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19 Feb 2016, 10:38
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
51% (02:11) correct
49%
(02:16)
wrong
based on 352
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The ratio of the present ages of a man and his wife is 5 : 4. Which of the following can't be a possible ratio of their ages 20 years ago?
A) 7: 5
B) 3: 2
C) 13:10
D) 6: 5
E) 6: 4
A) 7: 5
B) 3: 2
C) 13:10
D) 6: 5
E) 6: 4
19 Feb 2016, 12:28
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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 -->ok
B) 3: 2 = 30:20 --> ok
C) 13:10 = 26:20 --> ok
D) 6: 5 = 24:20 --> NO
E) 6: 4 = 30:20 --> ok
So 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.
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 -->ok
B) 3: 2 = 30:20 --> ok
C) 13:10 = 26:20 --> ok
D) 6: 5 = 24:20 --> NO
E) 6: 4 = 30:20 --> ok
So 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.
Mesto
The question is based on the concept:
When we add the same positive integer to the numerator and the denominator of a positive fraction, the fraction increases if it is less than 1 (but remains less than 1) and decreases if it is more than 1 (but remains more than 1). That is, we can say, that the fraction is pulled toward 1 in both the cases.
When we subtract the same positive integer from the numerator and the denominator of a positive fraction, the fraction decreases further if it is less than 1 and increases further if it is more than 1. That is, we can say, that the fraction is pushed further away from 1 in both the cases. An assumption here is that the positive number subtracted is less than both the numerator and the denominator.
The given ratio is 5/4 which is the same as 25/20 or 50/40 etc.
When we subtract 20 from each of the numerator and the denominator of this fraction, it will be pushed away from 1 i.e. will become greater than 5/4. All the given options are greater than 5/4 except 6/5.
Hence answer will be (D).
