GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
n is a number which lies between m and m. Which of the following must
[#permalink]
20 Mar 2023, 03:02
20 Mar 2023, 03:02
Expert Reply
1
Bookmarks
00:00
Question Stats:
9% (01:40) correct
90% (01:16) wrong based on 53 sessions
Hide Show timer Statistics
n is a number which lies between m and –m. Which of the following must be true?
Indicate all that apply
n – m > 0
m + n > 0
n > 0
|n| > 0
m > 0
|m| > 0
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE INEQUALITIES
Indicate all that apply
n – m > 0
m + n > 0
n > 0
|n| > 0
m > 0
|m| > 0
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE INEQUALITIES
Re: n is a number which lies between m and m. Which of the following must
[#permalink]
30 Mar 2023, 03:54
30 Mar 2023, 03:54
1
We are given that n is a number which lies between m and -m.
Since m is greater than -m, we know that n is greater than -m and less than m. Therefore, we can say that:
-m < n < m
Now, let's consider each statement:
n - m > 0: This statement may or may not be true, depending on the value of n and m. If n is greater than m, then n - m is positive. But if n is less than m, then n - m is negative.
m + n > 0: This statement is always true, since we know that -m < n < m. Adding m to both sides of the inequality gives:
m - m < n + m < m + m
0 < m + n < 2m
Since m and n are both less than m, their sum must be positive.
n > 0: This statement may or may not be true, depending on the value of n. If n is positive, then this statement is true. But if n is negative, then this statement is false.
|n| > 0: This statement is always true, since the absolute value of any number is always greater than or equal to 0.
m > 0: This statement may or may not be true, depending on the value of m. If m is positive, then this statement is true. But if m is negative, then this statement is false.
|m| > 0: This statement is always true, since the absolute value of any non-zero number is always greater than 0.
Therefore, the statements that must be true are:
m + n > 0
|n| > 0
|m| > 0
Answer: (B), (D), (F)
Since m is greater than -m, we know that n is greater than -m and less than m. Therefore, we can say that:
-m < n < m
Now, let's consider each statement:
n - m > 0: This statement may or may not be true, depending on the value of n and m. If n is greater than m, then n - m is positive. But if n is less than m, then n - m is negative.
m + n > 0: This statement is always true, since we know that -m < n < m. Adding m to both sides of the inequality gives:
m - m < n + m < m + m
0 < m + n < 2m
Since m and n are both less than m, their sum must be positive.
n > 0: This statement may or may not be true, depending on the value of n. If n is positive, then this statement is true. But if n is negative, then this statement is false.
|n| > 0: This statement is always true, since the absolute value of any number is always greater than or equal to 0.
m > 0: This statement may or may not be true, depending on the value of m. If m is positive, then this statement is true. But if m is negative, then this statement is false.
|m| > 0: This statement is always true, since the absolute value of any non-zero number is always greater than 0.
Therefore, the statements that must be true are:
m + n > 0
|n| > 0
|m| > 0
Answer: (B), (D), (F)
Re: n is a number which lies between m and m. Which of the following must
[#permalink]
30 Mar 2023, 04:01
30 Mar 2023, 04:01
Expert Reply
The answer is ONLY F sir
