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is the product cd positive?
1) $$3c=-8d^3$$
2) d>c+4
1) $$3c=-8d^3$$
2) d>c+4
Target question: Is the product cd positive?vaibhav101 wrote:is the product cd positive?
1) 3c = -8d³
2) d > c + 4
Statement 1: 3c = -8d³
Divide both sides by d to get: 3c/d = -8d²
Divide both sides by 3 to get: c/d = -8d²/3
Rewrite as: c/d = (-8/3)(d²)
Since d² is greater than or equal to zero for all values of d, and since -8/3 is NEGATIVE, we can rewrite our equation as: c/d = (NEGATIVE)(some number greater than or equal to zero)
(NEGATIVE)(some number greater than or equal to zero) = some number that is less than or equal to zero
So, c/d = some number less than or equal to zero
This means the quotient c/d CANNOT be positive
It also mean the product cd CANNOT be positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
ASIDE: the important concept here is that, if c/d is positive, then cd is also positive. Likewise, if c/d is negative, then cd is also negative.
Statement 2: d > c + 4
There are several values of c and d that satisfy statement 2. Here are two:
Case a: c = 1 and d = 10. Here, cd = (1)(10) = 10, so the answer to the target question is YES, cd IS positive
Case b: c = -1 and d = 5. Here, cd = (-1)(5) = -5, so the answer to the target question is NO, cd is NOT positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
