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# In a shop, 40% socks are white & rest are black. 60% socks a

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In a shop, 40% socks are white & rest are black. 60% socks a [#permalink]  16 Sep 2011, 08:10
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64% (02:46) correct 36% (01:45) wrong based on 14 sessions

In a shop, 40% socks are white & rest are black. 60% socks are made of cotton & rest are made of wool. 25% white socks are made of cotton & 20 of the black socks are made of wool. how many are black socks are made of cotton?
A)100 B)80 C)60 D)50 E)25
[Reveal] Spoiler: OA
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Re: Percent Problem [#permalink]  16 Sep 2011, 08:42
newmoon wrote:

In a shop, 40% socks are white & rest are black. 60% socks are made of cotton & rest are made of wool. 25% white socks are made of cotton & 20 of the black socks are made of wool. how many are black socks are made of cotton?
A)100 B)80 C)60 D)50 E)25

I'll prefer to solve this with plug n play method.

As we know, White Cotton socks are only 25% and Total Cotton socks is 60% - Hence Black Cotton socks has to be [highlight]HIGH[/highlight]number. Thats why we've to pick high number... say 100 or 80.

100 fits perfectly after relevant calculations. Hence answer A.

Cheers.
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Re: Percent Problem [#permalink]  16 Sep 2011, 08:48
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newmoon wrote:

In a shop, 40% socks are white & rest are black. 60% socks are made of cotton & rest are made of wool. 25% white socks are made of cotton & 20 of the black socks are made of wool. how many are black socks are made of cotton?
A)100 B)80 C)60 D)50 E)25

ok here u go.... lets say total number of socks = x

40% is white -> wht = 0.4x
Blk = 0.6 x

also 60% socks are made of cotton - > ct = 0.6x
wl = 0.4x

we know 25% of the white socks is cotton --> 1/4 (0.4x) = 0.1x = wh-ct
=> 0.3x = wh-wl

total wool is 0.4x => black wool socks = 0.4 x (total) - 0.3 x (wh-wl) = 0.1x given as 20

=> total number of socks = 200

= > total black socks = .6x = 120
total cotto black socks = 120 - 20 (bl-wl) = 100 hence A
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Re: Percent Problem [#permalink]  16 Sep 2011, 12:47
Good solution viks4gmat.
+1.
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Re: Percent Problem [#permalink]  16 Sep 2011, 19:32
total cotton 60T/100

total wool 40T/100

black wool = 20

total white = 40T/100
total black = 60T/100

total = T

given
25% of white is cotton . => (25/100)(40T/100) = 10T/100

=> white and wool = (40T/100) - (10T/100) = 30T/100

=> black and cotton = 50T/100 = T/2

also given black and wool = 20 = > 10T/100 = 20 => T = 200

=> black and cotton = 200/2 = 100

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Re: Percent Problem [#permalink]  20 Sep 2011, 05:18
Hi

I like this post:

You create good material for community.

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Re: Percent Problem [#permalink]  03 Oct 2011, 12:26
let total socks = 100x
w (white) = 40x, so b (black) = 60x
c (cotton) = 60x, so wl (wool) = 40x

wc (white + cotton) = 40x/4 = 10x
so, wwl (white + wool) = 40x-10x = 30x

bwl (black + wool) = 40x-30x = 10x -----> this is equal to 20
10x = 20 ...... x=2

bc (black + cotton) = 60x-10x = 50x OR 50*2 = 100
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Re: Percent Problem [#permalink]  03 Oct 2011, 18:21
All of the above approaches are great, but I always find these problems so much easier after making a table outlining all the information received. If you are not familiar with this method it is worth exploring.

Step 1) Put all information as given into table. We represents unknowns as 'x'. It's important to note that from the information given, we are told that there are 20 Black & Woolen socks
Step 2) Find an equation such that we can solve for x, solve for x
Step 3) Put information back into table and pluck out the number we need, in this case 100.
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Re: Percent Problem [#permalink]  03 Oct 2011, 20:51
newmoon wrote:

In a shop, 40% socks are white & rest are black. 60% socks are made of cotton & rest are made of wool. 25% white socks are made of cotton & 20 of the black socks are made of wool. how many are black socks are made of cotton?
A)100 B)80 C)60 D)50 E)25

Ok, let's try a different approach. We know that 60% of total socks(T) = Black socks (B). or we can rewrite it as 0.6 * T = B or T = B/0.6 or T = 10B/6 = 5B/3. Now, we know Total socks (T) can't be a fraction so B has to be a multiple of 3. Now we know B = Wool + Cotton or B = 20 + Cotton. Plug in the value of Cotton socks from options for which B becomes multiple of 3. Only options (A) & (E) are satisfying this criteria. For (E), T = 75 and white socks = 30. Now we know, 60% of the total socks are made from cotton i.e 60% of 75 = 45. Black cotton socks are 25 so white cotton socks should be 20 or 25% of 30 should be 20 which is not possible. So we can eliminate (E). Only option left is (A)

I hope it helps!!

Cheers!!
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Re: In a shop, 40% socks are white & rest are black. 60% socks a [#permalink]  05 Oct 2011, 09:17
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In a shop, 40% socks are white & rest are black. 60% socks are made of cotton & rest are made of wool. 25% white socks are made of cotton & 20 of the black socks are made of wool. how many are black socks are made of cotton?
A)100 B)80 C)60 D)50 E)25

White = 40 %
Blank = 60 %

Cotton = 60%
Wool = 40%

25 % of the total white socks are made of cotton,so 10 % of the total socks are white and cotton

Remaining 75 % of the White socks are wool.(30 % of overall)

10% of the wool socks are lack = 20

from here remaining 50% black socks are cotton = 5*20 = 100

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Re: In a shop, 40% socks are white & rest are black. 60% socks a   [#permalink] 05 Oct 2011, 09:17
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