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n is a number which lies between m and m. Which of the following must
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20 Mar 2023, 03:02
20 Mar 2023, 03:02
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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
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30 Mar 2023, 04:01
30 Mar 2023, 04:01
Expert Reply
The answer is ONLY F sir
