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

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by Vincen » Sun Oct 15, 2017 2:46 pm
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 OA is C.

Why option B is wrong? If m=-2, then m<0 too. What is wrong?
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Source: — Problem Solving |

by Brent@GMATPrepNow » Sun Oct 15, 2017 2:51 pm
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
Brent Hanneson - Creator of GMATPrepNow.com
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by Brent@GMATPrepNow » Sun Oct 15, 2017 2:53 pm
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
Brent Hanneson - Creator of GMATPrepNow.com
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by Brent@GMATPrepNow » Sun Oct 15, 2017 2:59 pm
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
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Fri Dec 15, 2017 10:51 am
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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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