ari.banerjee wrote:

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

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?