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S is a finite set of numbers. Does S contain more negative numbers tha

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S is a finite set of numbers. Does S contain more negative numbers tha  [#permalink]

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New post 22 Dec 2010, 20:48
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S is a finite set of numbers. Does S contain more negative numbers than positive numbers?

(1) The product of all the numbers in S is -1,200.
(2) There are 6 numbers in S.

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Re: S is a finite set of numbers. Does S contain more negative numbers tha  [#permalink]

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New post 22 Dec 2010, 22:00
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metallicafan wrote:
Is there an algebraic way to solve this question rather than picking numbers?

S is a finite set of numbers. Does S contain more negative numbers than positive numbers?
(1) The product of all the numbers in S is -1200.
(2) There 6 numbers in S.


Hi,

in general, there are two ways to attack DS questions: picking numbers and using concepts. Almost all questions can be done both ways.

If we want to attack this one using concepts:

(1) negative product means we have an odd number of negative terms and an unknown number of positive terms. So, no clue which we have more of - insufficient.

(2) no clue how many are negative or positive - insufficient.

Together: from (1), we know we must have 1, 3 or 5 negative terms. So, there could be:

1 negative, 5 positive
3 negative, 3 positive
5 negative, 1 positive

Are there more negatives than positives? It's still uncertain - choose (E).
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Re: S is a finite set of numbers. Does S contain more negative numbers tha  [#permalink]

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New post 22 Dec 2010, 22:27
Thanks skovinsky!
In your opinion, which way is better?
IMO, using concepts and algebraic solutions are better because when you pick numbers, there could be the possibility that you are not picking the right numbers, or maybe you are forgetting to review an important scenario.

What do you think?
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Re: S is a finite set of numbers. Does S contain more negative numbers tha  [#permalink]

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New post 23 Dec 2010, 02:01
metallicafan wrote:
Thanks skovinsky!
In your opinion, which way is better?
IMO, using concepts and algebraic solutions are better because when you pick numbers, there could be the possibility that you are not picking the right numbers, or maybe you are forgetting to review an important scenario.

What do you think?


If the concepts jump out at you, great - that's probably going to be the quickest approach.

However, some questions test abstract concepts which won't be immediately apparent. Also, there are quite a few number property questions for which picking numbers is quicker than abstract reasoning. For example, odd/even questions are great for picking numbers, since only the "oddness" or "evenness" matters, not the actual values - so once you choose 1 odd and 1 even, you know you've exhausted all the possibilities.

When you do a question in untimed practice, you should always ask yourself "what are all the different ways that I could approach this question?" and then try the question using each approach. It's only by practicing different methods that they'll be in your toolbox on test day.
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Re: S is a finite set of numbers. Does S contain more negative numbers tha  [#permalink]

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New post 24 May 2016, 05:16
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metallicafan wrote:
S is a finite set of numbers. Does S contain more negative numbers than positive numbers?

(1) The product of all the numbers in S is -1,200.
(2) There are 6 numbers in S.

Is there an algebraic way to solve this question rather than picking numbers?


Hi, this question doesn't require any analysis at all

A) Even 1 -ve number can cause the product to be -ve. A plethora of -ve numbers (totalling to an even no.) can still give +ve. No use
B) 6 numbers. So what? Of any number of combinations you pick, I can make any 2 +ve no.s(x and y) into -ve( -x and -y : product : xy) and they give same solution.

Answer is clearly E
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Re: S is a finite set of numbers. Does S contain more negative numbers tha  [#permalink]

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New post 15 Jul 2016, 22:06
metallicafan wrote:
S is a finite set of numbers. Does S contain more negative numbers than positive numbers?

(1) The product of all the numbers in S is -1,200.
(2) There are 6 numbers in S.

Is there an algebraic way to solve this question rather than picking numbers?


Statement 1) The product of all the numbers in S is -1,200.
We know that there are odd numbers of negative in the set
Insufficient

(2) There are 6 numbers in S.
No info about how many odd and even i
Insuffcient

Combine
We know that there are 6 numbers and either one, three or five of them are negative.

Not sufficient

E
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Re: S is a finite set of numbers. Does S contain more negative numbers tha  [#permalink]

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New post 05 Jul 2019, 07:35
From the question stem, we need to know each number in a finite set of numbers, let's have a look in each given statement:
ST1: This piece of info reminds us about Geometric Progressions, but we have no info about the total number in a sequence and its ratio. In the other hands, the product of an even number will be always positive; meanwhile, the product of an odd number is always negative if it contains both negative & positive numbers in a sequence---->NS

ST2: We know nothing more than the total number in a sequence, it can result in either a positive product or negative product which we couldn't define--->NS

ST1 + ST2: Combining all given info, we still don't know the number of positive and negative values in a sequence------>E
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Re: S is a finite set of numbers. Does S contain more negative numbers tha  [#permalink]

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New post 27 Jul 2019, 15:39
First tackled Statement 1 since it indicates product, so can utilize number properties of products/multiplication of negative/positive numbers.
If the product of all of the numbers is -1,200, then then only sets of - * + = - since according to number properties/theory + * + = + and - * - = +, and only - * + (or + * -) = -
However just knowing the product of the numbers does not tell you anything about the number of numbers within the set.
Statement 1 Insufficient by itself.

Statement 2 indicates there are 6 numbers in set S. Insufficient by itself because no information on the value of the numbers or total sum of set S.

Then trying to take Statement 1 and Statement 2 together, still insufficient because although we know the product of all 6 numbers in set S is -1,200, that could mean that a single number of the set is negative while all the rest are positive, or that an odd number like 5 of the set are negatives and one positive. Information is insufficient to determine if there are more negative or positive numbers in the set.

metallicafan wrote:
S is a finite set of numbers. Does S contain more negative numbers than positive numbers?

(1) The product of all the numbers in S is -1,200.
(2) There are 6 numbers in S.
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Re: S is a finite set of numbers. Does S contain more negative numbers tha   [#permalink] 27 Jul 2019, 15:39
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