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# Six distinct integers are multiplied with each other. Is the product

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Six distinct integers are multiplied with each other. Is the product  [#permalink]

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13 Mar 2019, 12:08
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Difficulty:

85% (hard)

Question Stats:

26% (01:10) correct 74% (00:51) wrong based on 38 sessions

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Six distinct integers are multiplied with each other. Is the product of these six integers positive?

(1) Exactly three of these six distinct integers are positive.
(2) Exactly two of these six distinct integers are negative.
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Re: Six distinct integers are multiplied with each other. Is the product  [#permalink]

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14 Mar 2019, 07:06
Using Statement 1 alone, if we have three positive values, we have either three negative values, and a negative product, or we have a zero in there, and thus a product of zero, so the product of the six numbers is definitely not positive, and Statement 1 is sufficient.

Using Statement 2 alone, we don't know if we have a zero in the set, so the product might be zero or it might be positive. So the answer is A.
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Six distinct integers are multiplied with each other. Is the product  [#permalink]

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Updated on: 19 Mar 2019, 02:47
amanvermagmat wrote:
Six distinct integers are multiplied with each other. Is the product of these six integers positive?

(1) Exactly three of these six distinct integers are positive.
(2) Exactly two of these six distinct integers are negative.

below is my take on the question

given ; 6 distinct integers ; so they can be either +ve or -ve or 0
#1
Exactly three of these six distinct integers are positive : so if any of 3 integers are +ve , rest will be -ve or 0 ;product wont be +ve at all; sufficient
#2
Exactly two of these six distinct integers are negative ;so rest integers ; +ve product of all six integers ; +ve or it can be 0 ; so product may or may not be +ve; in sufficient

IMO A

Originally posted by Archit3110 on 17 Mar 2019, 23:56.
Last edited by Archit3110 on 19 Mar 2019, 02:47, edited 1 time in total.
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Re: Six distinct integers are multiplied with each other. Is the product  [#permalink]

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18 Mar 2019, 11:16
Archit3110 wrote:
amanvermagmat wrote:
Six distinct integers are multiplied with each other. Is the product of these six integers positive?

(1) Exactly three of these six distinct integers are positive.
(2) Exactly two of these six distinct integers are negative.

Hello amanvermagmat ; could you please provide solution on why A is correct..

below is my take on the question

given ; 6 distinct integers ; so they can be either +ve or -ve ; integer cannot be 0 because question has not specified that there are six non-negative integer..

#1
Exactly three of these six distinct integers are positive : so if any of 3 integers are +ve , rest will be -ve ; the product of all 6 integers = -ve ; sufficient
#2
Exactly two of these six distinct integers are negative ;so rest integers ; +ve product of all six integers ; +ve

we are getting both statements correct and with contradictory Yes /No answers?
IMO E would be correct answer..

Hello Archit

Why have you assumed that integers can only be either +ve or -ve. The question just says 'six distinct integers'; and 0 is also an integer.
From first statement, exaclty three integers are positive, so remaining three could be -ve or 0.
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Re: Six distinct integers are multiplied with each other. Is the product  [#permalink]

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19 Mar 2019, 02:45
amanvermagmat wrote:
Archit3110 wrote:
amanvermagmat wrote:
Six distinct integers are multiplied with each other. Is the product of these six integers positive?

(1) Exactly three of these six distinct integers are positive.
(2) Exactly two of these six distinct integers are negative.

Hello amanvermagmat ; could you please provide solution on why A is correct..

below is my take on the question

given ; 6 distinct integers ; so they can be either +ve or -ve ; integer cannot be 0 because question has not specified that there are six non-negative integer..

#1
Exactly three of these six distinct integers are positive : so if any of 3 integers are +ve , rest will be -ve ; the product of all 6 integers = -ve ; sufficient
#2
Exactly two of these six distinct integers are negative ;so rest integers ; +ve product of all six integers ; +ve

we are getting both statements correct and with contradictory Yes /No answers?
IMO E would be correct answer..

Hello Archit

Why have you assumed that integers can only be either +ve or -ve. The question just says 'six distinct integers'; and 0 is also an integer.
From first statement, exaclty three integers are positive, so remaining three could be -ve or 0.

amanvermagmat
I have understood where I went wrong on the question..
Its DS yes/no type ; so #1 we get definite no and #2 we get yes/no which is why A is correct...
Re: Six distinct integers are multiplied with each other. Is the product   [#permalink] 19 Mar 2019, 02:45
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