If |m/5|1 , then which of the following must be true?

Question

If |m/5|>1 , then which of the following must be true? A. m>5 B. m<5 C. m=5 D. m not equal to 5 E. m<(-5)

shrouded1 · Accepted Answer

|m/5|>1 Hence |m| > 5 Which means either m>5 or m<-5 A. m>5 : Can be true (m=6) or false (m=-6) B. m<5 : Can be true (m=-6) or false (m=6) C. m=5 : Cannot be true. m is either >5 or <-5 D. m not equal to 5 : Has to be true as m is either >5 or <-5 E. m<(-5) : Can be true (m=-6) or false (m=6) So no ambiguity, answer is (d)

Bunuel · Answer

|\frac{m}{5}|>1

|m|>5

m<-5  or  m>5 .

Answer: D.

Or, you can simply notice that if m=5, then |m/5|=1, which violates |m/5|>1.

jimmy86 · Answer

I am still not convinced... we get m>5 from solving the inequality thus m>5 or m<-5 has to be true cause we derived it from a stated inequality.
Although i am certainly convinced with D.
So is the logic difference between MUST BE TRUE and CAN BE TURE??

shrouded1 · Answer

Yes, it's because the Q says must be true that ww have to rule out m>5

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lagomez · Answer

correct. M > 5 can be true but not must be true.

b2bt · Answer

I got the right anser but i'm still not satisfied what if m is 1 then 1/5 < 1

Bunuel · Answer

m cannot be 1, since in this case |m/5|>1 is not satisfied.

Ashleyyz · Answer

hi, I'm sorry but I don't understand why the answer is not A. if M is negative, it would violate the  >1 as well, so why is it M not greater than 5? Thank you in advance for explaining!

Bunuel · Answer

Notice that in  |\frac{m}{5}|>1 , |m/5| is in modulus. Now, if m is say -10, then we'd have  |\frac{-10}{5}|=2>1 .

Does this make sense?

saintsaurabh · Answer

Why can't the answer be A. M>5 would meet the need of the problem. Isn't it?
For that matter D does not fully answer it. For example, if M is 4 ("which is also not equal to 5") doesn't fit the problem.

Please explain. thanks in advance.
Saurabh

Bunuel · Answer

m>5 is not correct because m can be for example -10 (notice that this value of m satisfies |m/5|>1) and in this case m is NOT greater than 5.

As for D. The question asks: which of the following must be true? Ask yourself can m be 5? No, because if m=5, then the condition that |m/5|>1 is NOT satisfied, hence we can say for sure that m is not equal to 5.

Hope it's clear.

Archit3110 · Answer

one thing we can say seeing the expression is that whatever might be the sign of m be it would not be equal to 5 , since value of m irrespective of being > or< 5 .
and |m/5|>1 would be valid only when m not equal to 5
IMO D

If |m/5|>1 , then which of the following must be true?

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