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# From 6 positive numbers and 6 negative numbers, how many gro

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Intern
Joined: 15 Jun 2010
Posts: 9
From 6 positive numbers and 6 negative numbers, how many gro  [#permalink]

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15 Apr 2014, 15:42
6
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:41) correct 37% (02:01) wrong based on 149 sessions

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From 6 positive numbers and 6 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?

A. 720
B. 625
C. 30
D. 960
E. 255
Retired Moderator
Joined: 20 Dec 2013
Posts: 172
Location: United States (NY)
GMAT 1: 640 Q44 V34
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WE: Consulting (Venture Capital)
Re: From 6 positive numbers and 6 negative numbers  [#permalink]

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15 Apr 2014, 17:31
1
1
Potential combinations of 4 numbers that will yield positive product

++++ 4C6
---- 4C6
++-- 2C6*2C6

4C6 + 4C6 + 2C6*2C6
15 +15 + 15*15 = 255
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Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India
Re: From 6 positive numbers and 6 negative numbers  [#permalink]

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15 Apr 2014, 19:41
2
2
tauchmeister wrote:
Another question, from a set I found here at home.

I don't know from where the source is.

Thanks

From 6 positive numbers and 6 negative numbers,
how many groups of 4 numbers, yielding a
positive product, can be formed?
a) 720
b) 625
c) 30
d) 960
e) 255

When will the product of 4 numbers be positive? It is positive when the number of negative numbers in the product is even i.e. when we have 0 negative numbers or 2 negative numbers or 4 negative numbers.

3 cases:

- 0 negative numbers - All numbers are positive - Selected in 6C4 = 15 ways

- 2 negative numbers - 2 are positive and 2 are negative - Selected in 6C2*6C2 = 15*15 = 225 ways

- 4 negative numbers - All numbers are negative - Selected in 6C4 = 15 ways

Total number of ways = 15 + 225 + 15 = 255

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Karishma
Veritas Prep GMAT Instructor

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Posts: 9459
Re: From 6 positive numbers and 6 negative numbers, how many gro  [#permalink]

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01 Nov 2018, 23:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: From 6 positive numbers and 6 negative numbers, how many gro &nbs [#permalink] 01 Nov 2018, 23:58
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