How often have you made mistakes in CR and later realized that it was because of a tiny word – Some or Most? These tiny words that usually seem unimportant can make or break your performance in CR and are popularly known as Quantifiers. In this article, we will talk about these tiny-yet-significant words in detail and sort your worries around the same.
Flow of the article:
First, we will understand the importance of Quantifiers.
Then, we will take up the commonly tested Quantifiers and their negation in detail.
Next, we will solve 2 Official Questions to solidify our understanding.
And lastly, we will understand the takeaway with the help of a table.
Why are Quantifiers important?
Quantifiers define the size of the given sample or what we call – the sample space. In order to correctly analyse and assess the argument, it is very important to know the sample space indicated by such words. An incorrect understanding of what these terms signify or an oversight leading to completely missing out on the significance of these terms almost always leads to an inaccurate assessment of the problem at hand.
Let’s look at a simple passage and question:
“The corn farmers of Norland have been facing reduced yields since the last three years. One of the major causes identified behind this low yield is attacks by locusts. Some farmers in the village have decided to use genetically modified seeds, which though expensive, give rise to locust resistant plants.”
Which of the following can be inferred from the passage?
- The corn yields in Norland is expected to increase significantly
- The corn yields in Norland is expected to increase but not by a significant margin
- The corn yields in Norland is expected to increase.
To answer the above question confidently, we need to know how many farmers used GM seeds.
The word “some” defines the sample space of the segment “farmers who have decided to use genetically modified seeds” – how many farmers does this “some” include? Does “some” signify an exact number? Does it signify a small number or a high number? Or does it simply signify a range which has a minimum and a maximum? A clear idea of the sample space will help us solve the question easily.
Commonly Tested Quantifiers
1. All, each, every
These quantifiers include all of the mentioned segment. For example,
Scenario 1: If there are 100 students in the class, “all students” would mean all 100 and no fewer than 100.
Scenario 2: However, “all students in the class with short hair” cannot mean 100 students. Here the segment has changed from all students to all students in the class with short hair.
Similarly, in
Scenario 3: Each student in the class has maintain a minimum of 75% attendance – all 100 students have to maintain a minimum of 75% attendance.
Scenario 4: Every student in the class who submits his homework late will get punished, cannot mean all 100 students will get punished. Here, the segment has changed from every student to every student who submits his homework late.
In Assumption questions, we often use the negation test to confirm the correct answer choice. The correct negation of these quantifiers is therefore essential. We will look at the correct way of negating these quantifiers.
1.1 Negation of all, each, every
We need to be careful while negating these quantifiers. Let’s see why –
The natural opposite of “all” is “none” but when we are negating “all”, it is incorrect to assume the natural opposite. Instead, we should consider the logical opposite of all.
So, if all = 100
Not all = not 100 but anything fewer than 100, i.e., between 0 to 99 and that would include “0” and “99”.
2. Most, Majority, More than Half
These quantifiers mean more than 51% and up to 100% of the segment.
For example, if there are 100 students in the class,
Scenario 1: “most students ” would mean at least 51 students and could include all 100.
Scenario 2: However, “most students in the class with short hair” cannot definitely mean 100 students. Here, the segment has changed from most students to most students in the class with short hair. So, if there are 50 students with short hair, then “most students with short hair = 26-50
Scenario 3: Majority of the students in the class has to maintain a minimum of 75% attendance = 51 -100 students have to maintain a minimum of 75% attendance.
Scenario 4: More than half of the students in the class who submit their homework late will get punished, cannot mean all 100 students will get punished. Here, the segment has changed from More than half of the students to More than half of the students who submit their homework late. So, if 50 students submit their homework late, then more than half of such students = 26 to 50
2.1 Negation of most, majority, more than half
The natural opposite of “most” seems to be “some” but when we are negating “most”, it is incorrect to assume the natural opposite. Instead, we should consider the logical opposite of all.
So, the negation of
- Most – Not most (which means half or less, 0-50). This would include “0” and “50”.
- Majority – Not the majority (which means half or less, 0-50). This would include “0” and “50”.
- More than half – Not more than half/ not more than 51% (which means half or less, 0-50). This would include “0” and “50”.
3. Some
Contrary to the common understanding that “some” always implies a “plural” number, the correct sample space covered by “some” is “at least one” and could be more than one.
For example, if there are 100 students in the class, “some students ” would mean at least one student and could include all up to 100. Note that “some” can never mean “0”.
3.1 Negation of some
The negation of “some” = Not some or in other words “None” – 0
You might wonder how! Well, remember that “some” starts at “at least one”. Thus, the logical opposite of this would be “not even at least one”.
Thus, in the example we took up earlier,
“Some farmers in the village have decided to use genetically modified seeds”
The maximum that we can infer with absolute surety is that at least one farmer in the village has decided to use genetically modified seeds. There could be more than one such farmer and, in fact, all the farmers could have so decided. But when taking into consideration the impact of “some”, we can only be completely sure of “at least one”.
Now, you can easily tell which of the following statements is a correct inference from that passage:
- The corn yields in Norland is expected to increase significantly
- The corn yields in Norland is expected to increase but not by a significant margin
- The corn yields in Norland is expected to increase.
Yes! Only statement C can be definitely inferred. Even if “at least one” farmer uses the GM seeds, an increase can be expected, though one cannot infer how significant that increase might be.
Quantifiers in action in official questions
Let us take two simple official questions and see the impact of these quantifiers.
Question 1 –
Neuroscientist: Memory evolved to help animals react appropriately to situations they encounter by drawing on the past experience of similar situations. But this does not require that animals perfectly recall every detail of all their experiences. Instead, to function well, memory should generalize from past experiences that are similar to the current one.
The neuroscientist’s statements, if true, most strongly support which of the following conclusions?
(A) At least some animals perfectly recall every detail of at least some past experiences.
B) Perfectly recalling every detail of all their past experiences could help at least some animals react more appropriately than they otherwise would to new situations they encounter.
(C) Generalizing from past experiences requires clear memories of most if not all the details of those experiences.
(D) Recalling every detail of all past experiences would be incompatible with any ability to generalize from those experiences.
(E) Animals can often react more appropriately than they otherwise would to situations they encounter if they draw on generalizations from past experiences of similar situations.
ANALYZING THE STIMULUS
- According to a neuroscientist, the memory of animals evolved in a particular manner for a specific reason
- The reason was – To help the animals remember how they dealt with past situations and this would in turn help them to deal with present similar situations
- What is not required – they need not remember all the details of the past experiences
- What is required – For functioning well, their memory should just generalize the data from the past experiences and this generalized knowledge would be good enough for the animal to use while approaching a similar situation in the present.
ANALYZING THE QUESTION STEM
If what the neuroscientist says is absolutely true, then which of the answer options finds the strongest support from the information given in the passage.
ANSWER CHOICE ELIMINATION
- At least some animals perfectly recall every detail of at least some past experiences.
There are two parts to this statement
- At least some animals recall every detail- means there is at least one animal that recalls all the details
- Of at least some past experiences – means “at least one past experience”
The passage clearly suggests that all animals in general are supposed to have the ability to recall. From the passage we know that for the memory to adequately serve the animals in their present situation, it is not necessary for the animals to remember all detail of that situation. But the passage does not tell us how many, if any, animals can recall “perfectly every detail”. It is possible that none of the animals can really recall all details but can still generalize. This is a might be true choice.
Incorrect choice.
(B) Perfectly recalling every detail of all their past experiences could help at least some animals react more appropriately than they otherwise would to new situations they encounter.
This choice presents an ability and its benefit
Ability: To perfectly recall every detail of all past experiences
Benefit: at least some animals will be able to deal more appropriately to situations.
This means that if this ability is present, at least some animals can deal better with situations than if they did not fulfill this requirement.
From the passage we know that for the memory to adequately serve the animals in their present situation, it is not necessary for the animals to remember every detail of that situation. They can simply generalize without remembering all details. It is also possible that remembering all details of all past experiences is not very helpful.
This choice is a distortion of the given information.
Incorrect choice.
(C) Generalizing from past experiences requires clear memories of most if not all the details of those experiences.
This choice presents a requirement and an outcome
Requirement: The animals must have clear memories of most or all the details of the past experiences
Outcome: Then only can they generalize from their past experiences.
As per the passage, for the memory to function well, all that is required is to draw generalizations from past experiences. In order to draw these generalizations, whether every detail or most of it needs to be remembered or not is not supported by the passage. The requirements for generalizing are out of scope of the argument.
Incorrect choice.
(D) Recalling every detail of all past experiences would be incompatible with any ability to generalize from those experiences
This option talks about incompatibility/lack of connectivity between
- The ability to recall every detail of all past experiences
- Any ability to generalize from those experiences
This means if the animal has the former ability, it would not aid or maybe even hinder the latter ability
The passage says that in order to generalize from past experiences it is not necessary to remember every detail of those experiences. But this does not mean that if an animal can remember every detail of all past experiences it will not be able to generalize from those experiences. In fact, it is possible with more detailed recall an animal may be able to generalize better. This choice is a distortion and half-truth.
Incorrect choice.
(E) Animals can often react more appropriately than they otherwise would to situations they encounter if they draw on generalizations from past experiences of similar situations.
This talks about how animals can react to situations they encounter
- If they are able to apply generalizations from past experiences of similar situations
- If they are not able to apply generalizations from past experiences of similar situations
And the verdict is they would react better in the first case.
- As per the passage, memory evolved to help animals remember past experiences so that they could draw generalizations from those and apply them to similar current situations. (The key word here is “appropriately”).
If the purpose of the memory evolving in a certain manner was to help animals react appropriately to situations, they encounter by drawing on the past experience of similar situations, then generalizations will definitely help to serve that purpose. Had their memories not evolved in this manner, they would have been able to deal with situations less appropriately.
Correct Choice.
Question 2
Enterprise Bank currently requires customers with checking accounts to maintain a minimum balance or pay a monthly fee. Enterprise plans to offer accounts with no monthly fee and no minimum-balance requirement; to cover their projected administrative costs of $3 per account per month they plan to charge $30 for overdrawing an account. Since each month on average slightly more than 10 percent of Enterprise’s customers overdraw their accounts, bank officials predict the new accounts will generate a profit.
Which of the following, if true, most strongly supports the bank officials’ prediction?
(A) Some of Enterprise Bank’s current checking account customers are expected to switch to the new accounts once they are offered.
(B) One third of Enterprise Bank’s revenues are currently derived from monthly fees tied to checking accounts.
(C) Many checking account customers who occasionally pay a fee for not maintaining a minimum balance in their account generally maintain a balance well above the minimum.
(D) Customers whose checking accounts do not have a minimum-balance requirement are more likely than others to overdraw their checking accounts.
(E) Customers whose checking accounts do not have a minimum-balance requirement are more likely than others to write checks for small amounts.
ANALYZING THE STIMULUS
- Current situation: EB Customers who have checking accounts (CA) need to maintain a minimum balance in their account or pay a monthly fee.
- EB’s Plan: Offer customers new accounts with no minimum balance + no monthly fee.
- Administrative Costs for the Plan: $3 per account/per month
- EB’s plan to cover the costs: Charge any customer $30 for overdrawing an account.
- Data: On average, slightly >10% customers overdraw their accounts every month.
- Conclusion: Because of the data, EB expects new accounts to make profits for the bank.
PRE-THINKING
- The reasoning -The data – slightly >10% customers overdraw their accounts every month – is about customers who have to either maintain a minimum balance or pay a fee for their accounts. In such a scenario, it is observed that slightly >10% of them overdraw their accounts.
- The Missing Link:
- What if this percentage remains the same or worse, goes down? In that case, even after the new accounts are on, this customer base that overdraws may not be enough to generate profits from the new accounts.
- But if the bank officials expect profits from the new accounts, this customer base of just slightly >more than 10% should ideally increase significantly.
- Strengthener#1: The percentage of customers overdrawing their accounts post the new accounts will increase significantly.
- What if the customers who have the new accounts are less likely to overdraw their accounts per month? In that case too profits may not increase.
- Strengthener#2: The customers who have these new accounts are more likely to overdraw their accounts than the ones who have the old accounts.
ANSWER CHOICE ELIMINATION
(A) Some of Enterprise Bank’s current checking account customers are expected to switch to the new accounts once they are offered.
“Some” could be just “at least one “ or more and up to “all”. Hence, it is not enough to strengthen the conclusion as we do not know how many will switch and how many of the ones who switch will actually overdraw. The impact of this choice is ambiguous.
Incorrect choice.
(B) One third of Enterprise Bank’s revenues are currently derived from monthly fees tied to checking accounts.
If 1/3rd of the revenues come from monthly fees tied to checking accounts, then the bank stands to lose a good source of revenue. The new plan likely will not be able to compensate for such a huge portion. This statement is more of a weakener.
Incorrect choice.
(C) Many checking account customers who occasionally pay a fee for not maintaining a minimum balance in their account generally maintain a balance well above the minimum.
This option is talking about those people who sometimes pay up for overdrawing their accounts. So, these are not the people who will really contribute much to the bank’s revenue under the new plan. This choice is out of scope.
Incorrect choice.
(D) Customers whose checking accounts do not have a minimum-balance requirement are more likely than others to overdraw their checking accounts.
This is in line with our pre-thinking.
Correct choice.
(E) Customers whose checking accounts do not have a minimum-balance requirement are more likely than others to write checks for small amounts
The amount of checks does not matter at all. This is completely irrelevant.
Incorrect choice.
The Takeaway
The following table gives a round-up of the sample space covered by the above quantifiers and their negation in a segment size of 100.
| QUANTIFIERS | SAMPLE SPACE | NEGATION |
| ALL | All 100 students | Not all – 0 to 99 students |
| NOT ALL | 0 to 99 students | All – 100 students |
| MOST | 51 to 100 students | Not more than half – 0 to 50 students |
| SOME | 1 to 100 students but not 0 students | None – 0 students |
| NONE | 0 students | Some – 1 – 100 students |
Special mention – Many, few, several
These quantifiers in the context of GMAT CR imply more than 2 or three and could include the entire segment. In most cases, these are equated along the lines of “some” and GMAT does not really test you for the difference.
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