The question stem says the consultant's conclusion follows logically if which of the following is assumed.

So conclusion follows logically if assumed means this is a sufficient assumption question.

The correct answer, if we add it to the premises, will guarantee the conclusion.

then she will lose to her opponent by a few percentage points among voters under 50,

while beating him by a bigger percentage among voters 50 and over.

So if she sticks to her current platform, then this is what's going to happen.

With the under 50 voters, she loses by a small percent.

With 50 and over, she wins by a bigger percent than she loses.

Now based on this fact, the author reaches this conclusion.

Therefore, sticking with her current platform will allow her to win the election.

Well hold on, how do I know that?

The author seems to think that these stats prove that she would win her election

if this situation happens.

If she loses the under 50 voters by a small percent and wins at 50 and over by a bigger percent.

But in order for her to win the election,

she would actually have to get more votes overall than her opponent.

And if all we know is the percentage that she will win certain categories by,

or lose certain categories by,

that doesn't tell me about the actual number of votes she's going to get,

and whether that's going to be higher than the number of votes that her opponent's going to get.

So if you understand that, at a minimum then,

you know that the author must be assuming something about the number of votes she's going to get.

Now let's explore that idea further.

Let's think about what situation would actually undermine the argument.

Because then it'll help us understand how we make the argument win.

Now we know that she's going to win 50 and over voters

by a bigger percentage than she loses the under 50 voters.

But what if we're in a city or a location

where the voters are just like overwhelmingly young people?

For some reason all the old people are not voting,

or there's just not many old people around compared to the young people.

If that's the case, then maybe what ends up happening is the 50 and over people,

let's say this circle represents the 50 and over people,

and sure maybe she wins this shaded portion,

but it's possible that the people under 50 are just so much more numerous,

and so if she loses the under 50 votes,

so let's say Wiley will win this shaded portion,

do you see how in this situation it's possible her opponent could actually get more votes?

Her opponent overall could win more votes

because the under 50 voters might just be so much more numerous

than the over 50 or the 50 and over voters.

So the author must be assuming that this situation won't happen.

In the author's mind, the number of votes that Wiley will get

over her opponent with the 50 and over crowd

is going to be greater than the number of votes that she'll lose

compared to her opponent with the under 50 crowd.

So that's what I would have in mind before going to these answers.

To make this argument valid, I want an answer that's going to establish

that she will in fact get more votes over her opponent from this category

than she will lose compared to her opponent from that category.

that would win over more voters under 50 than it would lose voters 50 and over.

Now if answer choice A were added to the premises,

that might help us show that her current platform is like the best one for her

because it would show that she wouldn't be able to change

and then get more votes from the younger voters

than she would lose from the older voters.

But the problem with answer choice A

is that it doesn't guarantee that her current platform would win the election.

We're not trying to prove that her current platform is like the best one

and that there's no other better one that she could get by changing.

That's not what we're trying to prove.

We're trying to prove that with her current platform, she will win.

And answer choice A isn't doing that

because we don't know anything about the comparative number of votes

that she'll get from the 50 and over versus under 50.

We would still have the exact same problem that I described earlier

where the number of people 50 and over

could just be very, very small compared to the people under 50.

So even if she wins this group,

that might not actually mean that many votes

compared to the votes that she'll lose by losing this group.

So because A doesn't solve that problem, it's not correct.

are different from those that most concern voters 50 and over.

Okay, but even if that's true,

that doesn't tell me anything about the comparative number of voters in each group.

That's what I need to know something about in order to say

that because of these percentages, she's going to win with her current platform.

All that B is doing is telling me that the issues

that the different kinds of voters care about are different from each other.

But how many voters is she going to get from this group?

And is it going to exceed the number of voters she'll lose in this group?

B doesn't tell me that. That's why B is wrong.

why do we care about whether Wally changes her platform?

The argument is that her current platform will allow her to win.

The author is not trying to make a conclusion

about what would happen if she changes.

And so if you add C to the argument, it would just have no effect.

C tells me what happens if Wally changes,

but I want to know what happens if she doesn't change.

I want to know specifically that she's going to win if she doesn't change.

And C doesn't do that, so it's wrong.

who are 50 and over than there will be voters under 50.

And this answer, if we add it to the argument, will guarantee the conclusion.

What D is saying is that the number of people, the number of voters rather,

who are in this group is greater than the number of voters who are in this group.

And so if she's winning the 50 and over group by a bigger percentage

than she's losing the under 50 group,

and there are more people or more voters overall in the 50 and over group,

then that would guarantee the number of voters she will get over her opponent

from this group is going to be higher than the number of voters she'll lose

compared to her opponent in the under 50 group.

Now, if you'd like, you can go ahead and come up with some sample numbers

to prove that to yourself.

But once you actually come up with the sample numbers,

you'll see that D does guarantee that she will get more votes overall than her opponent.

It's mathematically impossible for her to get fewer votes than her opponent

if you add D to the premises.

Now, by the way, I know that sometimes people are thrown off by D

because they think that what D says doesn't have to be true.

And the thing is, you're right about that if that's what you thought.

D is not a necessary assumption.

But this is a sufficient assumption question.

So we're just looking for an answer that, if it is true, would guarantee that she'll win.

Technically, D is not necessary to the argument

because the argument doesn't have to assume that the 50 and over group

is larger than the under 50 group.

It just has to assume that Wally will get more votes overall.

And so, for example, here's a possibility that could also have been a correct answer,

and that is that each group was equal in size.

If each group was equal in size, we would still know that Wally would win

because she is winning a bigger percentage of the 50 and over than the under 50.

So answer choice D is not necessary to the argument.

The author didn't have to assume that there will be more voters who are over 50.

There could have been an equal number of voters in each group.

Or there actually could have been fewer voters in the 50 and over group,

but just not so much fewer as to make the overall number of votes

she gets from this category less than the overall number of votes

she gets from the other category.

So all that is to say, if you thought D was not necessary, you're right.

But this is not a necessary assumption question.

This is a sufficient assumption question.

So D is still correct.

if she thought it would give her a better chance to win.

Well, whether Wally would change her platform

doesn't help me prove that her current platform would allow her to win.

The argument has nothing to do with whether Wally will change or won't change,

the conditions that would cause her to change.

All we're trying to do is show that her current platform will win.

Answer choice E doesn't do that because it's not telling me anything

about the comparative numbers of voters in each category.