x is a positive integer divisible by 4; as x increases from 1824 to 1896, which of the following must decrease?
I. 4x2 - 4x + 4
II. -10 - 1/x2
III. 4/x2
A) I only
B) II only
C) III only
D) II and III only
E) None
OA is C
can someone give me an explanetion why D is incorrect
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which must decrease
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grockit_jake
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The difference between C and D is that D says II will decrease.
II. -10 - 1/(x^2)
The -10 is a constant so don't worry about that. Let's take it one step at a time. When x increases, x^2 increases. Since x^2 is in the denominator, the entire term 1/(x^2) DECREASES. Since that entire term is being subtracted from the constant, the entire expression -10 - 1/(x^2) INCREASES. If you subtract a smaller number, then your result is higher.
An increase in x results in increase in II, so C. III only is correct
II. -10 - 1/(x^2)
The -10 is a constant so don't worry about that. Let's take it one step at a time. When x increases, x^2 increases. Since x^2 is in the denominator, the entire term 1/(x^2) DECREASES. Since that entire term is being subtracted from the constant, the entire expression -10 - 1/(x^2) INCREASES. If you subtract a smaller number, then your result is higher.
An increase in x results in increase in II, so C. III only is correct
