During a sale, linen shirts are discounted by $10 each, and

Question

During a sale, linen shirts were discounted by $10 each, and all other shirts were discounted by $5 each. Craig bought six more silk shirts than linen shirts, and half as many linen shirts as cotton shirts. If more than $\frac{2}{5}$ of the shirts he bought were cotton, what is the minimum total discount Craig could have received?

(A) 180
(B) 190
(C) 200
(D) 205
(E) 210

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Official Answer

D

(A) 180
(B) 190
(C) 200
(D) 205
(E) 210

somya9 · Answer

Can someone explain why is not A ?

kevincan · Answer

What made you choose A ?

Adit_ · Answer

See the point is:
Always take critical point first I think you did just that.

40% cotton lets take.
Then 20% will be linen.
Remaining 40% = Silk.
Now we know Silk = 6+Linen.
If you notice this difference 6 = the diff in percentage too.
Which means = 20% of total = 6
Thus we get total good to be 30 from here.
We have 12 cotton, 12 silk, 6 linen from here.
This is when cotton is 40% but we have cotton>40%.

Now we have a combo of 12,12,6 like I mentioned but sadly we need to consider cotton over 40%.
Hmm well lets try increasing no.of cotton manually to next value.
If we take cotton=13 then 13/2 is not an integer so we need to take only even numbers.

So cotton = 14 now.
We have 14 cotton, then 14/2 = 7 linen and 7+6 = 13 silk.
Our new combo = 14,7,13
To check 14/34 is just over 40% as well.

Now discount here = 7*10 + 5*27 = 70+135 =  205 .

Hope it helps.

_____________________________

IMO this is pretty tough and needs quite a few layers in crisp thought process.
What is the exact source you are getting such lovely question  kevincan ? Thanks!

SnowGate · Answer

if you solved like me by setting up 2/5 ( cot + lin + silk ) = cot and you end up with lin = 6

1/2 cot = lin --> 2(6) = cot = 12

but we solved for when cotton is exactly 2/5 but the question said  more than

so just add +1 to linen in order for cotton to end up = 14

7 + Lin = Silk = 13

= 205

if you dont +1 you get A

Aman2487 · Answer

I got total shorts as 30 
L = 6
S=12
C=12 
So 6 x10 +12x5 + 12x5 = 180
Please explain why this is not right

During a sale, linen shirts are discounted by $10 each, and

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During a sale, linen shirts are discounted by $10 each, and

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