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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Tue Sep 22, 2020 7:27 am

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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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Source: Beat The GMAT — Data Sufficiency | Tue Sep 22, 2020 7:27 am

swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: A bottle manufacturing company has $5$ identical machines, each of which produces bottles at the same constant rat

by swerve » Tue Sep 22, 2020 12:08 pm

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

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