Without resorting to messy calculations and variables, the solution can be found relatively quickly be understanding what happens to ratios when you add the same constants to both parts.

Imagine two people whose ages are 10 years apart. The older one is 20 and the younger one is 10, and the ratio of their ages is 20:10, or 2:1. Now as they age, they both gain the same number of years. So if we look at the ratio of their ages again in 20 years, it becomes 40:30 or 4:3. The ratio

decreases - 4:3 < 2:1. This is true of any ratio greater than 1*. It will decrease if the same value is added to both sides, and conversely, it will increase if the same value is subtracted from both sides.

*Now it should be pointed out that it would be more accurate to talk about the ratios getting closer to, or further away from 1, instead of increasing or decreasing, since it would be the opposite for ratios that are less than 1. In our example above, if we took the ratio of the smaller age to the older age 1:2, then added 20 years, the ratio would become 3:4. Here the ratio increased when we added the same value to both sides. But in both cases the ratios moved closer to 1.

Conclusion: Adding a (positive) constant to both sides of a ratio makes the ratio move closer to 1:1, and subtracting a constant from both sides of a ratio makes the ratio further away from 1:1.

Ok, now to solve our problem.

In our case we have the ratio 5:4, and we are subtracting a constant from both sides. That means the new ratio must be further from 1 than the original ratio. In other words, since the original ratio is greater than 1, the new ratio must be greater than the the original (5:4). So for an answer choice to be impossible, it will have to be less than the original ratio (closer to 1). So now we can check our answer choices and see which is the odd one out.

5:4 = 25:20

A) 7: 5 = 28:20 -->

okB) 3: 2 = 30:20 -->

okC) 13:10 = 26:20 -->

okD) 6: 5 = 24:20 -->

NOE) 6: 4 = 30:20 -->

okSo the only answer choice that is less than (or closer to 1 than) the original ratio is D.

Answer: D

You could have also noticed that D is the same as (5+1):(4+1), and since a constant was added to both sides of the ratio, the result must be closer to 1, and is therefore our answer. It would still be a very good idea to check the rest of the answers though, just to make sure your logic and process are correct.

_________________

Dave de Koos

GMAT aficionado