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OG 13 30

This topic has 2 expert replies and 0 member replies
oquiella Master | Next Rank: 500 Posts Default Avatar
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OG 13 30

Post Thu Dec 24, 2015 9:37 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The only gift certificates that a certain store sold yesterday were worth either $100 each or $10 each. If the store sold a total of 20 gift certificates yesterday. how many gift certificates worth $10 each did the store sell yesterday?


    1. The gift certificates sold by the store yesterday were worth a total of between $1650 and $1800.
    2. Yesterday the store sold more than 15 gift certificates worth $100 each.

    Answer: A


    Please explain why A is sufficient when there could have been a range between $1650 and $1800.

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    Post Fri Dec 25, 2015 6:57 am
    oquiella wrote:
    The only gift certificates that a certain store sold yesterday were worth either $100 each or $10 each. If the store sold a total of 20 gift certificates yesterday. how many gift certificates worth $10 each did the store sell yesterday?


    1. The gift certificates sold by the store yesterday were worth a total of between $1650 and $1800.
    2. Yesterday the store sold more than 15 gift certificates worth $100 each.

    Answer: A


    Please explain why A is sufficient when there could have been a range between $1650 and $1800.
    The key here is to recognize that we have a total of 20 gift certificates and that the number of gift certificates of each type must be an integer value. Say the store sold 17 of $100 certificates and 3 of the $10. That would give us 17*100 + 3*10 = 1730. That's between 1650 and 1800, so that's one possible scenario.

    Now let's see if anything else can work. What if there were 18 of the $100 certificates and 2 of the $10? That gives us a total of 1820 -not between 1650 and 1820 so this not a possibility that satisfies the statement.

    What if there were 16 of the $100 certificates and 4 of the $10? That gives us a total of 1640 - not between 1650 and 1800, so we can't use this scenario either.

    The only possibility that satisfies the statement is that there were 17 of the $100 certificates and 3 of the $10 certificates. So the answer is
    A

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    Post Fri Dec 25, 2015 7:04 am
    oquiella wrote:
    The only gift certificates that a certain store sold yesterday were worth either $100 each or $10 each. If the store sold a total of 20 gift certificates yesterday. how many gift certificates worth $10 each did the store sell yesterday?


    1. The gift certificates sold by the store yesterday were worth a total of between $1650 and $1800.
    2. Yesterday the store sold more than 15 gift certificates worth $100 each.

    Answer: A


    Please explain why A is sufficient when there could have been a range between $1650 and $1800.
    Algebraically, we can say that 'x' is the number of $10 certificates and '20-x' is the number of $100 certificates. (Because we know there are 20 total.) We know that 10x + 100(20-x) is the total value of the certificates. 10x + 100(20-x) = 10x + 2000 - 100x = 2000 - 90x. We know this value is between 1650 and 1800. Now test x's.

    x = 1 --> 2000 - 90 = 1910. Nope
    x = 2 --> 2000 - 180 = 1820. Nope
    x=3 ---> 2000 - 270 = 1730. Satisfies!
    x = 4 ---> 2000 - 360 = 1640. Nope

    Only one value works, so we know that x = 3.

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