Help! Confusing 11+ Maths question

Ambitious1999

So I’m helping my nephew study for his 11+ exams and we saw a confusing maths problem:

Two numbers have a difference of 18 and a product of 40. What is the largest of the two numbers?

A) 16
B) 24
C) 20
D) 18
E) 42

The correct answer was C) 20.

But we’re confused as to how this was worked out.

So I googled the question and

found a site which showed the working but gave a completely different answer to the 11+ practice paper.

https://adding.info/Sum-Difference/the-sum-of-two-numbers-is-40-and-their-difference-is-18.html

Can anyone show the workings as to how the answer is 20?

Thanks for any help.

(edited 1 year ago)

2*20
20-2

Original post by mqb2766

2*20
20-2

That’s what we thought but it could also be 16.

16 + 18 = 34

40 - 34 = 6

giving 6 and 16 and 16 would be the biggest.

it could also be any other number but obviously not B) 24 or D) 42.

Reply 3

mqb2766

Original post by Ambitious1999

That’s what we thought but it could also be 16.

16 + 18 = 34

40 - 34 = 6

giving 6 and 16 and 16 would be the biggest.

it could also be any other number but obviously not B) 24 or D) 42.

It cant be 16 as the largest number as the other would be 40/16 = 5/2 and their difference is 13 1/2.

One way to do it is a bit of intelligent guessing, so as the difference, product and the largest value are all integers, so must be the smallest number. So the two numbers are factor pairs of 40
40,1 has diff 39
20,2 - bingo,
all other factor pairs have a difference less than 18

You can set it up as a quadratic problem but this is beyond 11+.