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Math Help - SAT questions I did not understand

  1. #1
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    SAT questions I did not understand

    Can someone give me an explanation for Q1? I am still confused.




    Q1.
    In a supermarket, Shakira bought 5 items from aisles 1 through 7, inclusive, and 7 items from aisles 4 through 10, inclusive. Which of the following could be the total number of items that Shakira bought?
    I. 9
    II. 10
    III. 11
    A. II only
    B. I and II only
    C. I and III only
    D. II and III only
    E. I, II, and III
    A purchase from aisles 4 through 7, inclusive, would count in both Shakira’s purchases from aisles 1 through 7, inclusive, and those from aisles 4 through 10, inclusive. So, for example, she could have bought as few as 7 items total: say 5 items from aisle 6 and 2 from aisle 9. Or the total could be as high as 12: say 5 items from aisle 1 and 7 from aisle 10. Any total number of items between 7 and 12 is also possible. In particular, Shakira could have bought 9 items total (for example, 2 items from aisle 1, 3 from aisle 6, and 4 from aisle 10), 10 items total (for example, 3 items from aisle 1, 2 from aisle 6, and 5 from aisle 10), or 11 items total (for example, 4 items from aisle 1, 1 from aisle 6, and 6 from aisle 10). Therefore, the correct answer is I, II, and III.




    (ANSWERED)
    Q2. Maria is 6 times as old as Tina. In 20 years, Maria will be twice as old as Tina. How old is Maria now?
    ( I'm recalling this from memory. Correct me if you've seen a problem like this before and this one doesn't make sense.)

    Q3. Let T be the sum of numbers 1 to 51 and let Q be the sym of numbers 51 - 100. What is Q-T?
    (Same thing, I'm recalling this from memory. Correct me if i'm wrong.)

    Q4.
    At Central High School, the math club has 15 members and the chess club has 12 members. If a total of 13 students belong to only one of the two clubs, how many students belong to both clubs?



    Last edited by Masterthief1324; January 9th 2010 at 09:48 AM.
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  2. #2
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    Quote Originally Posted by Masterthief1324 View Post
    Q2. Maria is 6 times as old as Tina. In 20 years, Maria will be twice as old as Tina. How old is Maria now?
    ( I'm recalling this from memory. Correct me if you've seen a problem like this before and this one doesn't make sense.)

    Q2. Maria is 6 times as old as Tina. In 20 years, Maria will be twice as old as Tina. How old is Maria now?
    Hi Masterthief,

    Let t = Tina's age now.

    Let 6t = Maria's age now.

    Let t + 20 = Tina's age in 20 years.

    Let 6t + 20 = Maria's age in 20 years.

    Use your second sentence to set up the equation.

    6t+20=2(t+20)
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  3. #3
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    Q1: you can see that the minimum and maximum amount of items purchased will be if all items are purchased in isles 4-7. this means the maximum amount of items purchased
    will be 5+7 = 12
    and the minimum will be 7 (if the 5 are part of those 7 in isles 4-7).
    the answer could be any number between those two, therefore the answer is E.

    Q2: we will call tina's age - x and from the first condition, maria will be - 6x
    in 20 years, tina will be - (x + 20) years old and maria will be (6x + 20) years old.
    and from the other condition you know that maria will be then two times older than tina.
    2(x+20) = 6x+20
    2x+40 = 6x+20
    20 = 4x
    x = 5
    and all that's left to do is check if it fits.

    Q3: the sum of arithmatic seires is (n/2)*(a1+an)

    Q4: both clubs have together 27 members.
    if you know that 13 of them belong only to one of the clubs,
    that means that the other 14 belong to both.
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  4. #4
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    Thanks.
    I still have trouble understanding question 1, can someone help clarify?
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  5. #5
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    Q1.
    In a supermarket, Shakira bought 5 items from aisles 1 through 7, inclusive, and 7 items from aisles 4 through 10, inclusive. Which of the following could be the total number of items that Shakira bought?


    What a weird question, I think a venn diagram would make it easier to solve, but here's an example of all 3:

    If she buys two items from aisle 1, three from aisle 4, and four from aisle 9, for example, She will have bought her five items from aisles 1-7 and seven from aisles 4 to 10, but have 9 items in total.
    If she buys three items from aisle 1, two from aisle 4, and five from aisle 9, she will have bought 10 items in total, but still only five from aisles 1-7 and seven from 4-10.
    If she buys four items from aisle 1, one from aisle 4, and six from aisle 9, she will have bought 11 items in total, but still only five from aisles 1-7 and seven from 4-10.

    It's because if she buys something from aisles 4-7, it would count as both an item from aisles 1-7, and an item from aisles 4-10.
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  6. #6
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    Quote Originally Posted by vonflex1 View Post
    Q1: you can see that the minimum and maximum amount of items purchased will be if all items are purchased in isles 4-7. this means the maximum amount of items purchased
    will be 5+7 = 12
    and the minimum will be 7 (if the 5 are part of those 7 in isles 4-7).
    the answer could be any number between those two, therefore the answer is E.
    It is impossible for her to both purchase only 5 items in aisles 4-7, and also purchase 7 items in aisles 4-7 (at least in the context of this problem). This is if I'm reading your solution correctly in that the only purchases were made in aisles 4 through 7.
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