   SEARCH HOME Math Central Quandaries & Queries  My name is Jordan and I am from London, England. I had a maths test the other day, and I could have a full score on the test if only I had understood this question: 'Look at these expressions' n-2, 2n,  n2, n/2, and 2/n A) Which expression gives the greatest value when n is between 1 and 2? B) Which expression gives the greatest value when n is between 0 and 1? C) Which expression gives the greatest value when n is negative? As you can see, this IS ONE question split in to three parts lol! Can you tell me how I go about tackling this question? I lost marks on the test because of not understanding the question. Thanks Regards Jordan, London Hi Jordan.

Let's look at (A) and you can use similar logic for parts (B) and (C).

If n is between 1 and 2 then:

n-2 is between 1-2 and 2-2 which is between -1 and 0.

2n is between 2(1) and 2(2) which is between 2 and 4.

n2 is between 12 and 22 which is between 1 and 4.

n/2 is between 1/2 and 2/2 which is between ½ and 1.

2/n is between 2/1 and 2/2 which is between 2 and 1.

So which of these has the greatest possible value? Both 2n and n2 go up to 4, so these two expressions tie for the greatest value.

You can solve the other problems using the same approach, Jordan.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.