A certain list consists of ten non-zero integers. Are all the integers

Question

A certain list consists of ten non-zero integers. Are all the integers in the list negative?
1) The sum of any pair of integers in the set is negative
2) The product of any pair of integers in the set is positive

yashikaaggarwal · Answer

1) The sum of any pair of integers in the set is negative
Case 1: 10 numbers are -1,-2,-3,-4.............-10 (consecutive negative numbers from -1 to -10)
the sum of any pair of integers in the set is negative (correct)
all no.s are negative

Case 2: 10 numbers are = 1,-2,-3,-4.............-10 (consecutive negative numbers from -2 to -10 and 1 is positive)
the sum of any pair of integers in the set is negative (correct)
But not all no. in the set are negative. 
INSUFFICIENT

2) The product of any pair of integers in the set is positive
Case 1: 10 numbers are -1,-2,-3,-4.............-10 (consecutive negative numbers from -1 to -10)
the product of any pair of integers in the set is positive (correct)
And, all no.s are negative

Case 2: 10 numbers are = 1,2,3,4.............10 (consecutive negative numbers from 1 to 10)
the product of any pair of integers in the set is positive (correct)
But all no.s in the set are non-negative. 
INSUFFICIENT

Combining both: 
only negative no. set have sum = -ve (for any 2 no.)
and product = +ve (for any 2 no.)
Sufficient

Answer is C

Primordialsage · Answer

How can you assume that the numbers are consecutive when it is not mentioned in the question?

chetan2u · Answer

A certain list consists of ten non-zero integers. Are all the integers in the list negative?
So the list could contain any integer except 0.
1) The sum of any pair of integers in the set is negative
If any pair picked from list adds up to a negative number,  then surely we cannot have more than ONE positive integer in the list or else they both will add up to a positive number. 
So we can have -3, -7..... -15 and 1. OR all negatives.
Insuff

2) The product of any pair of integers in the set is positive
So we can have all the numbers as positive or all the number as negative.
Insuff

Combined
Statement II tells us  all positive or all negative , and statement I tells us  all negative or all but 1 negative .
Hence, only possibility is that  all are negative .
C

A certain list consists of ten non-zero integers. Are all the integers

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