Double negation in assumptions

[ishanbhat455]

Hi,

How do we negate an answer choice containing double negatives in assumptions CR question? Do we have to simply convert both the negatives into positives?

For example, consider these two options:

1. One of the firm's products could never stay profitable unless it was offered with a discount.

2. There is no way a product can stay profitable if that product is not sold without a discount.

[RonPurewal]

Don't try to make "rules" for this stuff. It's essentially impossible to do that.

Instead, just use common sense to think about what it means for the statement to be false.

1. Product X could never stay profitable unless it was offered with a discount.

(I changed "one of the firm's products" -- which doesn't have a clear meaning -- to "Product X".)

If this is false, then product X can stay profitable without a discount.

2. There is no way a product can stay profitable if that product is not sold without a discount.

This is a generalization about all products. For a generalization to be false, all you need is some counterexample.

So, if this is false, then there must be product(s) that can be profitable without a discount.

[ishanbhat455]

Don't try to make "rules" for this stuff. It's essentially impossible to do that.

Instead, just use common sense to think about what it means for the statement to be false.

1. Product X could never stay profitable unless it was offered with a discount.

(I changed "one of the firm's products" -- which doesn't have a clear meaning -- to "Product X".)

If this is false, then product X can stay profitable without a discount.

2. There is no way a product can stay profitable if that product is not sold without a discount.

This is a generalization about all products. For a generalization to be false, all you need is some counterexample.

So, if this is false, then there must be product(s) that can be profitable without a discount.

Thanks Ron for clarifying. While I agree with your explanation for the first example, I have a different opinion about the second.

Here's my thought process for the second:

Original sentence

2. There is no way a product can stay profitable if that product is not sold without a discount.

We can simplify the sentence as- "There is no way a product can stay profitable if that product is sold with a discount."

Then negate it this way-
"There is some way a product can stay profitable if that product is sold with a discount"

Our answers to this second example seem to be opposite to each other. Please let me know what you think about my solution above.

[RonPurewal]

Ah, yeah, you're right. I don't think I even noticed the second "not".

Where did you get these statements? There is no way GMAC would ever present you with such a circuitous statement on the official test. No way. At most, they'd provide your simplified version.
I tried Google, but all of the statements lead only back to this thread. Where did you get them?

[RonPurewal]

--

It's possible to make a sentence involving "not ... without" that can't be simplified -- just not in the case above.
E.g., let's say you have 2 dogs.
If each dog is not taken out regularly without the other one, it will be unable to overcome separation anxiety.

Here, not walked regularly without the other dog is not quite the same thing as walked regularly with the other dog. The first says you don't normally take one dog unless you also take the other one, but implies nothing about the frequency. The second implies that both dogs are taken out together often -- and allows for (though doesn't require) the idea that the dogs are also frequently walked separately.

Still, in this case, there are much more transparent ways to write the statement, e.g., To overcome separation anxiety, each dog should be walked regularly without the other one.

[JbhB682]

Hi - how you negate something with an adjective

Example 1

Example : normal levels of unemployment are rarely exceeded

Is the negation the following : normal levels of unemployment are frequently exceeded ?

Example 2

Example : knowledge about X generates more fear about UFO's than does knowledge of Y

Is the negation the following : knowledge about X DOES NOT generate more fear about UFO's than does knowledge of Y

[Sage Pearce-Higgins]

If you're applying the negation test to answer choices in CR, then the simplest way is simply to add the words 'It is not the case that...' to the beginning of the sentence. Alternatively, you can put the word 'not' in front of the main verb.

This is fairly easy to do for your second example:
It is not the case that knowledge about X generates more fear about UFO's than does knowledge of Y.
Or: Knowledge about X does not generate more fear about UFO's than does knowledge of Y.
This means that either knowledge of Y generates more fear than knowledge about X, or they generate the same amount of fear.

The first example is trickier:
It is not the case that normal levels of unemployment are rarely exceeded.
Or: Normal levels of unemployment are not rarely exceeded.
The problem seems to be that 'not rarely' could mean 'frequently' (or at least 'more often than rarely') or 'never' (i.e. 'less than rarely'). I would probably go for the first option (frequently). However, it depends on the context.

As always, we're looking for practical ways to solve problems. The Negation Test is a useful tool, but it definitely works more easily for some problems than for others.