Samantha picked a total of 10 integers, some positive and some negative, for a certain game. Did she choose more positive integers than negative integers?

(1) The sum of the integers she picked is less than zero.
(2) The product of the integers she picked is less than zero.
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Total integers picked = 10
Are positive integers more than negative integers?

Statement 1: The sum of the integers she picked is less than zero
Since nothing is said about the range of the numbers, we can pick any number.

Case 1: Negative number = - 1000
Positive numbers = 1, 2, 3, 4, 5, 6,7 , 8, 9

Case 2: Negative numbers = - 1, -2, -3, -4, -5, -6, -7, -8, -9
Positive Number = 10
Nothing can be said.
Insufficient

Statement 2: The product of the integers she picked is less than zero
This means the number of -ve numbers are odd.
Case 1: Number of negative numbers = 7.
Number of positive numbers = 3

Case 2: Number of negative numbers = 1
Number of positive number = 9
Again nothing can be said.
Insufficient

Combining both statements:
Still nothing can be said about the numbers.
Insufficient.

Option E

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Done. Thank you.
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