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NandishSS Master | Next Rank: 500 Posts
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A taxi company charges $1.75 for the first Sun Jul 16, 2017 6:01 am Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) A taxi company charges$1.75 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90? A. 4 miles B. 4 (1/4) miles C. 4 (3/4 )miles D. 5 (1/2) miles E. 6 (1/4) miles OA: D Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 13584 messages Followed by: 1796 members Thanked: 13052 times GMAT Score: 790 Sun Jul 16, 2017 11:25 am NandishSS wrote: A taxi company charges$1.75 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90? A. 4 miles B. 4 (1/4) miles C. 4 (3/4 )miles D. 5 (1/2) miles E. 6 (1/4) miles We can PLUG IN THE ANSWERS, which represent the greatest distance someone could travel with$4.90.
Since the question stem asks for the maximum possible distance, start with the greatest answer choice.
When the correct answer choice is plugged in, the total cost of the trip will not exceed $4.90. E: 6.25 miles Cost of the first quarter-mile =$1.75.
Remaining distance = (total distance - first quarter) = 6.25 - 0.25 = 6 miles = 24 quarter-miles.
At a rate of 15 cents per quarter-mile, the cost of the remaining 24 quarter-miles = (24)(15) = 360 cents = $3.60. Total cost = (cost of the first quarter-mile) + (cost of the remaining quarter-miles) =$1.75 + $3.60 =$5.35.
The total cost is too great.
Eliminate E.

D: 5.5 miles
Cost of the first quarter-mile = $1.75. Remaining distance = (total distance - first quarter) = 5.5 - 0.25 = 5.25 miles = 21 quarter-miles. At a rate of 15 cents per quarter-mile, the cost of the remaining 21 quarter-miles = (21)(15) = 360 cents =$3.15.
Total cost = (cost of the first quarter-mile) + (cost of the remaining quarter-miles) = $1.75 +$3.15 = $4.90. Success! The correct answer is D. _________________ Mitch Hunt GMAT Private Tutor GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "Thank" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Thanked by: NandishSS Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. GMAT/MBA Expert ceilidh.erickson GMAT Instructor Joined 04 Dec 2012 Posted: 1696 messages Followed by: 224 members Thanked: 1443 times Sun Jul 16, 2017 1:29 pm I would test the answer choices, as Mitch has done. You could also use algebra here, though. The formula for this type of word problem: Total cost = (fixed cost) + (rate)(variable cost) In this case: T = 1.75 + (0.15)(x - 1), where x = total # of quarter-miles. We'll have to convert that to miles later. 4.90 = 1.75 + 0.15(x - 1) 4.90 = 1.75 + 0.15x - 0.15 4.90 = 1.5 + 0.15x 3.40 = 0.15x 340 = 15x x = 22 2/3 22 2/3 quarter-miles is slightly greater than 5.5 miles (22/4) and slightly less than 5.75 miles (23/4). This question assumes that distance can only be in perfect quarter-miles with no fractional charges. Assuming that, then 5.5 miles is the maximum distance one could travel. The answer is D. _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Thanked by: NandishSS Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. GMAT/MBA Expert ceilidh.erickson GMAT Instructor Joined 04 Dec 2012 Posted: 1696 messages Followed by: 224 members Thanked: 1443 times Sun Jul 16, 2017 1:37 pm Another easy way to solve would be to create a chart to ballpark: ttps://postimg.org/image/lqav1fhih/" target="_blank"> We can see that 4.90 will cover over 5 miles, but not 6. We just then have to test whether 5.5 works, as Mitch did. _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Thanked by: NandishSS Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 11001 messages Followed by: 1217 members Thanked: 5251 times GMAT Score: 770 Sun Jul 16, 2017 2:01 pm NandishSS wrote: A taxi company charges$1.75 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90? A. 4 miles B. 4 (1/4) miles C. 4 (3/4 )miles D. 5 (1/2) miles E. 6 (1/4) miles OA: D Let's follow the money Start with$4.90

The taxi company charges $1.75 for the first quarter of a mile So, after 0.25 miles, we've spent$1.75

$4.90 -$1.75 = $3.15 So, we have$3.15 remaining, and we've traveled 0.25 miles so far.

The taxi company charges $0.15 for each additional 0.25 miles In other words, for every$0.15, we can travel 0.25 miles
$3.15/$0.15 = 21

So, our remaining $3.15 will buy us 21 additional 0.25-mile advances. (21)(0.25) = 5.25 miles TOTAL DISTANCE = 0.25 + 5.25 = 5.5 miles Answer: D _________________ Brent Hanneson â€“ Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our free resources Thanked by: NandishSS GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 8921 messages Followed by: 466 members Thanked: 2861 times GMAT Score: 800 Sun Jul 16, 2017 6:53 pm Hi NandishSS, Since the answers are NOT nice 'round' numbers, you can use a variation on TESTing THE ANSWERS - but instead of using the answers that are given, you can use round numbers to eliminate options. We're told that the first 1/4 mile costs$1.75 and each additional 1/4 mile costs $0.15. We're asked for the maximum distance that could be traveled for$4.90

Based on the answer choices, I'll start with what a 5 mile trip cost...
The first mile would cost $1.75 + 3($0.15) = $2.20 Each additional mile would cost 4($0.15) = $0.60 So a 5 mile trip would cost$2.20 + 4($0.60) =$2.20 + $2.40 =$4.60

Since we're dealing with $4.90, we will clearly end up going more than 5 miles (so we can eliminate Answers A, B and C)... but we wouldn't travel that much more than 5 miles... From here, it's fairly easy to determine that the additional$0.30 would get us an extra 1/2 mile.

Final Answer: D

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Rich

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Contact Rich at Rich.C@empowergmat.com

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Matt@VeritasPrep GMAT Instructor
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Sun Jul 23, 2017 5:40 pm
1.75 + .15q = 4.90

subtract 1.75:

.15q = 3.15

multiply by 100:

15q = 315

divide by 15:

q = 21

So we could travel an extra 21 quarter miles, or 5.25 miles. Adding the first 1/4 mile to the trip (the one for which we paid $1.75), we have a total of 5.50 miles. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! GMAT/MBA Expert Jeff@TargetTestPrep GMAT Instructor Joined 09 Apr 2015 Posted: 413 messages Followed by: 6 members Thanked: 39 times Tue Jul 25, 2017 11:08 am NandishSS wrote: A taxi company charges$1.75 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90? A. 4 miles B. 4 (1/4) miles C. 4 (3/4 )miles D. 5 (1/2) miles E. 6 (1/4) miles We can let x = the number of Â¼-miles traveled with$4.90 and create the following equation:

1.75 + 0.15(x - 1) = 4.90

175 + 15x - 15 = 490

160 + 15x = 490

15x = 330

x = 22

We see that 22 quarter-miles can be traveled with \$4.90 and 22 x Â¼ = 5 Â½ miles.

Answer: D

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