answer as if \(rate=40.9\) or if \(rate=50.01\) then these possible values of the average rate are not covered by the range from this answer choice, which is (4150). Answer: C. Hi Bunuel, Refering to the rounding chapter in Number Theory examples Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep. Example: 5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5. 5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5. 5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5. Shouldn't the range for distance be 224.5 < D< 225.4 > If we take the higher value of distance i.e 225.4 and drop the last digit (4) then it gets rounded off to 225 but if we keep 225.5 then after dropping (5) it should be rounded off to 226. Similarly for Time it should 4.5 <T< 5.4 Calculating Lowest Avg rate : 224.5/5.4 = 41.57 Highest : 225.4/4.5 = 50.08 The Answer remains C. Please confirm the range selection Thanks
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Math Expert
Joined: 02 Sep 2009
Posts: 58452

Re: Inequalities word problem
[#permalink]
Show Tags
25 Jul 2013, 02:21
mridulparashar1 wrote: Bunuel wrote: ENAFEX wrote: Isn't the answer supposed to be D?
224.5/5.4 = 41.57 AND 225.5/4.5 = 50.1
41 and 50 mph A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5 hrs, rounded to the nearest hour, then his average speed must be between:A. 38 and 50 mph B. 40 and 50 mph C. 40 and 51 mph D. 41 and 50 mph E. 41 and 51 mph Length of a path is 225 miles long, rounded to the nearest mile > \(224.5\leq{distance}<225.5\); The trip took him 5 hrs, rounded to the nearest hour > \(4.5\leq{time}<5.5\); Lowest average rate is \(\frac{224.5}{5.5}\approx{40.8}\) (take the lowest value of nominator and highest value of denominator); Highest average rate is \(\frac{225.5}{4.5}\approx{50.1}\) (take the highest value of nominator and lowest value of denominator); \(40.8<rate<50.1\). Now, the question is: "the average speed must be between..." hence the range from correct answer choice MUST cover all possible values of rate, so must cover all the range: \(40.8<rate<50.1\). Only C does that: \((40)<40.8<rate<50.1<(51)\). D can not be the answer as if \(rate=40.9\) or if \(rate=50.01\) then these possible values of the average rate are not covered by the range from this answer choice, which is (4150). Answer: C. Hi Bunuel, Refering to the rounding chapter in Number Theory examples Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep. Example: 5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5. 5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5. 5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5. Shouldn't the range for distance be 224.5 < D< 225.4 > If we take the higher value of distance i.e 225.4 and drop the last digit (4) then it gets rounded off to 225 but if we keep 225.5 then after dropping (5) it should be rounded off to 226. Similarly for Time it should 4.5 <T< 5.4 Calculating Lowest Avg rate : 224.5/5.4 = 41.57 Highest : 225.4/4.5 = 50.08 The Answer remains C. Please confirm the range selection Thanks Should be as written. What about 225.499999? So, take 225.5 but exclude the endpoints, by writing < and > instead of <= and >=. Hope it's clear.
_________________



Director
Joined: 25 Apr 2012
Posts: 660
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: Inequalities word problem
[#permalink]
Show Tags
25 Jul 2013, 02:46
Bunuel wrote: mridulparashar1 wrote: Bunuel wrote: A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5 hrs, rounded to the nearest hour, then his average speed must be between: A. 38 and 50 mph B. 40 and 50 mph C. 40 and 51 mph D. 41 and 50 mph E. 41 and 51 mph
Length of a path is 225 miles long, rounded to the nearest mile > \(224.5\leq{distance}<225.5\); The trip took him 5 hrs, rounded to the nearest hour > \(4.5\leq{time}<5.5\);
Lowest average rate is \(\frac{224.5}{5.5}\approx{40.8}\) (take the lowest value of nominator and highest value of denominator); Highest average rate is \(\frac{225.5}{4.5}\approx{50.1}\) (take the highest value of nominator and lowest value of denominator);
\(40.8<rate<50.1\).
Now, the question is: "the average speed must be between..." hence the range from correct answer choice MUST cover all possible values of rate, so must cover all the range: \(40.8<rate<50.1\). Only C does that: \((40)<40.8<rate<50.1<(51)\). D can not be the answer as if \(rate=40.9\) or if \(rate=50.01\) then these possible values of the average rate are not covered by the range from this answer choice, which is (4150).
Answer: C.
Hi Bunuel, Refering to the rounding chapter in Number Theory examples Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep. Example: 5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5. 5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5. 5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5. Shouldn't the range for distance be 224.5 < D< 225.4 > If we take the higher value of distance i.e 225.4 and drop the last digit (4) then it gets rounded off to 225 but if we keep 225.5 then after dropping (5) it should be rounded off to 226. Similarly for Time it should 4.5 <T< 5.4 Calculating Lowest Avg rate : 224.5/5.4 = 41.57 Highest : 225.4/4.5 = 50.08 The Answer remains C. Please confirm the range selection Thanks Should be as written. What about 225.499999? So, take 225.5 but exclude the endpoints, by writing < and > instead of <= and >=. Hope it's clear. Hi Bunuel, Can you elaborate a bit more. I am not able to get the message. Thanks
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Math Expert
Joined: 02 Sep 2009
Posts: 58452

Re: Inequalities word problem
[#permalink]
Show Tags
25 Jul 2013, 03:06
mridulparashar1 wrote: Bunuel wrote: mridulparashar1 wrote: Hi Bunuel,
Refering to the rounding chapter in Number Theory examples
Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep.
Example: 5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5. 5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5. 5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.
Shouldn't the range for distance be 224.5 < D< 225.4 > If we take the higher value of distance i.e 225.4 and drop the last digit (4) then it gets rounded off to 225 but if we keep 225.5 then after dropping (5) it should be rounded off to 226.
Similarly for Time it should 4.5 <T< 5.4
Calculating Lowest Avg rate : 224.5/5.4 = 41.57 Highest : 225.4/4.5 = 50.08
The Answer remains C. Please confirm the range selection
Thanks Should be as written. What about 225.499999? So, take 225.5 but exclude the endpoints, by writing < and > instead of <= and >=. Hope it's clear. Hi Bunuel, Can you elaborate a bit more. I am not able to get the message. Thanks When you take maximum distance as 225.4 you exclude distance from 225.4 to 225.5. For example d could be 225.47, 225.43, 225.4111111. So, take 225.5 as max distance but write rate<225.5/4.5 instead of rate<=225.5/4.5.
_________________



Manager
Joined: 11 Jan 2011
Posts: 57
GMAT 1: 680 Q44 V39 GMAT 2: 710 Q48 V40

Re: Inequalities word problem
[#permalink]
Show Tags
23 Oct 2013, 14:13
WoundedTiger wrote: Bunuel wrote: ENAFEX wrote: Isn't the answer supposed to be D?
224.5/5.4 = 41.57 AND 225.5/4.5 = 50.1
41 and 50 mph A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5 hrs, rounded to the nearest hour, then his average speed must be between:A. 38 and 50 mph B. 40 and 50 mph C. 40 and 51 mph D. 41 and 50 mph E. 41 and 51 mph Length of a path is 225 miles long, rounded to the nearest mile > \(224.5\leq{distance}<225.5\); The trip took him 5 hrs, rounded to the nearest hour > \(4.5\leq{time}<5.5\); Lowest average rate is \(\frac{224.5}{5.5}\approx{40.8}\) (take the lowest value of nominator and highest value of denominator); Highest average rate is \(\frac{225.5}{4.5}\approx{50.1}\) (take the highest value of nominator and lowest value of denominator); \(40.8<rate<50.1\). Now, the question is: "the average speed must be between..." hence the range from correct answer choice MUST cover all possible values of rate, so must cover all the range: \(40.8<rate<50.1\). Only C does that: \((40)<40.8<rate<50.1<(51)\). D can not be the answer as if \(rate=40.9\) or if \(rate=50.01\) then these possible values of the average rate are not covered by the range from this answer choice, which is (4150). Answer: C. Hi Bunuel, Refering to the rounding chapter in Number Theory examples Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep. Example: 5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5. 5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5. 5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5. Shouldn't the range for distance be 224.5 < D< 225.4 > If we take the higher value of distance i.e 225.4 and drop the last digit (4) then it gets rounded off to 225 but if we keep 225.5 then after dropping (5) it should be rounded off to 226. Similarly for Time it should 4.5 <T< 5.4 Calculating Lowest Avg rate : 224.5/5.4 = 41.57 Highest : 225.4/4.5 = 50.08 The Answer remains C. Please confirm the range selection Thanks Also, your method would actually change the answer to E (between 41 and 51 miles) since 41.57 would not need the 40 min set by answer C



Intern
Joined: 15 Sep 2013
Posts: 4

Re: Inequalities word problem
[#permalink]
Show Tags
22 Dec 2013, 09:41
Should be as written. What about 225.499999? So, take 225.5 but exclude the endpoints, by writing < and > instead of <= and >=.
Hi Bunuel, Found your explanations so helpful, thanks! I just came across this problem and given your answer above, I understand why we would use 225.5 and 5.5 as the maximum distance and time for the calculation, but still, the inequality range for distance and time excludes these values as the maximum endpoints, so isn't our answer going to be inaccurate? After all, 225.5 rounds up to 226 mi and 5.5 to 6 hr... I calculated with max's 225.4 and 5.4 but yes, that would exclude the .4.499's... so does this mean that for similar questions we have to use the max endpoint even if it is NOT inclusive in the range? This was a problem in a MGMAT book, but are there similar examples of actual GMAT questions where we would have to use the maximum endpoint like we had to for this question? Thanks much! Fabs



Math Expert
Joined: 02 Sep 2009
Posts: 58452

Re: Inequalities word problem
[#permalink]
Show Tags
22 Dec 2013, 23:35




Re: Inequalities word problem
[#permalink]
22 Dec 2013, 23:35



Go to page
1 2
Next
[ 21 posts ]



