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# In the first 2 hours after Meadow's self-service laundry opens, m larg

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Re: In the first 2 hours after Meadow's self-service laundry opens, m larg [#permalink]
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gmatt1476
In the first 2 hours after Meadow's self-service laundry opens, m large washing machines and n small washing machines are in continual use. Including the time for filling and emptying the washing machines, each load of laundry takes 30 minutes in a large washing machine and 20 minutes in a small washing machine. What is the total number of loads of laundry done at Meadow's self-service laundry during this 2-hour period?

(1) n = 3m
(2) 2m + 3n = 55
DS01451.01
1. If there is only 1 large and 1 small machine then, in 2 hours, the large washing machine will process 4 loads $$(120/30 = 4)$$ and the small washing machine will process 6 loads $$(120/20 = 6)$$ of laundry
2. Hence, if there were $$m$$ large washing machines and $$n$$ small washing machines, then in a 2 hour period these would process $$4m + 6n$$ loads of laundry
3. We need the value of $$4m + 6n$$ to answer the question

Option A
$$4m + 6 * 3m = 4m + 18m = 22m$$

Option B
$$2m + 3n = 55$$

Multiplying the equation by 2 yields,

$$4m + 6n = 110$$

Ans B
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Re: In the first 2 hours after Meadow's self-service laundry opens, m larg [#permalink]
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Large washer = 30 minutes per load
small washer = 20 minutes per load

In a 2 hour period, a large washer can complete 4 loads. A small washer can complete 6 loads.

We can use the equation 4m+ 6n for our total loads.

(1) n = 3m

We can't obtain the total loads from this equation. Insufficient.

(2) 2m + 3n = 55

4m + 6n = 110

SUFFICIENT

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Re: In the first 2 hours after Meadow's self-service laundry opens, m larg [#permalink]
KNOW: m Large machines --> 30 minutes each --> 4 loads in 2 hrs
n Small machines --> 20 minutes each --> 6 loads in 2 hrs

Find: 4m + 6n

STATEMENTS
(1) n = 3m

INSUFFICIENT

(2) 2m + 3n = 55
Multiple both sides by 2
=> 4m + 6n = 110

SUFFICIENT

Hope this helps.

NOTE: Make sure you read the question carefully and write down the equations and expressions on the scratch paper.
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Re: In the first 2 hours after Meadow's self-service laundry opens, m larg [#permalink]
Classic reducing equation trap option, in 2nd condition, forcing students to look for another equation. But if its proportional to the question stem, then you dont need the 2nd equation. The trick in this question is basically translating the question into this equation -> 4m + 6n

Each m laundry can do 2 washes in an hour and thus 4 washes in the 2 hour period. Similarly, n can do 6n.

Thus, Statement 2 is adequate, since we can just multiply the given info by 2 and arrive at 4m + 6n
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In the first 2 hours after Meadow's self-service laundry opens, m larg [#permalink]
gmatt1476
In the first 2 hours after Meadow's self-service laundry opens, m large washing machines and n small washing machines are in continual use. Including the time for filling and emptying the washing machines, each load of laundry takes 30 minutes in a large washing machine and 20 minutes in a small washing machine. What is the total number of loads of laundry done at Meadow's self-service laundry during this 2-hour period?

(1) n = 3m
(2) 2m + 3n = 55

DS01451.01
n = the number of small machines
m = the number of large machines

4 = the number of loads in two hrs from a large machine
6 = the number of loads in two hrs from a small machine

(2) gives us an equation for the number of machines, however this equation can be solved in more than one way:

A) if m = 20 (large machines), then n = 5 (small machines)
2*20 + 3*5 = 55 machines

B) if m = 5 (large machines), then n = 15 (small machines)
2*5 + 3*15 = 55 machines

A) gives us a total of 20*4 + 5*6 = 190 loads in two hours
B) gives us a total of 5*4 + 15*6 = 110 loads in two hours

The correct answer must be C?
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In the first 2 hours after Meadow's self-service laundry opens, m larg [#permalink]
Now I get it.

We know that the number of loads will be 4m + 6n in two hours. Therefore we dont need the number of machines if we know the solution to 4m + 6n.

4m + 6n = 110 (number of machines AND number of loads)

This was intuitively upside down for me first.

If (2) would have been like 2m + 4n = 55 we would not be able to find an answer.

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Re: In the first 2 hours after Meadow's self-service laundry opens, m larg [#permalink]
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Re: In the first 2 hours after Meadow's self-service laundry opens, m larg [#permalink]
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