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clarification on GMAT 2016 DS problem

This topic has 2 expert replies and 0 member replies
datonman Senior | Next Rank: 100 Posts Default Avatar
Joined
28 May 2014
Posted:
53 messages

clarification on GMAT 2016 DS problem

Post Thu Nov 12, 2015 12:35 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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.

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    Post 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

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    Post 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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