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Re: From 6 positive numbers and 6 negative numbers, how many [#permalink]
19 Apr 2014, 23:56

1

This post received KUDOS

6 +ves 6 -ves

Combinations can be taken for forming positive product.

(1).

-- ++

6c2*6c2

(2).

----

6c4

(3).

++++

6c4

Total = (1) + (2) + (3)

900/4 + 30

255 _________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

It get confused whenever we're supposed to add combinations vs multiply them.

Help is much appreciated.

Not sure I understand your logic there but hope that the solution below will clear your doubts.

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

For the product of 4 numbers to be positive there must be:

0 positive numbers and 4 negative numbers --> choosing all 4 numbers from 6 positive: C^4_6=15; 2 positive numbers and 2 negative numbers --> choosing 2 numbers from 6 positive numbers and 2 numbers from 6 negative numbers: C^2_6*C^2_6=225; 4 positive numbers and 0 negative numbers --> choosing all 4 numbers from 6 negative: C^4_6=15.

Total = 15 + 225 + 15 = 255.

Answer: E.

Also, note that the order of the chosen numbers is not important here. Meaning that if the positive numbers are 1, 2, 3, 4, 5, and 6 and negative numbers are -1, -2, -3, -4, -5, and -6, then {1, 2, 3, 4} selection is the same as {4, 3, 2, 1} selection, {-1, -2, -3, -4} selection is the same as {-4, -3, -2, -1} selection, {1, 2, -1, -2} selection is the same as {1, -1, 2, -2} selection...

It get confused whenever we're supposed to add combinations vs multiply them.

Help is much appreciated.

Not sure I understand your logic there but hope that the solution below will clear your doubts.

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

For the product of 4 numbers to be positive there must be:

0 positive numbers and 4 negative numbers --> choosing all 4 numbers from 6 positive: C^4_6=15; 2 positive numbers and 2 negative numbers --> choosing 2 numbers from 6 positive numbers and 2 numbers from 6 negative numbers: C^2_6*C^2_6=225; 4 positive numbers and 0 negative numbers --> choosing all 4 numbers from 6 negative: C^4_6=15.

Total = 15 + 225 + 15 = 255.

Answer: E.

Also, note that the order of the chosen numbers is not important here. Meaning that if the positive numbers are 1, 2, 3, 4, 5, and 6 and negative numbers are -1, -2, -3, -4, -5, and -6, then {1, 2, 3, 4} selection is the same as {4, 3, 2, 1} selection, {-1, -2, -3, -4} selection is the same as {-4, -3, -2, -1} selection, {1, 2, -1, -2} selection is the same as {1, -1, 2, -2} selection...

Hope it's clear.

Hi Bunuel,

Your answer is very clear but i'm stuck on one part(and this is the same part that I get on stuck on with every problem). How do you know when the order is important vs. when the order isn't important? Meaning, I can almost never decipher if I need to use the P or C formula. I've read the GMAT club book but haven't had any luck differentiating between "ordered" vs. "unordered" pairs.

Thanks, Russ

This should come with practice.

Not an universal rule, but below might help to distinguish: The words "Permutation" and "Arrangement" are synonymous and can be used interchangeably (order matters). The words "Combination", "Group" and "Selection" are synonymous and can be used interchangeably (order does not matters). _________________

selecting 4C6 of each group would give 30 as an ans. But if we can select 2C6 pos and 2C6 neg then it would give 225. Finally we can have a combination of both which gives 255.Think it is a bit unclear

We got 2 sets of 6 elements each.
In order for the product of 4 numbers to be positive we need even number (0,2,4,..) of -ve numbers. The following permutations of 4 numbers will yield a +ve product

# of -ve numbers, # of +ve numbers
0, 4
2, 2
4, 0

Assuming different elements in each set and given that we are trying to identify "groups of numbers" we have:
6P0*6P4 + 6P2*6P2 + 6P4*6P0
= 1*360 + 30*30 + 360*1
= 360 + 900 + 360
= 1620

On a second thought, I think going with combinations Vs permutations makes sense because:
# of -ve numbers, # of +ve numbers 0, 4 could be {}, {1,2,3,4}
2, 2 could be {-1,-2}, {1/2,100}
4, 0 could be {-1,-4,-6,-9.9},{}

For example, in the 2nd case above the group of 4 numbers formed by taking {-1,-2}, {1/2,100} together is {-1,-2,1/2,100}, which is no different from the re-arranged group {100,-1,1/2,-2} as far as the product of those 4 elements is concerned.

Since order isn't an issue, go combinations!
6C0*6C4 + 6C2*6C2 + 6C4*6C0
= 1*15 + 15*15 + 15*1
= 15 + 225 + 15
= 255 Still getting an F (none of the above)

mbaqst wrote:

I am getting F!

We got 2 sets of 6 elements each. In order for the product of 4 numbers to be positive we need even number (0,2,4,..) of -ve numbers. The following permutations of 4 numbers will yield a +ve product

# of -ve numbers, # of +ve numbers 0, 4 2, 2 4, 0

Assuming different elements in each set and given that we are trying to identify "groups of numbers" we have: 6P0*6P4 + 6P2*6P2 + 6P4*6P0 = 1*360 + 30*30 + 360*1 = 360 + 900 + 360 = 1620

The solution is C. I don't have the OE and my reasoning was the same that you all used to reach to 255. I will be working on this....

Any suggestion??

I think there is something wrong with your OA, as I think this is a combination problem rather than a permutation as what it matters is the sign of the number and not its order.

so in that case 12c4 would be the maximum amount of groups that could be made with that set, ignoring the sign of its multiplication and that is equal to 495 that is less than C

It get confused whenever we're supposed to add combinations vs multiply them.

Help is much appreciated.

Not sure I understand your logic there but hope that the solution below will clear your doubts.

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

For the product of 4 numbers to be positive there must be:

0 positive numbers and 4 negative numbers --> choosing all 4 numbers from 6 positive: C^4_6=15; 2 positive numbers and 2 negative numbers --> choosing 2 numbers from 6 positive numbers and 2 numbers from 6 negative numbers: C^2_6*C^2_6=225; 4 positive numbers and 0 negative numbers --> choosing all 4 numbers from 6 negative: C^4_6=15.

Total = 15 + 225 + 15 = 255.

Answer: E.

Also, note that the order of the chosen numbers is not important here. Meaning that if the positive numbers are 1, 2, 3, 4, 5, and 6 and negative numbers are -1, -2, -3, -4, -5, and -6, then {1, 2, 3, 4} selection is the same as {4, 3, 2, 1} selection, {-1, -2, -3, -4} selection is the same as {-4, -3, -2, -1} selection, {1, 2, -1, -2} selection is the same as {1, -1, 2, -2} selection...

Hope it's clear.

Thank you very much Bunuel, somehow I was reading that we needed to make 3 groups of 4 out of the 12 numbers. I have no idea why I interpreted the problem like that.

It get confused whenever we're supposed to add combinations vs multiply them.

Help is much appreciated.

Not sure I understand your logic there but hope that the solution below will clear your doubts.

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

For the product of 4 numbers to be positive there must be:

0 positive numbers and 4 negative numbers --> choosing all 4 numbers from 6 positive: C^4_6=15; 2 positive numbers and 2 negative numbers --> choosing 2 numbers from 6 positive numbers and 2 numbers from 6 negative numbers: C^2_6*C^2_6=225; 4 positive numbers and 0 negative numbers --> choosing all 4 numbers from 6 negative: C^4_6=15.

Total = 15 + 225 + 15 = 255.

Answer: E.

Also, note that the order of the chosen numbers is not important here. Meaning that if the positive numbers are 1, 2, 3, 4, 5, and 6 and negative numbers are -1, -2, -3, -4, -5, and -6, then {1, 2, 3, 4} selection is the same as {4, 3, 2, 1} selection, {-1, -2, -3, -4} selection is the same as {-4, -3, -2, -1} selection, {1, 2, -1, -2} selection is the same as {1, -1, 2, -2} selection...

Hope it's clear.

Hi Bunuel,

Your answer is very clear but i'm stuck on one part(and this is the same part that I get on stuck on with every problem). How do you know when the order is important vs. when the order isn't important? Meaning, I can almost never decipher if I need to use the P or C formula. I've read the GMAT club book but haven't had any luck differentiating between "ordered" vs. "unordered" pairs.

Re: From 6 positive numbers and 6 negative numbers, how many [#permalink]
24 Apr 2014, 18:23

Bunuel wrote:

russ9 wrote:

Hi Bunuel,

Your answer is very clear but i'm stuck on one part(and this is the same part that I get on stuck on with every problem). How do you know when the order is important vs. when the order isn't important? Meaning, I can almost never decipher if I need to use the P or C formula. I've read the GMAT club book but haven't had any luck differentiating between "ordered" vs. "unordered" pairs.

Thanks, Russ

This should come with practice.

Not an universal rule, but below might help to distinguish: The words "Permutation" and "Arrangement" are synonymous and can be used interchangeably (order matters). The words "Combination", "Group" and "Selection" are synonymous and can be used interchangeably (order does not matters).

Thanks a ton! I'll give this a shot.

gmatclubot

Re: From 6 positive numbers and 6 negative numbers, how many
[#permalink]
24 Apr 2014, 18:23