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Bunuel
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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I. (1000 - 120) > (1000 - 160)..straight forward (true)

II. 160/161= 1/((1+(1/160)), and 120/121= 1/((1+(1/120)) , (1/160)<(1/120), so denominator of former is is lesser and denominator value for 1/(1+(1/160)) is lesser and dividing by 1/lesser number will give an overall higher value for 160 (false)

III. When we replace 160 with 120, same as above but inverse result because the denominator has 1-value...so 120 will give a higher value replacing 160 (true)


Answer : E
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