Problem Solving

swerve wrote:In the quotient a/b positive, which of the following must be true?

A. a > 0
B. b > 0
C. ab > 0
D. a - b > 0
E. a + b > 0

GIVEN: a/b is positive
This means that a and b have the SAME SIGN (e.g., both are negative or both are positive)
Scan the answer choices....

Since a and b have the SAME SIGN, we know that the product ab must be positive
Answer: C

Cheers,
Brent

swerve wrote:In the quotient a/b positive, which of the following must be true?

A. a > 0
B. b > 0
C. ab > 0
D. a - b > 0
E. a + b > 0

Another approach...

The key word here is MUST

So, if we can find values of a and b that make an answer choice FALSE, then we can eliminate that answer choice.

For example, a = -3 and b = -1 satisfies the given condition that a/b is positive [since (-3)/(-1) = 3, and 3 is positive]

Now take the answer choices and plug in a = -3 and b = -1

We get:
(A) -3 > 0. FALSE. ELIMINATE A
(B) -1 > 0. FALSE. ELIMINATE B
(C) (-3)(-1) > 0 TRUE. KEEP C
(D) (-3) - (-1) > 0. FALSE. ELIMINATE D
(E) (-3) + (-1) > 0. FALSE. ELIMINATE E

By the process of elimination, the correct answer is C

Cheers,
Brent

swerve wrote:In the quotient a/b positive, which of the following must be true?

A. a > 0
B. b > 0
C. ab > 0
D. a - b > 0
E. a + b > 0

Since a/b is positive, we see that a and b must be the same sign, either both negative or both positive. In either case, we see that ab > 0.

Answer: C