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In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and

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In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and  [#permalink]

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New post 30 Jun 2017, 03:20
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In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and (3/7)th of the Canadian stamps were issued before 1940. If 192 stamps in Diana’s collection are Canadian stamps that were issued in 1940 or later, how many stamps in her collection are not Canadian?

(A) 84
(B) 88
(C) 96
(D) 104
(E) 112

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In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and  [#permalink]

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New post 30 Jun 2017, 03:37
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Bunuel wrote:
In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and (3/7)th of the Canadian stamps were issued before 1940. If 192 stamps in Diana’s collection are Canadian stamps that were issued in 1940 or later, how many stamps in her collection are not Canadian?

(A) 84
(B) 88
(C) 96
(D) 104
(E) 112


Let total number of stamps be \(= x\)

(4/5)th of the stamps are Canadian \(= \frac{4}{5}x\)

Number of stamps that are Not Canadian \(= (1 - \frac{4}{5})x = (\frac{5-4}{5})x = \frac{1}{5}x\)

(3/7)th of the Canadian stamps were issued before 1940 \(= \frac{3}{7}*\frac{4}{5}x\)

Canadian stamps that were issued in 1940 or later \(= (1-\frac{3}{7})\frac{4}{5}x = (\frac{7-3}{7})\frac{4}{5}x = \frac{4}{7}*\frac{4}{5}x\)

192 stamps in Diana’s collection are Canadian stamps that were issued in 1940 or later

\(\frac{4}{7}*\frac{4}{5}x = 192\)

\(x = \frac{192 * 5 * 7}{4 *4} = 420\)

Therefore Total number of Stamps \(= 420\)

Stamps in Diana’s collection are not Canadian \(= \frac{1}{5}x = \frac{420}{5} = 84\)

Answer (A)...
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Re: In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and  [#permalink]

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New post 30 Jun 2017, 09:12
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Eliminate options B,C,D since they are not divisible by 7 (3/7th of Canadian Stamps is an integer- which implies the total also must be divisible by 7). The total hence has to be either 84*5=420 or 112*5 =560. If it is 420, 420*4/5 * 4/7 = 192. Hence option A is the correct answer.
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Re: In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and  [#permalink]

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New post 02 Jul 2017, 06:23
Let S be total stamps
S*4/5*4/7 = 192
S=420
Non Canadian stamps = 1/5*420 = 84
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In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and  [#permalink]

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New post 03 Jul 2017, 08:12
Bunuel wrote:
In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and (3/7)th of the Canadian stamps were issued before 1940. If 192 stamps in Diana’s collection are Canadian stamps that were issued in 1940 or later, how many stamps in her collection are not Canadian?

(A) 84
(B) 88
(C) 96
(D) 104
(E) 112


Let x be the total number of stamps. Then

4x/5 * 4/7 = 192 (since 3/7 of the canadian stamps were issued before 1940, the remaining i.e. 4/7 would have been issued after 1940, which is equal to 192.)

solving this we will get x = 420

1/5 of 420 is 84.

Hence, answer is (A)
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Re: In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and  [#permalink]

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New post 04 Jul 2017, 07:53
Bunuel wrote:
In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and (3/7)th of the Canadian stamps were issued before 1940. If 192 stamps in Diana’s collection are Canadian stamps that were issued in 1940 or later, how many stamps in her collection are not Canadian?

(A) 84
(B) 88
(C) 96
(D) 104
(E) 112


We can let n = the total number of stamps.

Since 4/5 of the stamps are Canadian:

4n/5 = Canadian stamps, so n/5 = non-Canadian stamps

Since 3/7 of the Canadian stamps were issued before 1940:

(3/7)(4n/5) = 12n/35 Canadian stamps issued before 1940, so (4/7)(4n/5) = 16n/35 = the number of Canadian stamps issued in or after 1940. Thus:

16n/35 = 192

n = (192 x 35)/16

n = 12 x 35

n = 420

Thus, 420/5 = 84 stamps are not Canadian.

Answer: A
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Re: In Diana’s stamp collection, (4/5)th of the stamps are Canadian, and   [#permalink] 04 Jul 2017, 07:53
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