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A certain electronic circuit is produced in seven stages. The cumulati

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A certain electronic circuit is produced in seven stages. The cumulati  [#permalink]

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14 Jun 2015, 03:24
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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¢.

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Re: A certain electronic circuit is produced in seven stages. The cumulati  [#permalink]

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15 Jun 2015, 06:57
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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 variable

Question Redefined: We need the value of m to answer this question

Statement 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, SUFFICIENT

Statement 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, SUFFICIENT

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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A certain electronic circuit is produced in seven stages. The cumulati  [#permalink]

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16 Jul 2016, 03:40
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¢.

Sequence Formula is given in the question stem. We don't even have to worry if this is AP or GP
Statement 1) Gives value of 5th term ; putting this in formula we can find the value of 4th term==> SUFFICIENT
Statement 2) Gives value of 6th term; putting this in formula we can find the value of 4th term==>SUFFICIENT

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Re: A certain electronic circuit is produced in seven stages. The cumulati  [#permalink]

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28 Jan 2019, 10:06
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Re: A certain electronic circuit is produced in seven stages. The cumulati   [#permalink] 28 Jan 2019, 10:06
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