research question

largest difference have to be with best subject and worst subject. so we have
d = e + 11
and we know
d - c = 2
2 is the minimum, so r - e must be more than 3.

We should have:
e
r = e + x (x >= 3)
c = e+ 9
d = e +11
total = 4*e + 20 + x = 48.

obviously, 4*e, 20 and 48 is divisible by 4, so x is also divisible by 4
which leave us with x = 4, 8 or larger.
Now you try and see x = 4 give r = 10 is an answer.
8 give a smaller answer than what is available (it gives 9) so anything bigger than 8 can be rejected.

it says d and c were his two best sections, not d was his best section, so surely d could be plus or minus c as we don't know whether c or d is the best section? It ends up making 4e + x + 24 = 48 (24 divisible by four)

largest difference have to be with best subject and worst subject

so the best subject has to be d
(because if c > d, then c - e > d - e, so largest difference won't be d - e, but c - e)

Oh I see, that makes sense! Sorry for misreading

largest difference have to be with best subject and worst subject. so we have
d = e + 11
and we know
d - c = 2
2 is the minimum, so r - e must be more than 3.

We should have:
e
r = e + x (x >= 3)
c = e+ 9
d = e +11
total = 4*e + 20 + x = 48.

obviously, 4*e, 20 and 48 is divisible by 4, so x is also divisible by 4
which leave us with x = 4, 8 or larger.
Now you try and see x = 4 give r = 10 is an answer.
8 give a smaller answer than what is available (it gives 9) so anything bigger than 8 can be rejected.

I’m stuck with 4e+20+x=48
Simplifying:
e+(x/4)=7
Since x>=3
x=4, 8, 12 or larger
If x=4, e=6
Therefore R=10

But if x=8, e=5 therefore R=13 which is also an option.

Ooops my mistake there, if x = 8 then c - r = 1 then it will be the smallest difference.
Sorry, not my best day lol

I’m quite lost. Is my working out wrong?

If x = 8 then
e = 5
r = e + 8 = 13
c = e + 9 = 14
d = e + 11 = 16
so the smallest difference is between c - r = 1, not d - c = 2 as required.

Thank you 🙏
BTW when I first read that the difference between design and construction was 2, I was confused by it because it made it seem like it was possible to have both of these scenarios:
D-C=2 or C-D=2

In case you're still confused I answered that earlier.
In a problem like this, if you see ambiguous information, immediately try to find a way to eliminate one of the possibilities. those questions should be solvable in 2 - 3 minutes (or less) ideally, so they won't give you too much, or too little info.

Just read it and it makes sense to me now
I really appreciate your help.