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21 Feb 2025, 01:30
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C
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Difficulty:
25%
(medium)
Question Stats:
81% (01:40) correct
19%
(01:47)
wrong
based on 59
sessions
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If University of Virginia's total expenditure for books, periodicals, and newspapers last year was $60,000, how much of the expenditure was for books?
(1) The expenditure for newspapers was 20 percent greater than the expenditure for periodicals and books.
(2) The expenditure for newspapers was 30 percent greater than the expenditure for books.
(1) The expenditure for newspapers was 20 percent greater than the expenditure for periodicals and books.
(2) The expenditure for newspapers was 30 percent greater than the expenditure for books.
21 Feb 2025, 01:53
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B+P+N = 60000
B=?
B = 60000 - P - N - (1)
Statement 1
N = 1.2(P+B)
Substituting in 1
B = 60000 - P -1.2(P+B)
2.2B = 60000 - 2.2P
We don't know the value of P
Insufficient
Statement 2
N = 1.3B
Substituting in 1
B = 60000 - P -1.3B
2.3B = 60000 - P
We don't know the value of P
Insufficient
Combined, we have 2 equations with different coefficients. We should be able to get value for B. Sufficient
B=?
B = 60000 - P - N - (1)
Statement 1
N = 1.2(P+B)
Substituting in 1
B = 60000 - P -1.2(P+B)
2.2B = 60000 - 2.2P
We don't know the value of P
Insufficient
Statement 2
N = 1.3B
Substituting in 1
B = 60000 - P -1.3B
2.3B = 60000 - P
We don't know the value of P
Insufficient
Combined, we have 2 equations with different coefficients. We should be able to get value for B. Sufficient
Bunuel
21 Feb 2025, 09:36
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Let B, P, and N represent the expenditures for books, periodicals, and newspapers, respectively.
We are given that:
B + P + N = 60,000
Statement (1):
It states that the expenditure for newspapers was 20% greater than the combined expenditure for books and periodicals.
N = 1.2(B + P)
Substituting into the total expenditure equation:
B + P + 1.2(B + P) = 60,000
2.2(B + P) = 60,000
B + P = 60,000 / 2.2
Since we only know the sum of B and P but not their individual values, Statement (1) alone is insufficient.
Statement (2):
It states that the expenditure for newspapers was 30% greater than the expenditure for books.
N = 1.3B
Substituting into the total expenditure equation:
B + P + 1.3B = 60,000
2.3B + P = 60,000
Since we do not have a separate equation for P, Statement (2) alone is insufficient.
Combining Statements (1) and (2):
From Statement (1):
B + P = 60,000 / 2.2 ≈ 27,273
From Statement (2):
2.3B + P = 60,000
Substituting B + P from Statement (1) into Statement (2):
2.3B + (27,273) = 60,000
2.3B = 60,000 - 27,273
2.3B = 32,727
B ≈ 14,230
Since we can determine the value of B, both statements together are sufficient.
ANSWER: C (Both statements together are sufficient, but neither alone is sufficient).
We are given that:
B + P + N = 60,000
Statement (1):
It states that the expenditure for newspapers was 20% greater than the combined expenditure for books and periodicals.
N = 1.2(B + P)
Substituting into the total expenditure equation:
B + P + 1.2(B + P) = 60,000
2.2(B + P) = 60,000
B + P = 60,000 / 2.2
Since we only know the sum of B and P but not their individual values, Statement (1) alone is insufficient.
Statement (2):
It states that the expenditure for newspapers was 30% greater than the expenditure for books.
N = 1.3B
Substituting into the total expenditure equation:
B + P + 1.3B = 60,000
2.3B + P = 60,000
Since we do not have a separate equation for P, Statement (2) alone is insufficient.
Combining Statements (1) and (2):
From Statement (1):
B + P = 60,000 / 2.2 ≈ 27,273
From Statement (2):
2.3B + P = 60,000
Substituting B + P from Statement (1) into Statement (2):
2.3B + (27,273) = 60,000
2.3B = 60,000 - 27,273
2.3B = 32,727
B ≈ 14,230
Since we can determine the value of B, both statements together are sufficient.
ANSWER: C (Both statements together are sufficient, but neither alone is sufficient).
