Absolute value question from Kaplan

Question

Hello Guys,
This is my first qs post here. I came across this problem and the answer explaination doesnt make any sense. Can someone please give me a good reason to the answer?

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

Thank you,
Ari

cxa0897 · Answer

The solution set to this problem is that |m| is greater than 5. i.e. 7 or -7 both satisfy this equation. A,B,E, are all possible solutions to the equations, but not the only solution so we can't say any of them must be true. For example, if m = -7, A is not true or if m is 7, B and E are not true. C is not true, because the equation states that m/5 cannot be equal to 1. Therefore, the solution has to be D. D is the only answer that is true under ALL SOLUTIONS for this equation. D satisfies 7 and -7, and any other possible number in the solution

generis · Answer

Glad you posted, ari.banerjee

Expanding a bit on cxa0897 's good answer; my focus is CAN vs. MUST It's an interesting question. It could boggle if you think too much. The crucial distinction: CAN vs. MUST it be true? We are looking for the latter. |\frac{m}{5}| > 1 . Solve for m Case One: \frac{m}{5} > 1 , so m > 5 Case Two: \frac{m}{5} < -1 , so m < -5 m > 5 OR m < -5 Which of the following MUST be true? A) m>5: Can be true. If m = 10, |\frac{10}{5}| > 1 MUST it be true? No. If m = -10, then m is NOT greater than 5, but |\frac{-10}{5}| is > 1 Can, not must. REJECT B) m<5: can be true If m < - 5, |-10/2| > 1 But can be FALSE. This choice violates the excluded interval from -5 to 5. If m = 3: |\frac{3}{5}| < 1 . REJECT c) m=5: CANNOT be true. \frac{5}{5} equals 1. The result should be greater than 1. REJECT d) m not equal to 5: MUST be true. \frac{5}{5}= 1 , and 1 will never be greater than 1. MUST be true is the logical converse of Answer C, stated a little more strongly. From reasoning in C, where 5/5 equals 1: that result is never going to be greater than 1. Hence m can never = 5. m not equal to 5 MUST be true. KEEP e) m<-5: same as (A) Can be true If m = -10, |-10/5| > 1 MUST be true? No. When m = 10 |10/2| > 1, but 10 is not less than -5. REJECT Answer D Does that help? If not, could you be a little more specific about what does not make sense?

bluetrain · Answer

I think A, D, E also be "must be true"

Sujan, Jack, and Mike are my family --> Mike is my family (must be true)
M>5 or M<-5 --> M>5 (must be true)
M<-5 (must be true)
of course M not equal to 5 must be true

Bunuel · Answer

Discussed here: if-m-5-1-then-which-of-the-following-must-be-true-103336.html Please follow the rules when posting a question: rules-for-posting-please-read-this-before-posting-133935.html TOPIC IS LOCKED AND ARCHIVED.

Absolute value question from Kaplan

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