• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A certain military vehicle can run on pure Fuel X, pure Fuel ##### This topic has 2 expert replies and 1 member reply ### Top Member ## A certain military vehicle can run on pure Fuel X, pure Fuel ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any mixture of X and Y. Fuel X costs$3 per gallon; the vehicle can go 20 miles on a gallon of Fuel X. In contrast, Fuel Y costs $5 per gallon, but the vehicle can go 40 miles on a gallon of Fuel Y. What is the cost per gallon of the fuel mixture currently in the vehicleâ€™s tank? (1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles. (2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank OA D Source: Gmat Prep ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 1104 messages Followed by: 2 members Top Reply Let gallons of fuel X = x Let gallons of fuel Y = y What is the cost per gallon of the full mixture currently in the vehicle tank $$\frac{\left(3x+5y\right)}{x+y}=\ ratio\ of\ x:y$$ Statement 1 Using fuel currently in its tank , the vehicle burned 8 gallons to cover 200 miles x + y = 8 y = 8 - x 20x + 40y = 200 20x + 40(8x) = 200 $$-\frac{20x}{20}=\frac{\left(200-320\right)}{-20}$$ $$x=\frac{-120}{-20}=6$$ $$from\ x+y=8$$ $$\ 6+y=8$$ $$y=8-6=2$$ $$\cos t\ per\ gallon=\frac{3x+5y}{x+y}$$ $$=\frac{3\left(6\right)+5\left(2\right)}{8}$$ $$=\frac{18+10}{8}$$ $$=\frac{28}{8}$$ $$=3.5\ dollars$$ Statement 1 is INSUFFICIENT Statement 2 The vehicle can cover 7 hours 1/7 miles for every dollar of fuel currently in the tank $$\frac{\left(Total\ miles\ it\ can\ cover\right)}{Total\ \cos t}=\frac{50}{7\ }=7\ \frac{1}{7}$$ $$\frac{\left(20x+40y\right)}{3x+5y}=\frac{50}{7\ }$$ $$7\left(20x+40y\right)=50\left(3x+5y\right)$$ $$7\left(20x+40y\right)=50\left(3x+5y\right)$$ $$\left(140x+280y\right)=\left(150x+250y\right)$$ $$\left(280y-250y\right)=\left(150x-140x\right)$$ $$3y=x$$ For every dollar spent of the mixture of ratios 3y : 1x, the vehicle can travel a distance of 11 1/7 miles Statement 2 is SUFFICIENT. Hence both statement together are SUFFICIENT $$answer\ is\ Option\ D$$ . ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any mixture of X and Y. Fuel X costs$3 per gallon; the vehicle can go 20 miles on a gallon of Fuel X. In contrast, Fuel Y costs $5 per gallon, but the vehicle can go 40 miles on a gallon of Fuel Y. What is the cost per gallon of the fuel mixture currently in the vehicleâ€™s tank? (1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles. (2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank Statement 1: X = 20 miles per gallon. Y = 40 miles per gallon. Since the mixture of X and Y in the tank allows 200 miles to be covered using 8 gallons, we get: X+Y = 200/8 = 25 miles per gallon. To determine how X and Y must be combined to yield a rate of 25 miles per gallon, use ALLIGATION. Step 1: Plot the 3 rates on a number line, with the rates for X and Y on the ends and the rate for the mixture in the middle X 20------------25-------------40 Y Step 2: Calculate the distances between the percentages. X 20-----5-----25-----15-----40 Y Step 3: Determine the ratio in the mixture. The ratio of X to Y is equal to the RECIPROCAL of the distances in red. X:Y = 15:5 = 3:1. Of every 4 gallons in the tank, X= 3 gallons and Y = 1 gallon. Since X =$3 per gallon and Y = $5 per gallon, the cost for 3 gallons of X and 1 gallon of Y = (3*3) + (1*5) =$14.
Since 4 gallons costs $14, the cost per gallon = 14/4 = 7/2 =$3.50.
SUFFICIENT.

Statement 2:
The cost of the 8 gallons used in Statement 1 to travel 200 miles = (8)(7/2) = $28, implying that the miles per dollar = 200/28 = 100/14 = 50/7 = 7 1/7 miles. Implication: Statement 2 -- which requires that 7 1/7 miles be covered for every dollar -- conveys the SAME INFORMATION as Statement 1. Since Statement 1 is SUFFICIENT, so must be Statement 2. SUFFICIENT. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 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 GMAT Instructor Joined 22 Aug 2016 Posted: 1975 messages Followed by: 30 members Upvotes: 470 BTGmoderatorDC wrote: A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any mixture of X and Y. Fuel X costs$3 per gallon; the vehicle can go 20 miles on a gallon of Fuel X. In contrast, Fuel Y costs $5 per gallon, but the vehicle can go 40 miles on a gallon of Fuel Y. What is the cost per gallon of the fuel mixture currently in the vehicleâ€™s tank? (1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles. (2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank OA D Source: Gmat Prep Say there be x gallons of fuel X, and y gallons of fuel Y in the tank. Cost per gallon = (3x + 5y)/(x + y) We have to get the value of (3x + 5y)/(x + y). Let's take each statement one by one. (1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles. => x + y = 8; and 20x + 40y = 200 => x + 5y = 10. We have two unique linear equations, we can get the unique values of x and y, thus, of (3x + 5y)/(x + y). Sufficient. (2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank. => Total miles can cover / total cost = 7 and 1/7 miles = 50/7 miles/dollar => (20x + 40y)/(3x + 5y) = 50/7 (2x + 4y)/(3x + 5y) = 5/7 14x + 28y = 15x + 25y x = 3y Thus, (3x + 5y)/(x + y) => (3*3y + 5y)/(3y + y) = 14y / 4y = 7/2. Sufficient The correct answer: D Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GMAT Classes Denver | GMAT Tutoring San Francisco | GRE Prep San Houston | TOEFL Prep Classes Philadelphia | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

199 posts
2 Max@Math Revolution

Math Revolution

84 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 Ian Stewart

GMATiX Teacher

65 posts
5 GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts