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Daily Math Questions

maraudersmapmaraudersmap Posts: 14Registered User New Member
edited November 2012 in SAT Preparation
Hey guys, I'm prepping for the Dec SAT and I think a daily math questions would help me improve. Can anyone help me with these questions? If you nee help too, feel free to post.

1. Kyle's lock combination consists of 3 two-digit numbers. The combination satisfies the three conditions below.

-One number is odd
-One number is a multiple of 5
-One number is the day of the month of Kyle's birthday

If each number satisfies exactly one of the conditions, which of the following could be the combination of the lock?

A. 14-20-13
B. 14-25-13
C. 15-18-16
D. 20-15-20
E. 34-30-21

I'm confused because A, B, and D all fit the conditions...
Post edited by maraudersmap on
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Replies to: Daily Math Questions

  • ReckieReckie Posts: 346Registered User Member
    I'm not agreeing with how the question is given to us; but I'll give you the answer they're looking for.

    The only thing you missed was the word "one." ONE number is odd. ONE number is a multiple of 5. And ONE number.. you get it.

    A. 14-20-13
    B. 14-25-13 - Eliminate because it has 2 odd numbers.
    C. 15-18-16 - Eliminate because 15 can't satisfy two requirements.
    D. 20-15-20 - Eliminate because it has two multiple of 5's.
    E. 34-30-21 - Eliminate because 21 and 30 work, but 34 doesn't satisfy the birthday requirement.

    A!
  • maraudersmapmaraudersmap Posts: 14Registered User New Member
    Omg I feel so stupid. Thank you so much!

    Here's another one I need help with:

    Let x be defined as [x]=x^2-x for all values of x. If [a]=a-2, what is the value of a?

    A. 1
    B. 1/2
    C. 3/2
    D. 6/5
    E. 3
  • rspencerspence Posts: 2,118Registered User Senior Member
    This is not an SAT question, it's just an SAT-level question I made up.

    Q: If p and q are positive integers such that pq = 50, which of the following cannot equal (p^2)q?

    A: 50
    B: 100
    C: 200
    D: 250
    E: 500
  • rspencerspence Posts: 2,118Registered User Senior Member
    @maraudersmap, are you sure your question is correctly typed? Here's what I did:

    [a] = a^2 - a = a - 2

    a^2 - 2a + 2 = 0

    a = (2 +- sqrt(4 - 8))/2, i.e. two complex solutions.
  • CaLLM3KoB3CaLLM3KoB3 Posts: 43Registered User Junior Member
    I'm pretty sure the question is: Let x be defined as [x]=x^2-x for all values of x. If [a]=[a-2], what is the value of a?
  • maraudersmapmaraudersmap Posts: 14Registered User New Member
    The question is typed correctly, [ ] is one of those weird symbols
  • rspencerspence Posts: 2,118Registered User Senior Member
    [a] = a-2 and [a] = [a-2] mean completely different things...
  • maraudersmapmaraudersmap Posts: 14Registered User New Member
    sorry, you guys are right. It's [a-2]
  • rspencerspence Posts: 2,118Registered User Senior Member
    Then it's just

    a^2 - a = (a-2)^2 - (a-2)

    a^2 - a = a^2 - 5a + 6 (upon expanding, simplifying). a^2 cancels, leaving

    -a = -5a + 6 --> a = 3/2
  • maraudersmapmaraudersmap Posts: 14Registered User New Member
    Thank you very much! I'll post when I have more questions, I'm currently not at home haha [:
  • JackTCJackTC Posts: 91Registered User Junior Member
    rspence, is the answer to your question C. ?
  • rspencerspence Posts: 2,118Registered User Senior Member
    ^JackTC yep. All the other answer choices are in the form 50p, where p is a factor of 50.
  • kooshbagkooshbag Posts: 62Registered User Junior Member
    Can you go over how you got that question exactly? The way I did it took too long
  • rspencerspence Posts: 2,118Registered User Senior Member
    The solution involves thinking of (p^2)(q) as p(pq). Since pq = 50, this is equal to 50p. All the answer choices are multiples of 50, but note that p must be a factor of 50, so 50p must be (a factor of 50) times 50.

    200 is 50*4, and 4 is not a factor of 50, so C is the answer.
  • neatoburritoneatoburrito Posts: 3,449Registered User Senior Member
    That's a good example, rspence. The SAT loves the give you an expression and then tell you what a part of the factored form of the expression equals. They particularly like to do this with the difference of two squares and the occasional square of a sum or difference. The moral is, " If it can be factored, factor it." Or more colloquially, "Take it apart so that you can see more clearly what it's made of." It's a shame that schools tend to spend months teaching kids how to factor and little time explaining why you might want to do it.
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