Search our library of University questions

Top answers

All subjects

University

Find all positive integers n such that 12n-119 and 75n-539 are both perfect squares. Let N be the sum of all possible values of n. Find N.

Let 75n - 539 = l^2 and 12n - 119 = k^2 . where n is a natural number.

Multiply 75n - 539 = l^2 by 4 to give 300n - 2156 =4l^2 and 12n - 119 = k^2 by 25 to give 300n - 2975 = 25k^2.

Subtract...

Answered by Soham K. • STEP tutor

7606 Views

The UKCAT test has a lot of questions and not very long to complete them. How can I make sure I get through them all in the time allowed?

Time pressure is one of the hardest aspects of the UKCAT but luckily it is an aspect that you can train for. Practicing questions under time pressure is very important. Questions can be obtained from...

Answered by Nick O. • UCAT tutor

1824 Views

How do I evaluate something like 3070^2-3069^2?

This looks pretty daunting, but the key to this sort of a problem, which has come up a couple of times in previous PAT tests, is to recognise that this expression is actually the difference of two squa...

Answered by Sam C. • PAT tutor

2798 Views

I am worried about the quantitative reasoning section of the UKCAT as it doesn't look like A-Level maths! How can I best prepare?

The quantitative reasoning section of the UKCAT is designed to assess general numerical skill, and so may appear quite contrasting from the sort of maths you will be used to in A-Level. You almost need...

Answered by Eleanor B. • UCAT tutor

6615 Views

I'm most worried about how to approach multiple choice questions - do you have any tips or general techniques?

First advice I have for you - don't panic! As soon as you enter the room panicking, you will lose control of timing, won't pay as much attention to the wording of the passages, and will ultimately not ...

Answered by Natasha B. • LNAT tutor

8158 Views