reto wrote:

A certain electronic circuit is produced in seven stages. The cumulative expenditure on each circuit, in cents, after completing production stage n, is given by the formula \(x=\frac{45}{1/m+4/2^n}\)where m is constant and 1≤n≤7. What is the cumulative expenditure on each circuit, in cents, after completing production stage 4?

(1) The cumulative expenditure on each circuit, after completing production stage 7 is 160¢.

(2) The cumulative expenditure on each circuit, after completing production stage 6 is 144¢.

Given: Expenditure after n stages is given by the formula \(x=\frac{45}{1/m+4/2^n}\)

Question: for n=4, Expenditure after 4 stages \(x=\frac{45}{1/m+4/2^n} = ?\) i.e. m is the only unknown variableQuestion Redefined: We need the value of m to answer this questionStatement 1: The cumulative expenditure on each circuit, after completing production stage 7 is 160¢.i.e. \(x=\frac{45}{1/m+4/2^7} = 160\)

Which, on solving will give us a unique value of m as the equation is a linear equation in single variable.

Hence,

SUFFICIENTStatement 2: The cumulative expenditure on each circuit, after completing production stage 6 is 144¢i.e. \(x=\frac{45}{1/m+4/2^6} = 144\)

Which, on solving will give us a unique value of m as the equation is a linear equation in single variable.

Hence,

SUFFICIENTAnswer: option

Please Note: We don't have to solve the entire equation when we are confident of getting a unique solution. GMAT DS checks our ability to understand whether statement is SUFFICIENT or NOT to answer the question.
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