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A small factory that produces only..........

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A small factory that produces only..........

by VJesus12 » Sat Jan 27, 2018 7:59 am
A small factory that produces only upholstered chairs and sofas uses 1 cushion for each chair and 4 cushions for each sofa. If the factory used a total of 300 cushions on the furniture it produced last week, how many sofas did it produce last week ?

(1) Last week the factory produced more chairs than sofas.
(2) Last week the factory produced a total of 150 chairs and sofas.

The OA is the option B.

Experts, can you help me here? I don't know how can I solve this DS question? I ask for your help experts.
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Source: — Data Sufficiency |

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by ErikaPrepScholar » Mon Jan 29, 2018 6:23 am
Let's use what we know to build equations. We'll set the number of chairs produced as c and the number of sofas produced as s. This means that the number of cushions used in total is $$c\ +\ 4s$$
We know that the factory used 300 cushions: $$c\ +\ 4s=300$$
We want to solve for s.

Statement 1
We know that the factory produced more chairs than sofas. This doesn't seem to tell us much, so let's plug in some easy options for s to see if we can make x + 4s = 300 with multiple values for s, where c > s.
$$If\ s=1,\ then\ c\ +\ 4\left(1\right)=300,\ and\ c\ =\ 296.$$ $$If\ s=2,\ then\ c\ +\ 4\left(2\right)=300,\ and\ c\ =\ 292.$$
So in both of those cases, c > s. This means that we can have multiple values for s (the number of sofas produced) given this statement. Insufficient.

Statement 2
We know that the factory produce 150 chairs and sofas in total, or $$c+s=150$$
So now we have two variables (c and s) with two distinct equations (c+4s=300 and c+s=150). We know that to solve for any number of variables, we need at least the same number of distinct equations as variables. So because we have two variables and two distinct equations, we should be able to solve.

We can call statement 2 sufficient now and select B as our answer, but if we wanted to solve, we could isolate c in the first equation: $$c=300-4s$$
Then plug 300-4s in for c in the second equation: $$300-4s\ +s=150$$ $$300-3s=150$$ $$3s=150$$ $$s=50$$
So the factory produced 50 sofas. Sufficient.
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