#Flaw #CR Percent

This is a GMAT Prep question. So, if you haven’t gone through the Official practice tests yet, you might want to revisit this solution after you take those mock tests.

Question

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The violent crime rate (number of violent crimes per 1,000 residents) in Meadowbrook is 60 percent higher now than it was four years ago. The corresponding increase for Parkdale is only 10 percent. These figures support the conclusion that residents of Meadowbrook are more likely to become victims of violent crime than are residents of Parkdale.

The argument above is flawed because it fails to take into account

(Because of copyrights, the complete official question is not copied here. You can access the question here: GMAT Club)

Solution

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The Story

The violent crime rate (number of violent crimes per 1,000 residents) in Meadowbrook is 60 percent higher now than it was four years ago.– Violent Crime Rate is defined as the number of violent crimes per 1000 residents.

The VCR has gone up by 60% in the last four years in a particular town (Town 1). What’s gone up by 60%? The crime rate. So, say there used to be 10 violent crimes per 1,000 residents four years ago, now there are 16 crimes per 1,000 residents.

The corresponding increase for Parkdale is only 10 percent. – In another town (Town 2), the VCR  increased by 10%.

(I’m thinking: Since we don’t know the actual rate for either town, we can’t  say which town saw a bigger increase in the number of violent  crimes.)

These figures support the conclusion that residents of Meadowbrook are more likely to become victims of violent crime than are residents of Parkdale. – The author concludes that the residents of the first town have a higher chance of encountering a violent crime than do residents of the second town.

Gist: Residents of town 1 are more likely to encounter violent crimes than are residents of town 2 (main point), because town 1 has a higher percentage increase in VCR (60%) than town 2 (10%) (basis).

Gap(s) in logic:
The passage gives us only the percentage increases in VCR’s for the two towns. The argument does not tell us about the actual rates. To conclude that residents of the first town are more likely to become victims of violent crime, we need to know the actual violent crime rates for the two towns.

For example:

Town 1:  Say the VCR goes from 10 to 16. That’s a 60% increase. So, the town now has 16 violent crimes per 1,000 residents.

Town 2: Say the VCR goes from 50 to 55. That’s a 10% increase. So, the town now has 55 violent crimes per 1,000 residents. 

Do you see that in this scenario Town 2 residents would be more likely to encounter violent crimes?

Question Stem

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The argument above is flawed because it fails to take into account

We have come up with one gap above. There could, of course, be more gaps (flaws) in the argument too. Let’s go through the answer choices.

Answer choice analysis

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Additional Notes

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Answer choices A and B seem attractive to many GMAT candidates. At the time of writing this solution, 34% students mark A or B as their answer on GMAT Club. That is over one-third of the people who attempt this question – a significant chunk.

I have tried to explain a scenario below in which answer choices A and B would be correct. It is fairly long, and I discuss options A and B all the way in the end. But that’s the logical path I could think of to reach there.

Here goes.

To see clearly why the two answer choices are wrong, we need to be clear that the argument is not dealing with the number of violent crimes but with violent crime rates.

What if the passage did deal with an increase in the number of violent crimes?

I.

The number of violent crimes in Town 1 is 60 percent higher now than it was four years ago. The corresponding increase for Town 2 is only 10 percent. These figures support the conclusion that residents of Town 1 are more likely to become victims of violent crime than are residents of Town 2.

(I have replaced ‘violent crime rate’ with ‘number of violent crimes’. That’s the only change I have made in the argument.)

Does this argument make sense? Do you notice any gaps here?

The argument is not logical. Let’s start with some new towns – X and Y – to understand why the argument isn’t logical.

Say, 

1. Town X had 10 murders last year.
2. Town Y had 100 murders last year. 

Does that mean that residents of Town Y are more likely to get murdered than are residents of Town X?
Don’t we need to know about the populations of the two towns? We do, right?
10 murders in a town of population 100 means there’s a 10% likelihood of someone getting murdered.
100 murders in a town of population 10,000 means there’s a 1% likelihood of someone getting murdered.
So, just knowing the number of murders on its own is not enough to conclude about the likelihood of getting murdered.

Now let’s go to the variation of the argument I have created above.

Say,

1. Town 1:
   Number of violent crimes: 100 → 160 (60% increase)
2. Town 2:
   1. Number of violent crimes: 50 → 55 (10% increase)
   2. Number of violent crimes: 200 → 220 (10% increase)
      (I’ve made two cases – one in which the final number of violent crimes in this town is lower and one in which it is higher.)

Based on 160 v/s 55, can we say that residents of Town 1 are more likely to become victims of violent crime than are residents of Town 2?

Based on 160 v/s 220, can we say that residents of Town 2 are more likely to become victims of violent crime than are residents of Town 1?

The answer to both these questions is NO. We need to know the populations of the two towns (the base or the denominator) to be able to make such claims.

II.

Now, what if we knew the populations of the two towns also? In fact, let’s say the populations of the two towns were equal four years ago. And then we’re given that the number of violent crimes increased by 60% and 10% respectively.

Can we then conclude that residents of Town 1 are more likely to become victims of violent crime than are residents of Town 2?

I think we can’t. Because we still need to know the initial numbers of violent crimes in the two towns. 

Let me explain this with numbers:

Population of each town four years ago: 10,000
Number of violent crimes in Town 1: 50 → 80
Number of violent crimes in Town 2: 300 → 330

Is it now logical to conclude that residents of Town 1 are more likely to become victims of violent crime than are residents of Town 2?

Still not. Let’s take a look at the third flaw. That’s the one highlighted by options A and B.

III.

Ok, now let’s say we were also given the initial number of violent crimes for each town too. In fact, let’s say, the initial numbers were equal.

Four years ago:

Population of Town 1: 10,000
Population of Town 2: 10,000
Number of violent crimes in Town 1: 100
Number of violent crimes in Town 2: 100

Current situation:
Number of violent crimes in Town 1: 100 → 160
Number of violent crimes in Town 2: 100 → 110

Can we then conclude that residents of Town 1 are more likely to become victims of violent crime than are residents of Town 2?

We still can’t. We need to know how the populations of the two towns changed in the last four years.

E.g. If the population of Town 1 increased by 60% (10,000 → 16,000) and the population of Town 2 increased by 10% (10,000 → 11,000), the likelihood of encountering a violent crime would be the same in both the towns.

To summarise,

1. We need to know the initial population of the each of the two towns
2. We need to know the initial violent crime rates for the two towns
3. We need to know the rate at which the population of each town has increased*

Answer choices A and B highlight the third gap (*) mentioned above. So, answer choices A and B would point out a flaw in this modified argument about the number of violent crimes. 

If the argument were about the number of violent crimes instead of violent crime rates, both answer choices A and B would be correct.

If you have any doubts regarding any part of this solution, please feel free to ask in the comments section.