Assumption questions can often be the most difficult questions on Logical Reasoning. You are presented with an argument and asked to find what the missing assumption in the argument is. Essentially, you must identify what the hole is in the argument, the thing that is not stated on the page but is evidently being assumed by the argument. (Yes, there is an important practical difference between necessary and sufficient assumption questions, but we’ll get to that later.)
These questions can be tough so this guide may be a bit dense, but read all the examples slowly and carefully and it will all make sense.
On easier assumption questions, there will be a gaping hole in the argument that is simple to identify and predict. On tougher assumption questions, it might be harder to map out and identify and there might even be more than one possible answer, but you should aim to ideally at least have an idea of what possible holes exist in the argument before you look at the answers.
Think of the missing assumption as the gap between the evidence and the conclusion. So, here’s a simple example. I’ve underlined the conclusion of the argument (even though it should be self-evident as it follows the word therefore – see here for more on that.)
Today is Sunday. Therefore, Stacy will buy groceries.
The only hole in between the support and the conclusion here is to assume that:
On Sundays, Stacy buys groceries.
That is clearly what is being assumed by the person making this argument – otherwise, why would the fact that it’s Sunday prove that Stacy will buy groceries?
Here’s another very simple one (with the conclusion underlined again), so you can get good at recognizing the missing assumption just from reading the argument. See if you can identify the thing being assumed here:
Wilson wants what’s best for this city. Thus, he would make a good mayor.
The answer is:
Anyone who wants what’s best for this city would make a good mayor.
It’s as simple as that – you just need to find the disconnect between the support and the conclusion and tie it up.
Here’s another one – once again, see if you can find the missing hole:
Lucy must be in good shape. After all, she won the neighborhood race, and only fast runners win the neighborhood race.
Here’s what you should be thinking when you read that:
All the argument has proven is that Lucy is a fast runner (since she won the race, and only fast runners can win the race, thus she must be a fast runner). But the conclusion that is actually drawn is not that she’s a fast runner. It’s that she is in good shape. Those two things are not synonymous.
Thus, the missing assumption in this argument is that:
All fast runners are in good shape.
This is because the argument takes the fact that Lucy is a fast runner and uses it to draw the conclusion that she must be in good shape. Therefore it is evident that this is the assumption being made.
Another way to think about it is that had the argument said the following, it would have been seal-tight with no missing gaps:
Lucy must be a fast runner. After all, she won the neighborhood race, and only fast runners win the neighborhood race.
Thus, the difference between that and what it actually said (fast runner = good shape) must be the missing assumption.
You can map out the argument (before the assumption is added in) as follows:
A must be D. After all, A is B, and all B are C.
…where A = Lucy, B = neighborhood race winner, C = fast runner, and D = in good shape.
Mapping out arguments this way makes it self-evident what the missing gap is. Read it again and you’ll see that it’s missing a link between C and D.
In other words, the following sums up the argument, with the assumption shown with a transparent arrow:
Lucy ➔ won neighborhood race ➔ fast runner ⇨ good shape
Lucy ➔ good shape
Sometimes, the argument can be much more convoluted and the missing gap can be harder to identify. Here’s a much trickier example from my definitive guide to sufficient and necessary conditions (again with the conclusion underlined):
Listening to classical music often has the effect of calming one’s nerves. Therefore, listening to classical music before bedtime can make it easier to fall asleep, since melatonin promotes sleep, and a reduction in blood pressure is always accompanied by a stimulation of melatonin.
There is a longer chain of logic here. Think of this conclusion as a bridge connecting listening to classical music with ease of falling asleep (just like the previous conclusion linked Lucy with good shape), and think of all of the pieces of supporting info as tiles in the bridge between them, like we just did with the last one. Each tile connects the previous item with the next item, and if you put the tiles in order you should be able to identify which tile is empty and predict the answer!
OK, time to try to link everything up to find the missing link. Try it first on your own.
When you’re ready, here’s the argument mapped out in logical order:
Listening to classical music calms nerves.
Reduction in blood pressure causes stimulation of melatonin.
Stimulation of melatonin promotes sleep.
Therefore, classical music promotes sleep.
I purposely left a blank space in the map between the two elements that were not explicitly connected!
It becomes clear that the missing assumption would have to be something to the effect of:
Calming nerves has the effect of reducing blood pressure.
Notice how it doesn’t mention anything about sleep or classical music! Those parts were neatly tied up – the dots that were left unconnected were buried in the middle of the argument.
Mapping this out in terms of letters would look like this:
A causes B.
C causes D.
D causes E.
Therefore, A causes E.
…where A = listening to classical music, B = calming nerves, C = reduction in blood pressure, D = melatonin, and E = sleep.
Connect everything back to the argument and you’ll see that it matches up!
The point is, if you can do this then the answer becomes clear! What’s the missing link in the above chain? That’s right:
B causes C.
Therefore, the missing assumption would have to be connecting calming nerves with reducing blood pressure.
Identifying the missing gap can often be quite tricky, but the point is that it is possible just from reading the argument. Being able to quickly map these arguments out, find the missing link, and predict the answer can transform these questions into a piece of cake!
(Note: Assumption questions are kind of like flaw questions, in that you are finding a hole in the argument in both. The difference is that in assumption questions, you have to fill in the hole. In flaw questions, you just have to identify and point it out.)
Necessary vs Sufficient Assumptions
Now, while all assumption questions involve finding a hole in the argument between the support and the conclusion, there are two distinct types of assumption questions: necessary assumption questions and sufficient assumption questions. Simply put, a necessary assumption is one that is required for the argument to work (in other words, the argument won’t work without it). A sufficient assumption is one that guarantees that the argument works.
So, while you should approach all assumption questions by trying to identify the hole in the argument, remember this small practical difference: a sufficient assumption, if true, makes the argument true. A necessary assumption, if false, makes the argument false.
Now, it’s true that many times an assumption that fills a hole in an argument can be both sufficient and necessary. In the examples above, for example, this distinction is irrelevant, because the holes in the arguments can only be filled one way, so the missing assumptions were both necessary and sufficient. But, as we’ve said elsewhere, necessary conditions may not be sufficient and sufficient conditions may not be necessary.
So, you want to make sure that when you are looking through answers in a necessary assumption question, you’re looking for something that if false would ruin the argument. When you are looking through answers in a sufficient assumption question, you’re looking for answers that if true would guarantee the argument.
In other words, sufficient assumptions can be sometimes go farther than they have to to complete the argument – necessary assumptions cannot. Conversely, necessary assumptions can sometimes be insufficient to complete the argument (in other words, they can still leave the argument in doubt even if true). Sufficient assumptions, however, always guarantee the conclusion is true.
This difference is borne out in the following litmus test, which you can use on all assumption questions. If you’re down to more than one answer and you’re not sure which one it is, always try this:
On sufficient assumption questions, make the answer choice true and see if that guarantees the conclusion.
On necessary assumption questions, make the answer choice false and see if that ruins the conclusion.
You can tell from the way the question is worded whether it is asking for a necessary or sufficient assumption.
Possible necessary assumption question wordings:
- The argument requires/relies on/depends on which one of the following assumptions?
- Which one of the following is an assumption required by the argument?
- The argument makes the assumption that
- The argument requires/depends on/relies on assuming which one of the following?
Possible sufficient assumption question wordings:
- The conclusion follows logically if which one of the following is assumed?
- Which one of the following, if true, allows the conclusion to be properly drawn?
- The conclusion of the argument can be properly drawn if which one of the following is assumed?
- Which one of the following principles, if true, justifies the conclusion?
Let’s look at an actual example of a sufficient assumption question from June 2007:
The conclusion here is that Murray cannot be accepted as Executive Administrator, and the rest of the paragraph is brought as support.
Many people make a mistake on this question, but see if you can identify the missing gap between the support and the conclusion. (Often, the gap will be between two things that appear to be the same thing, but they’re not – that’s what can make it so tricky to spot!)
The gap is the following:
The only thing that this information proves is that Murray cannot be appointed to the executive board (since he is a felon and no felons can be appointed to the board). That much is explicit. But, the conclusion says something slightly different. It says that Murray cannot be accepted as Executive Administrator.
Thus, the gap is between those two things. Since Murray can’t be appointed to the board, it’s taken for granted that he can’t be accepted as administrator. The missing assumption that would complete this argument, therefore, is that anyone ineligible to be appointed to the executive board also cannot be accepted as Executive Administrator. This looks like (B) here.
Using our litmus test from above, if we make (B) true, that guarantees the argument’s conclusion – since we already know that Murray can’t be appointed to the board, if (B) is true, that guarantees that he can’t become Executive Administrator, which is the conclusion being argued here.
Let’s look at a necessary assumption example from the same test:
Here, the conclusion is the first sentence. (How do I know that? Because it’s followed by the words “after all”.) The conclusion is that symmetrical spine exercise is needed for a healthy back.
The main piece of evidence is cited immediately following the conclusion – namely, that balanced muscle development is needed for a healthy back.
This argument is very simple, despite how long and wordy the paragraph is! Everything else was supplementary to this basic structure.
Can you find the missing link?
I’ll give you a hint – you can map this argument out as follows:
A is needed for C. After all, B is needed for C.
Thus, A = symmetrical spine exercise, B = balanced muscle development, and C = healthy back.
Recall what you know about conditional chains. The missing assumption must be that…A is needed for B!
In other words, you must assume that symmetrical spine exercise is needed for balanced muscle development.
You can map out this argument as follows, with the missing assumption shown as a transparent arrow (here, the arrows mean “is needed for”):
Symmetrical spine exercise ⇨ balanced muscle development ➔ healthy back
Symmetrical spine exercise ➔ healthy back
The conclusion is always a bridge connecting the “beginning” of the evidence with the “end” of an evidence, and the assumption is the missing tile in the bridge.
Now, all you have to do is look for an answer in the answer choices that says something to the effect of “Symmetrical spine exercise is needed for balanced muscle development”.
That’s right, (B) says exactly that! (Saying that exercising the two sides unequally results in unbalanced muscle development is equivalent to saying that you need to exercise the two sides equally in order to have balanced muscle development.)
These questions can be very tricky, but use this guide as a reference, and practice makes perfect!
- Look for the gap as you read the argument in order to predict the answer
- Think of the evidence as a bridge to the conclusion, and the assumption as the missing tile in the bridge
- Necessary assumptions, if false, make the argument false
- Sufficient assumptions, if true, make the argument true
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