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Re: n is a number which lies between m and m. Which of the following must [#permalink]
Carcass wrote:
The answer is ONLY F sir


Uh, can you explain?
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Re: n is a number which lies between m and m. Which of the following must [#permalink]
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As 𝑛 is a number which lies between – 𝑚 and 𝑚 on the number line, hence 𝑚 cannot be 𝑧𝑒𝑟𝑜 but it can be negative or positive. And 𝑛 is between – 𝑚 and 𝑚. Hence, 𝑛 can have any value, i.e., negative, 0 or positive.

Considering the options, we get,

A) 𝑛 − 𝑚 > 0 i.e. 𝑛 > 𝑚 {Not a must condition, it may or may not be true. If 𝑚 is negative, then 𝑛 > 𝑚 However, if 𝑚 is positive, then 𝑛 < 𝑚 For example, 𝑚 = 2 𝑜𝑟 𝑚 = −2, for both these values −2 < 𝑛 < 2.
B) 𝑚 + 𝑛 > 0 i.e. 𝑛 > −𝑚 {Not a must condition, it may or may not be true} Both 𝑚 𝑎𝑛𝑑 𝑛 can be positive, then 𝑚 + 𝑛 > 0 However , Both 𝑚 and 𝑛 can be negative, then 𝑚 + 𝑛 < 0 For example, 𝑚 = 2 𝑜𝑟 𝑚 = −2, and 𝑛 can be 1 and -1, respectively. For both these values −2 < 𝑛 < 2
C) 𝑛 > 0 {Not a must condition as 𝑛 could be 𝑧𝑒𝑟𝑜 as well}
D) |𝑛| > 0 {Not a must condition as 𝑛 could be 𝑧𝑒𝑟𝑜 as well}
E) 𝑚 > 0 {Not a must condition as 𝑚 could be negative also}
F) |𝑚| > 0 {Since 𝑛 is a number which lies between – 𝑚 and 𝑚, hence 𝑚 cannot be 𝑧𝑒𝑟𝑜 but it can be negative or positive the absolute value will always be greater than 𝑧𝑒𝑟𝑜, hence the must be true condition}
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Re: n is a number which lies between m and m. Which of the following must [#permalink]
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