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700 Level Number Properities

This topic has 2 expert replies and 0 member replies

Top Member

700 Level Number Properities

Post Wed Nov 08, 2017 10:06 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    0 <2x + y <50, -50 I. x> 0
    II. Y> 0
    III. X> y

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    Post Wed Nov 08, 2017 10:39 pm
    mihai9 wrote:
    0 <2x + y <50, -50
    I. x> 0
    II. Y> 0
    III. X> y
    From the inequality 0 < 2x + y < 50, we get that the sum of two x and one y is positive (0 < 2x + y). When one x is replaced with a y, the inequality becomes -50 < x + 2y < 0. We see that now the sum of two y and one x is negative (x + 2y < 0). This implies that x is positive and y is negative; and x > y.

    Hope this helps!

    -Jay
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    Thanked by: mihai9
    Post Thu Nov 09, 2017 4:34 am
    mihai9 wrote:
    0 <2x + y <50, -50 I. x> 0
    II. Y> 0
    III. X> y
    Inequalities can be LINKED TOGETHER.
    Linking together x+2y < 0 and 0 < 2x+y, we get:
    x+2y < 0 < 2x+y
    x+2y < 2x+y
    ,y < x
    Thus, statement III must be true.

    We can ADD TOGETHER inequalities in which the inequality symbol faces the same direction.
    Adding together y y+0 < x+2x+y
    0 < 3x
    0 < x.
    Thus, statement I must be true.

    Adding together y y+x+2y < x+0
    3y < 0
    y < 0.
    Thus, statement II is NOT true.

    The correct answer is I and III.

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    Thanked by: mihai9
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