Question 65

If a, b, c and d are four different positive integers selected from 1 to 25, then the highest possible value of ((a + b) + (c +d ))/((a + b) + (c - d)) would be:

Name: If a, b, c and d are four different positive integers selected from 1 to 25, then the highest possible value of ((a + b) + (c +d ))/((a + b) + (c - d)) would be:
Uploaded: Aug. 6, 2020, 3:40 p.m.
Duration: 2 min 48 s
Description: If a, b, c and d are four different positive integers selected from 1 to 25, then the highest possible value of ((a + b) + (c +d ))/((a + b) + (c - d)) would be:

Solution

Expression : $$\frac{a + b + c + d}{a + b + c - d}$$

To maximize the above expression, we have to minimize the denominator

Minimum value of the denominator = 1

So we can make $$a + b + c = 26$$ and $$d = 25$$ (as maximizing d will give denominator the least value).

So required maximum value = $$\frac{a + b + c + d}{a + b + c - d}$$

= $$\frac{26 + 25}{26 - 25} = 51$$

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If a, b, c and d are four different positive integers selected from 1 to 25, then the highest possible value of ((a + b) + (c +d ))/((a + b) + (c - d)) would be:

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