Sometimes, It’s About Quantity and Not Quality: ALL Statements

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Alright, as we mentioned before Logical Reasoning is going to be around 50% of your score. So, let’s focus on it a bit shall we? Quantity questions seem to be the bane of a lot of my students, and I just will not stand this because quantity questions have a bit of a check system to them!

What are you talking about Melody? Okay, let’s throw you an example:

All of Melody’s friends are smart. All of Melody’s friends are brunettes. Some brunettes like to drink coffee.

What we can definitely infer from this is that “some smart people are brunettes.” How did you do that?!? Well, give me a second and I’ll explain it to you!

There are three categories of quantity words that they all fall into: ALL, MOST or SOME. All the other words fall somewhere under one of those. Let’s go over a few examples:

 ALL words:  always, every, each, etc.

 MOST words:  almost all, more than half, a majority, 51% or higher, etc.

 SOME words:  a few, many, a couple, once in a while, sometimes occasionally, often, etc.

Now some of those may have jumped out to you in the SOME category. Why are the words “many” and “often” in the SOME category? Well MOST in LSAT land has to mean 51% or higher. It has to be completely unambiguous that the words means only 51% or higher. If it could mean half or less than half, then it must go in the SOME category. For instance, if there are twenty birds in your backyard and ten of them are blackbirds, it would still be correct to say, “Many of the birds outside are blackbirds,” even though only half of them are blackbirds. The same goes for the words “often.” If it doesn’t only mean 51% or higher then it’s in the SOME column.

Now that we know how to categorize different quantity words, we need to get to the different formulas of combining them. You need to remember that not all quantity words can combine with one another:

(1) ALL can combine with ALL, MOST and SOME.

(2) MOST can combine with ALL and MOST.

(3) SOME can only combine with ALL.

Repeat that ten times! Today I will explain to you one of the ways to combine ALL statements. ALL statements can be combined in two ways. The first is the example that I gave in the second paragraph. Let’s write it out in symbols. “M” will stand for Melody’s friends, “S” will stand for smart, “B” will stand for brunettes, and “C” will stand for like to drink coffee.

All of Melody’s friends are smart.

M - S

S ? M

All of Melody’s friends are brunettes.

M - B

B ? M

Some brunettes like to drink coffee.

B-some-C

C-some-B

Okay, so how are those silly symbols read again? The first line states: If one of Melody’s friends, then smart. The contrapositives are written beneath each line in red. The contrapositive of the first line read, if not smart, then not one of Melody’s friends. The second line reads: If one of Melody’s friends, then brunette. It’s contrapositive read: If not brunette, then not one of Melody’s friends. The last line reads: Some brunettes like coffee. Obviously, the some in between the “B” and the “C” means some. SOME statements do not have contrapositives but they are reversible. You can switch the variables and keep them in their original form as long as you make sure to keep the SOME in between them.

Now that you have symbol-ed everything and lined it all up, we take a look at the sufficient sides. In almost all cases, if the sufficient sides are the same in two lines, you can safely combine them. Take lines one and two. Both have “M” on the sufficient side. Therefore you can combine them together.

We cannot combine our some statement with our ALL statements because the only variable our some statement has in common with our ALL statements is B.

M - B

B-some-C

Note that B is necessary in our ALL statement so its existence tells us nothing about whether or not M is present. It is possible the brunette in question is my friend but it is also possible that she is my nemesis. Therefore, we cannot combine these statements.

Since line one and two are ALL statements, when you combine them they will become a SOME statement, resulting in:

M - S                         S-some-B

+          =

M - B                         B-some-S

This reads: Some smart people are brunettes or some brunettes are smart people. It’s as simple as that.

Let’s do another quick example:

Frogs are crazy animals, and all not crazy animals are purple animals, and all animals that are not frogs are silly.

What can we infer? Please excuse my ridiculous examples. :) Let’s write it out.

Frogs are crazy animals.

F - C

C ? F

All not crazy animals are purple animals.

C - P

P ? C

All animals that are not frogs are silly.

F - S

S ? F

What sufficient sides do you see that are similar? We’ve got the contrapositive of line one and line two. They both have not crazy animals as their sufficient. Therefore you can combine them to say: Some animals that are not frogs are purple, or some purple animals are not frogs:

C ?F                         F-some-P

+          =

C ?P                         P-some-F

So I hope that made a little bit of sense to you! We’ll continue with our quantity word understanding slowly and steadily. It’s important to focus on Logical Reasoning during your LSAT prep as it is a big chunk of your score!

Happy Studying!

Naz signature Updated on Aug 18, 2016