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Please refer to the attachment. The answer is A. My approach (below)was to use test each answer option. Is there a quick way to do this? Is it obvious that it is 10?

If R=10, it leaves 38 for D, C and E.

R = 10

D = 17

C = 15

E = 6

This works, but if I tested the other options before 10. This question would have taken way to long. Is there any quick way to identify that 10 is the right answer?

If R=10, it leaves 38 for D, C and E.

R = 10

D = 17

C = 15

E = 6

This works, but if I tested the other options before 10. This question would have taken way to long. Is there any quick way to identify that 10 is the right answer?

Last edited by As.1997; 1 year ago

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#2

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.

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.

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#3

(Original post by

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.

**Arctic Kitten**)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.

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#4

(Original post by

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)

**joetr**)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)

(Original post by

largest difference have to be with best subject and worst subject

**Arctic Kitten**)largest difference have to be with best subject and worst subject

(because if c > d, then c - e > d - e, so largest difference won't be d - e, but c - e)

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#5

(Original post by

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)

**Arctic Kitten**)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)

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#6

(Original post by

Oh I see, that makes sense! Sorry for misreading

**joetr**)Oh I see, that makes sense! Sorry for misreading

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**Arctic Kitten**)

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.

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.

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#8

(Original post by

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.

**As.1997**)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.

Sorry, not my best day lol

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(Original post by

Ooops my mistake there, if x = 8 then c - r = 1 then it will be the smallest difference.

Sorry, not my best day lol

**Arctic Kitten**)Ooops my mistake there, if x = 8 then c - r = 1 then it will be the smallest difference.

Sorry, not my best day lol

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#10

(Original post by

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

**As.1997**)I’m quite lost. Is my working out wrong?

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.

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(Original post by

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.

**Arctic Kitten**)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.

I'm really quite amazed by how you avoided so many of the "traps".

In case you are interested, I went off track due to several issues which you resolved.

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

Similarly, for the largest difference, I had that same issue.

The other problems I had:

1) I didn't realise the biggest difference was the difference between the largest and smallest

2) I didn't realise x had to be greater than or equal to 3

Last edited by As.1997; 1 year ago

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#12

(Original post by

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

**As.1997**)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 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.

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(Original post by

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.

**Arctic Kitten**)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.

I really appreciate your help.

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