A bottle manufacturing company has \(5\) identical machines, each of which produces bottles at the same constant rate.

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A bottle manufacturing company has \(5\) identical machines, each of which produces bottles at the same constant rate. How many bottles will all \(5\) machines produce running simultaneously for \(x\) hours?

(1) Running simultaneously, \(3\) of the machines produce \(72,000\) bottles in \(2x\) hours?

(2) Running simultaneously, \(2\) of the machines produce \(24,000\) bottles in \(x\) hours?

Answer: D

Source: GMAT Paper Tests

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VJesus12 wrote:
Tue Sep 22, 2020 7:27 am
A bottle manufacturing company has \(5\) identical machines, each of which produces bottles at the same constant rate. How many bottles will all \(5\) machines produce running simultaneously for \(x\) hours?

(1) Running simultaneously, \(3\) of the machines produce \(72,000\) bottles in \(2x\) hours?

(2) Running simultaneously, \(2\) of the machines produce \(24,000\) bottles in \(x\) hours?

Answer: D

Source: GMAT Paper Tests
Let the rate of each machine be r. Thus we have to find out the value of \(5\cdot r \cdot x\). Thus, it is sufficient to find the value of \(r \cdot x\).

Statement 1 states that \(3 \cdot r \cdot 2x= 72000\). No need to calculate anything, as we know the value of \(r∗x\). Sufficient \(\Large{\color{green}\checkmark}\)

Statement 2 states that \(2∗r∗x = 24000\). Just as above, Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, D