Problem Solving

Vincen wrote:If m<0, which of the following must be true?
B) m ≤ -1
Why option B is wrong? If m=-2, then m<0 too. What is wrong?

If m < 0, then m could equal -0.5, in which case it is NOT TRUE that m ≤ -1

Cheers,
Brent

Vincen wrote:If m<0, which of the following must be true?

A. -100 < m < 100
B. m ≤ -1
C. m ≤ 1
D. m^2 ≥ 1/4
E. -100 < m < 0

Given: m < 0
In other words, m is NEGATIVE
If m is negative, then m is definitely less than (or equal to) 1
Answer: C

Vincen wrote:If m<0, which of the following must be true?

A. -100 < m < 100
B. m ≤ -1
C. m ≤ 1
D. m^2 ≥ 1/4
E. -100 < m < 0

The key word here is MUST
So, if we can show that an answer choice can be false, then we can ELIMINATE that answer choice.

If m is negative, then m COULD equal -200, in which case answer choices A and E are not true, because they state that m must be greater than -100
ELIMINATE A and E

Also, if m is negative, then m COULD equal -0.5, in which case answer choice B is not true, because it states that m must be less than -1
ELIMINATE B

Finally, if m is negative, then m COULD equal -1/5, which means m^2 = (-1/5)(-1/5) = 1/25, in which case answer choice D is not true, because it states that m^2 must be greater than 1/4
ELIMINATE D

By the process of elimination, the correct answer is C

Vincen wrote:If m<0, which of the following must be true?

A. -100 < m < 100
B. m ≤ -1
C. m ≤ 1
D. m^2 ≥ 1/4
E. -100 < m < 0

We are given that m is a negative number and must determine which of the answer choices must be true. Scanning the answers, we see that the only answer that has to be true IN ALL CASES is m must be less than or equal to 1, since all negative numbers are less than or equal to 1.

Answer: C