Question

Which calculation will ALWAYS have a result greater than 1? CLEAR CHECK 89 × a number less than 1 112 – a fraction less than 12 25 + a fraction less than 12 10 × a number less than 1

Answer 1

112 – a fraction less than 12

Explanation:

We need to look for only one value that will invalidate the claim.

We denote the unknown in the condition with
`x`.

Let's consider each individually:

1. 89 × a number less than 1

`89* x\le 1`

`x\le (1)/(89)`

We only need values that satisfy this inequality to invalidate the claim. Like 0, -1,...

2. 112 - a fraction less than 12

`112-x\le1`

`112-1\le x`

`111\le x`

`x\ge111`

But this is a contradiction because
`x` must be less than 12.

Hence, this is always true.

3. 25 + a fraction less than 12

`25+x\le1`

`x\le1-25`

`x\le-24`

Hence, all fractions less than or equal to
`-24` will invalidate the claim. Like -24, -25,...

4. 10 × a number less than 1

`10* x\le 1`

`x \le(1)/(10)`

We only need values that satisfy this inequality to invalidate the claim. Like 0, -1,...