How To Apply Negation Technique For Assumption Questions

[FA]

Hello,

My question is related to the application of Negation Technique while solving CR Assumption questions:

How should we apply the "Negation Technique" to CR questions which have the words some, any, few, none, either, neither, most, many etc. in the correct answer choices. In such cases, the negation becomes confusing. For example, what will be negation of any? would it be many or would it be none?

If we consider following to be the right answer choices to assumption questions, then how will the negation technique apply to them:

1 - Some of the school kids cheat on the exam.
2 - Any school kid can cheat on the exam.
3 - None of the school kids cheat on the exam.
4 - Few of the school kids cheat on the exam.
5- Either of the two school kids cheats on the exam.
6 - Neither of the two school kids cheats on the exam.
7 - Most of the school kids cheat on the exam.
8 - Many of the school kids cheat on the exam.

Negation is a powerful technique and the argument is killed if proper negation is applied to the right answer choices. But what if the application of negation gets confusing for the correct answer choices containing words some, none, few, either, neither, most, many, any etc.?

Regards
Farukh

[RonPurewal]

1/
in general, just think of "some xxxx..." as "this sort of thing happens". thus the negation is, essentially, that the thing doesn't happen.

so, if it's false that "some kids cheat", then, essentially, kids don't cheat.

3/
for exactly the same reason, you should negate this as "some of them cheat."
(if you wanted to be mathematically precise you'd write "at least one...", but you will never, ever, ever need that kind of nit-picky precision on this exam.)

[RonPurewal]

2/
this statement is the same as "there are no kids who can't".

so, the negation would be "some kids can't".

[RonPurewal]

4/
7/
"few" and "most" are essentially opposites, so these two statements work as negations of each other.

[RonPurewal]

6/
if this is false, then "one (or both) of them cheat".

5/
8/
these seem unlikely to appear in an assumption problem. can you cite any official problems in which these occur?

[FA]

Ron,

Thank you so much for replying. I am now clear about most of the concepts here. And I really appreciate the fact that you replied this early - it is still 4 am-ish in the Pacific time zone. Your dedication is exemplary.

You are right, I have not come across any Assumption question thus far that employs all of these points. The official questions where I got confused while using the negation method were:
1 OG12 (93) and OG13 (93)
2 OG12 (95) and OG13 (96)

These questions employ "any". But this made me think that perhaps the test takers may use the same ploy and use other words like some, none, most, few, either, neither etc. to confuse the test takers.

I will use my own examples to explain the point that I have now understood and the point where I am still a little stuck:

1 - For any two school kids, at least one cheats on the exam: In light of your prudent answers, this one is very straight forward now. The negation will be "For any two school kids, no one (or none) cheats on the exam


2 - Any school kid that doesn't cheat on the exam is not deceitful:This is where I am still stuck. How should we use negation in case there are multiple levels of similar words in the answer choices; like here we have any followed by doesn't followed by not. Will something like "No school kid that cheats on the exam is deceitful" work? because this is actually giving the same meaning as the original sentence I have used. So how should be negate such answer choices that have multiple levels of such negative words?


I hope you understand my question. I look forward to your response.

Regards
Farukh

[RonPurewal]

remember, statements of the kind described ("any x can do y") are, for the most part, equivalent to statements about "all x's".

we use "any" rather than "all" whenever it's clear that we're interested in individual instances.

e.g.,
if any person asks Raoul for a dollar, Raoul will give that person a dollar.
––> this is the same as "raoul is willing to give a dollar to all potential askers".
the logic is the same, but the wording above makes more sense because we're thinking in terms of individual actions.

vs.
All of the girls in the family are over six feet tall
––> you could also write this as "[i]Any girl in the family is over six feet tall". but, since "being 6 feet tall" isn't something that people individually do (or individually consider)--i.e., we can very easily picture all the girls in a row--"all" makes more sense.

from a pure logic standpoint there is no difference at all. so, when you negate one of these, you'll get "there is some exception".

[RonPurewal]

"for any two countries, xxx happens"
--> this is equivalent to saying that xxx exists for all possible pairings of two countries.

if that's false:
"there is (at least) one pair of two countries for which xxx DOES NOT happen"

e.g.,
this school is so small that any two people on campus will already know each other
negate: "there's (at least) one pair of people on campus who don't already know each other"
of course we could also write this in many ways; e.g., "one can find..."

[RonPurewal]

"any x that does xxxxx must do yyyy"
--> equivalent to saying that all "x's that do xxxx" also do yyyy.

if that's false:
"there is (at least) one x that does xxxx, but doesn't do yyyy".

e.g.,
anyone who looks at ron's face will turn to stone.
negate: there's someone who can look at ron's face without turning to stone.

[RutvikK933]

Hello Ron!

Excellent discussion. I came across a problem in PowerScore CR which doesn't use this for assumption, but uses it for an inference question. I'm not sure if I am allowed to reproduce it here so I'll just put in an excerpt and my query, if you please.

Page 77 of PowerScore CR Bible - [redacted]

I know it's there on the other manhattan forum, but it's not in as great detail and since it pertains to specific aspects asked on this thread, I thought I'd post here.

My question is this: The official explanation for not picking (C) is [redacted]


p.s. I am going through Thursdays with Ron one by one - it's AWESOME! Thanks for putting it together!

[RonPurewal]

hi, please check the forum rules regularly—the banned sources are sometimes updated.

powerscore has requested that we not use their questions on our forum, so powerscore is now a banned source.

(forum rules post: https://www.manhattanprep.com/gmat/foru ... t2718.html)

[RonPurewal]

also, even if you are posting questions from an allowed source, the rule is "one question per thread".
the point is to create a forum that's easily searchable, for future readers. if we start aggregating several "kinda sorta related" problems in a single thread, that purpose is undermined.
thanks.