ZArslan wrote:
Set S consists of more than two integers. Are all the numbers in set S negative?
(1) The product of any three integers in the list is negative
(2) The product of the smallest and largest integers in the list is a prime number.
Target question: Are all the numbers in set S negative? Statement 1: The product of any three integers in the list is negative There are only 2 scenarios in which the product of 3 integers is negative.
scenario #1: all 3 integers are negative
scenario #2: 2 integers are positive, and 1 integer is negative
So, here are two possible cases that satisfy statement 1:
Case a: set S = {-3, -2, -1}, in which case
all of the numbers in set S are negative Case b: set S = {-1, 1, 3}, in which case
not all of the numbers in set S are negative Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The product of the smallest and largest integers in the list is a prime number. Here are two possible cases that satisfy statement 2:
Case a: set S = {-3, -2, -1}, in which case
all of the numbers in set S are negative Case b: set S = {1, 2, 3}, in which case
not all of the numbers in set S are negative Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Earlier, we learned that, if the product of 3 integers is negative, then there are 2 possible scenarios:
- scenario #1: all 3 integers are negative
- scenario #2: 2 integers are positive, and 1 integer is negative
Statement 2 tells us that the product of the smallest and largest integers in the list is a prime number. In other word, the product of the smallest and largest integers is POSITIVE.
This allows us to eliminate scenario #2, because under this scenario, the smallest integer in set S would be negative and the largest would be positive, so the product would be NEGATIVE (and prime numbers, by definition, are positive)
This leaves us with scenario #1.
From here, we can conclude that, if the product of any three integers is ALWAYS negative, then
ALL of the integers in the set must be negative. Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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