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# In a certain department store, which has four sizes of a specific

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Joined: 02 Sep 2009
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In a certain department store, which has four sizes of a specific  [#permalink]

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05 Sep 2017, 21:34
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Difficulty:

45% (medium)

Question Stats:

69% (02:02) correct 31% (02:15) wrong based on 127 sessions

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In a certain department store, which has four sizes of a specific shirt, there are 1/3 as many small shirts as medium shirts, and 1/2 as many large shirts as small shirts. If there are as many x-large shirts as large shirts, what percent of the shirts in the store are medium?

(A) 10%
(B) 25%
(C) 33%
(D) 50%
(E) 60%

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Re: In a certain department store, which has four sizes of a specific  [#permalink]

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05 Sep 2017, 22:56
Bunuel wrote:
In a certain department store, which has four sizes of a specific shirt, there are 1/3 as many small shirts as medium shirts, and 1/2 as many large shirts as small shirts. If there are as many x-large shirts as large shirts, what percent of the shirts in the store are medium?

(A) 10%
(B) 25%
(C) 33%
(D) 50%
(E) 60%

S=M/3 , L=S/2 , X-L=L

M=3S ====> S=M/3
M=6L ===> L=M/6
M=6XL ====> XL=M/6

S+M+L+XL = TOTAL
(M/3) + M + (M/6) + (M/6) = TOTAL
(2M+6M+2M)/6 = TOTAL
(10M)/6 = TOTAL
M = 6/10 * TOTAL
M= 3/5 *TOTAL
M = 3 *(0.2) *TOTAL
M= 0.6 * TOTAL

THUS, M IS 60% OF TOTAL.
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Re: In a certain department store, which has four sizes of a specific  [#permalink]

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06 Sep 2017, 00:46
Bunuel wrote:
In a certain department store, which has four sizes of a specific shirt, there are 1/3 as many small shirts as medium shirts, and 1/2 as many large shirts as small shirts. If there are as many x-large shirts as large shirts, what percent of the shirts in the store are medium?

(A) 10%
(B) 25%
(C) 33%
(D) 50%
(E) 60%

x-large shirts = 60
large shirts = 60
small shirts = 120
medium shirts = 360

360/600 = 60%
E
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Re: In a certain department store, which has four sizes of a specific  [#permalink]

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06 Sep 2017, 03:49
Bunuel wrote:
In a certain department store, which has four sizes of a specific shirt, there are 1/3 as many small shirts as medium shirts, and 1/2 as many large shirts as small shirts. If there are as many x-large shirts as large shirts, what percent of the shirts in the store are medium?

(A) 10%
(B) 25%
(C) 33%
(D) 50%
(E) 60%

S= M/3
L = S/2 = M/6
XL = L = M/6
M = M
Total = M/3 + M/6 + M/6 + M = 5m/3
Ratio medium/ Total = M/(5M/3) = 3/5 = 0.6 = 60% Answer E
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Re: In a certain department store, which has four sizes of a specific  [#permalink]

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11 Sep 2017, 11:03
Bunuel wrote:
In a certain department store, which has four sizes of a specific shirt, there are 1/3 as many small shirts as medium shirts, and 1/2 as many large shirts as small shirts. If there are as many x-large shirts as large shirts, what percent of the shirts in the store are medium?

(A) 10%
(B) 25%
(C) 33%
(D) 50%
(E) 60%

We can let the the number of small shirts = a, medium shirts = b, large shirts = c, and x-large shirts = d.

Since there are 1/3 as many small shirts as medium shirts:

(1/3)b = a

b = 3a

Since there are 1/2 as many large shirts as small shirts:

c = (1/2)a

Since there are as many x-large shirts as large shirts:

c = d = (1/2)a

The total number of shirts, in terms of a, is:

a + b + c + d = a + 3a + a/2 + a/2 = a + 3a + a = 5a

So, medium shirts are 3a/5a = 3/5 = 60% of the total shirts.

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Re: In a certain department store, which has four sizes of a specific   [#permalink] 11 Sep 2017, 11:03
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