Math - inequality

[Electrons]

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How many integers do NOT satisfy the inequality n^2 > 2n?

a) 0
b) 1
c) 2
d) 3
e) more than 3

Answer is D. Why is it not E? After simplify, I get n > 2. If I do the n > 2 or n < -2 which mean it should be E?

 

[Streetwolf]

n^2 > 2n
n^2 - 2n > 0
n(n-2) > 0
n = 0, 2

So 0 and 2 are answers since they form the equality and are thus not strictly greater than.

You also find out that 1 is an answer because it doesn't follow the inequality. It would give you a less than answer.

Everything else works. Remember that it wants integers that cause it to be FALSE.

 

[Electrons]

Thanks for the explanation. I noticed I always seem to miss these "satisfy" question of absolute and inequality.

Btw, you have awesome scary looking scores.

 

[PorkChop2008]

Btw, you have awesome scary looking scores.

I agree, however he might want to double-check the math on them. None of the scores are a 29, yet the science average is 29? 🙂 The things that make you go hmmmmmm?

 

[TheRighteous]

You can also use graphical analysis to answer the question. It makes it a bit easier to see that "1" is also an integer that does not work.

n^2 > 2n
n^2 - 2n > 0
n(n-2) > 0
(n-0)(n-2) > 0

This is the equation for a parabola. X-intercepts are 0 and 2. You're only interested at the points on the x-axis since the inequality is set to be larger than 0. The only three values that you look at are 0, 1, and 2, because they lie on the x-axis and are part of the inequality. Plugging in these values to your equations reveals none of the three integers satisfy the inequality.

 

[Streetwolf]

I agree, however he might want to double-check the math on them. None of the scores are a 29, yet the science average is 29? 🙂 The things that make you go hmmmmmm?

TS is not the average of the 3 sections. It's a scaled score of 100 science questions without regard to subject. It's a way for the adcom to see how well you did on all 100 questions at a glance because it doesn't take into account if the questions were easy or hard.

That's why AA is derived from the 3 subject scores, because those DO take into account easy or hard questions.