Bunuel wrote:
For which of the following expressions would the value be greater if 160 were replaced by 120 ?
I. \(1000 - 160\)
II. \(\frac{160}{1+160}\)
III. \(\frac{1}{1-\frac{1}{160}}\)
A. None
B. I only
C. III only
D. I and II
E. I and III
Let’s examine each Roman numeral.
I. We see that 1000 - 120 is greater than 1000 - 160.
II. Originally we had 160/161, and after replacement we have 120/121, so we see the expression is smaller after the replacement.
III. When we replace 160 with 120, we see that the denominator 1 - 1/160 becomes 1 - 1/120 and thus it gets smaller. Since the numerator stays the same, the entire expression gets larger.
Answer: E
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