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Zorluk: OrtaRates, Ratios, Percentages, and Applied Word Problems

A cloud infrastructure provider operates two categories of servers: High-Memory servers and High-CPU servers. Last month, High-Memory servers accounted for 40%40\% of the total server-hours logged by the provider, and High-CPU servers accounted for the remaining 60%60\%. What was the average operational cost per server-hour across all servers operated by the provider last month?

(1) The operational cost per server-hour for a High-Memory server was $3.00\$3.00 greater than the operational cost per server-hour for a High-CPU server.

(2) The total operational cost for a combination of 200200 server-hours of High-Memory servers and 300300 server-hours of High-CPU servers was $1,400\$1,400.

  1. A
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.Cevap
  3. C
    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. D
    EACH statement ALONE is sufficient.
  5. E
    Statements (1) and (2) TOGETHER are NOT sufficient.

Cevap

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
The correct response is that statement (2) alone is sufficient while statement (1) alone is not. Rephrasing the question stem shows that the overall average cost per hour is 0.40m+0.60c0.40m + 0.60c, where mm and cc represent the hourly rates of High-Memory and High-CPU servers, respectively. Statement (1) gives only the difference m−c=3m - c = 3, which leaves the overall average dependent on an unknown base rate. Statement (2) provides the equation 200m+300c=1,400200m + 300c = 1,400. Dividing this equation by 500500 yields 0.40m+0.60c=2.800.40m + 0.60c = 2.80, directly matching the target expression without requiring individual values for mm or cc.

Adım Adım Çözüm

1
Rephrase the question stem algebraically.
Let mm be the hourly cost of High-Memory servers and cc be the hourly cost of High-CPU servers. The target average cost per server-hour is A=0.40m+0.60cA = 0.40m + 0.60c.
Rephrasing identifies the exact linear combination of variables required to solve the question.
2
Evaluate Statement (1) independently.
Statement (1) states m=c+3m = c + 3. Substituting into the target gives A=0.40(c+3)+0.60c=c+1.20A = 0.40(c + 3) + 0.60c = c + 1.20.
Since the value of cc remains unknown, a single numerical value for AA cannot be determined. Statement (1) alone is NOT sufficient.
3
Evaluate Statement (2) independently.
Statement (2) gives 200m+300c=1,400200m + 300c = 1,400. Dividing the entire equation by 500500 yields 200500m+300500c=1,400500\frac{200}{500}m + \frac{300}{500}c = \frac{1,400}{500}, which simplifies to 0.40m+0.60c=2.800.40m + 0.60c = 2.80.
The coefficients of the given equation match the target proportion (40%40\% and 60%60\%), directly providing the exact value A=$2.80A = \$2.80. Statement (2) alone IS sufficient.

Anahtar Kavram

Weighted Averages and Expression Rephrasing in Data Sufficiency
Tahmini Süre:2m 0s
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Rates, Ratios, Percentages, and Applied Word Problems

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