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(2) The company charges $1.20 for a 4-mile ride. I read a solution in the textbook where it gives the explanation for (1) f + m = .90 leading to f + 9 = 0.90 + 5m the same goes for (2) f + 3m = 1.20 leading to f + 9, = 1.20 + 6m. I want to know how that's the case for each of them. 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 Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 10763 messages Followed by: 1212 members Thanked: 5146 times GMAT Score: 770 Thu Nov 12, 2015 1:52 pm datonman wrote: A taxi company charges 'f' cents for the first mile of the taxi ride and 'm' cents for each additional mile. How much does the company charge for a 10 mile taxi ride? (1) The company charges$0.90 for a 2-mile ride.
(2) The company charges $1.20 for a 4-mile ride. Target question: How much does the company charge for a 10 mile taxi ride? Given: A taxi company charges 'f' cents for the first mile of the taxi ride and 'm' cents for each additional mile. 1 mile at f cents/mile will cost f cents 9 miles at m cents/mile will cost 9m cents So, the TOTAL cost of a 10-mile trip costs f + 9m cents REPHRASED target question: What is the value of f + 9m? Aside: We have a free video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100 Statement 1: The company charges$0.90 for a 2-mile ride
1 mile at f cents/mile will cost f cents
1 mile at m cents/mile will cost m cents
So, the total cost of this 2-mile ride = f + m cents
Since the cost is 90 cents, we can conclude that f + m = 90
Is this enough information to find the value of f + 9m? No!

Here's why. There are several values of f and m that satisfy the equation f + m = 90. Here are two:
Case a: f = 80 and m = 10, in which case f + 9m = 80 + 9(10) = 170
Case b: f = 85 and m = 5, in which case f + 9m = 85 + 9(5) = 130
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The company charges $1.20 for a 4-mile ride 1 mile at f cents/mile will cost f cents 3 miles at m cents/mile will cost 3m cents So, the total cost of this 4-mile ride = f + 3m cents Since the cost is 120 cents, we can conclude that f + 3m = 120 Is this enough information to find the value of f + 9m? No! Here's why. There are several values of f and m that satisfy the equation f + 3m = 120. Here are two: Case a: f = 90 and m = 10, in which case f + 9m = 90 + 9(10) = 180 Case b: f = 105 and m = 5, in which case f + 9m = 105 + 9(5) = 150 Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that f + m = 90 Statement 2 tells us that f + 3m = 120 We COULD solve this system of equation for f and m, which means we COULD determine the value of f + 9m Since we COULD answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT Answer = C Cheers, Brent _________________ Brent Hanneson – 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 GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Matt@VeritasPrep GMAT Instructor Joined 12 Sep 2012 Posted: 2560 messages Followed by: 113 members Thanked: 581 times Target GMAT Score: V51 GMAT Score: 780 Fri Nov 13, 2015 3:47 pm datonman wrote: A taxi company charges 'f' cents for the first mile of the taxi ride and 'm' cents for each additional mile. How much does the company charge for a 10 mile taxi ride? (1) The company charges$0.90 for a 2-mile ride.
(2) The company charges \$1.20 for a 4-mile ride.

I read a solution in the textbook where it gives the explanation for (1) f + m = .90 leading to f + 9 = 0.90 + 5m

the same goes for (2) f + 3m = 1.20 leading to f + 9, = 1.20 + 6m. I want to know how that's the case for each of them.
I think you mean f + 9m, but you're on the right track. The question wants the value of f + 9m, so if we can find this, we're set.

S1 gives f + m = 90¢. We can't solve this.

S2 gives f + 3m = 120¢. We can't solve this either.

Together, we can subtract the first equation from the second, giving 2m = 30¢, or m = 15¢. From there, plug m = 15 into either equation to get f = 75¢, and you're set: you know f and m, so you can find f + 9m, and the two statements together are SUFFICIENT.

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