Problem Solving Pack 3, Question 4 Two printing presses begin...

Hi All,

'Rate' questions on the GMAT often require an additional calculation (to convert one type of 'unit' to another), so it's important to pay careful attention to the unit measures involved.

Here, we have two different printing presses creating different currencies/minute.

Press F produces 1,000 5-dollar bills per minute --> or 5,000 dollars in currency per minute
Press T produces 200 20-dollar bills per minute --> or 4,000 dollars in currency per minute

We're asked to determine how long it would take (in SECONDS) for Press F to create 50 dollars MORE currency than Press T.

Since we know how much currency each press produces per minute, we just have to convert the necessary units to answer the question. The difference in dollars per MINUTE is 5,000 - 4,000 = 1,000. So Press F produces 1,000 dollars MORE per MINUTE than Press T. One minute = 60 seconds, so to create 50 dollars more, we need to divide both sides of the calculation by 20...

1,000 dollars = 60 seconds
1,000/20 dollars = 60/20 seconds
50 dollars = 3 seconds

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Machine A :
1 min = 5000$ (5*1000)
1 sec = \frac{5000}{60}

Machine B:
1 min = 4000$(20*200)
1 sec = \frac{4000}{60}

Given, difference is 50$ after 'what' seconds, say x seconds.
-->\frac{5000x}{60} - \frac{4000x}{60} = 50
-->\frac{100x}{6}= 50
-->x = \frac{300}{100}
-->x = 3

Machine F produce 1000 bill/minute, which is equal to $5000/minute.
Machine T produce 200 bill/minute, which is equal to $4000/minute.
We need $50 difference, use relative speed = $50/$5000-$4000 = 50/1000 mins= 3seconds