# Largest possible difference between two numbers

I came across this practise question for a government numeracy test:

What is the largest possible difference between 10 & 20 to 2 decimal places?

What is the answer? As far as I can tell, the difference between 10 and 20 does not have a largest or smallest solution, but only one, which is equal to 10.

• Do you have a link to this test? I'd be curious to see what else they were asking. – lulu Jun 8 at 18:23
• – Nick Jun 8 at 18:45
• The rest of the questions seem perfectly sensible...I think they just phrased this one poorly. – lulu Jun 8 at 18:48

Here's a possible interpretation.

Looking at the quiz linked in comments to the OP we find the following questions, with Q21 being the question from the OP:

1. What is the smallest number to 2 decimal places that can be rounded to 20?
2. What is the largest number to 2 decimal places that can be rounded to 20?
3. What is the largest possible difference between 10 & 20 to 2 decimal places?

I think that Q21 is meant to follow from the answers to Q19 and Q20, but the questions are badly worded and open to interpretation.

Is $$19.50$$ the answer to Q19 (the smallest number to two decimal places that rounds to the integer $$20$$)? Or is it $$19.995$$ (the smallest number that, when rounded to two decimal places, gives $$20.00$$)?

Similarly, does Q20 give $$20.49$$ or $$20.00499999...$$?

Suppose we take the first alternative in both cases, with the equivalent answer for the value $$10$$. Then I think the intended answer for Q21 would be:

$$20.49-9.50=10.99$$.

I do think the question is intended to highlight rounding up and rounding down. It just does so very poorly.

• While I think the answer from Ross is technically correct, I’m going to accept this one because it presents an interpretation of the question which the author probably meant to convey, albeit very badly. – Nick Jun 9 at 8:06

The best I can read it is to say there are two possible differences, $$+10.00$$ and $$-10.00$$ and $$+10.00$$ is larger. I agree it is badly worded.

• Great answer. Especially quoting the answer to two decimal places, which is the what the question asks. I think the question was probably intended to ask something different ... and it is of some concern if poor mathematics is being used to make administrative decisions. – Mark Bennet Jun 8 at 18:06