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10 Nov 2023, 10:26
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A stamp collection that has an appraised value of $600 consists of twice as many foreign stamps as domestic stamps. If there is a total of 1,200 stamps in the collection, what is the total appraised value of all of the foreign stamps in the collection?
(1) The average (arithmetic mean) appraised value of the foreign stamps in the collection is $0.06 greater than the average appraised value of the domestic stamps.
(2) The sum of the average (arithmetic mean) appraised values of the foreign stamps and the domestic stamps from the collection is $0.98.
(1) The average (arithmetic mean) appraised value of the foreign stamps in the collection is $0.06 greater than the average appraised value of the domestic stamps.
(2) The sum of the average (arithmetic mean) appraised values of the foreign stamps and the domestic stamps from the collection is $0.98.
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05 May 2025, 23:00
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averagedude23
Total value = $600
F: D = 2:1 and total 1200 stamps are there so F = 800 and D = 400 stamps
Question: We need to find Total appraised value of all of the foreign stamps i.e. we need to find (800 * Avg value of foreign stamps)
(1) The average (arithmetic mean) appraised value of the foreign stamps in the collection is $0.06 greater than the average appraised value of the domestic stamps.
If avg value of D is x, that of F is (x + .06)
Then 800 * (x + .06) + 400 * (x) = $600
From here, we will get x and hence the avg value of foreign stamps as (x + 0.06)
Sufficient alone
(2) The sum of the average (arithmetic mean) appraised values of the foreign stamps and the domestic stamps from the collection is $0.98.
So if avg domestic stamp value is x, avg foreign stamp value is (0.98 - x)
800 * (0.98 - x) + 400 * (x) = $600
From here, we will get x and hence the avg value of foreign stamps as (0.98 - x)
Sufficient alone
Answer (D)
General Discussion
10 Nov 2023, 12:22
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averagedude23
- Appraised values of the foreign stamps = \(v_f\)
- Appraised values of the domestic stamps = \(v_d\)
..A stamp collection that has an appraised value of $600..
\(v_d+v_f = 600\) --- (1)
- The number of the foreign stamps = \(n_f\)
- The number of the domestic stamps = \(n_d\)
..consists of twice as many foreign stamps as domestic stamps. If there is a total of 1,200 stamps in the collection..
\(n_f = 2n_d\)
\(n_f + n_d = 1200\)
Upon solving we get
- \(n_d = 400\)
- \(n_f = 800\)
Question: what is the total appraised value of all of the foreign stamps in the collection?
\(v_f = ?\)
Statement 1
(1) The average (arithmetic mean) appraised value of the foreign stamps in the collection is $0.06 greater than the average appraised value of the domestic stamps.
\(\frac{v_f}{800} - \frac{v_d}{400} = 0.06\)
\(v_f - 2v_d = 0.06*800\)
\(v_f - 2v_d = 48\) --- (2)
From (1) and (2) we can find the value of \(v_d\) and \(v_f\)
Hence, this statement alone is sufficient. Eliminate B, C, and E.
Statement 2
(2) The sum of the average (arithmetic mean) appraised values of the foreign stamps and the domestic stamps from the collection is $0.98.
\(\frac{v_f}{800} + \frac{v_d}{400} = 0.98\)
\(v_f + 2_vd = 0.98*800\)
\(v_f + 2_vd = 784\) -- (3)
From (1) and (3) we can find the value of \(v_d\) and \(v_f\)
Hence, this statement alone is sufficient.
Option D
