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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.

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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amanvermagmat
Archit3110
amanvermagmat
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...
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