A small factory that produces only upholstered chairs and sofas uses 1

Solution

Given:

• A small factory that produces only upholstered chairs and sofas uses 1 cushion for each chair and 4 cushions for each sofa
• The factory used a total of 300 cushions on the furniture it produced last week

To find:

• The number of sofas produced last week

Analysing Statement 1

• As per the information given in statement 1, last week the factory produced more chairs than sofas

o From this, we cannot conclude any specific number of chairs or sofas produced last week

Hence, statement 1 is not sufficient to answer

Analysing Statement 2

• As per the information given in statement 2, last week the factory produced a total of 150 chairs and sofas
• If we assume that C chairs and S sofas were produced last week, then we can write:

o C + S = 150
o C + 4S = 300
• Solving these 2 equations, we can find out the value of C and S

Hence, statement 2 is sufficient to answer

Hence, the correct answer is option B.

Answer: B
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Hi Bunuel, VeritasKarishma -

I got confused by the interpretation of this question.
Why is the total interpreted as "c + 4s" and not "c+4c."
My confusion stems from the part the that reads ".... uses 1 cushion for each chair and 4 cushions for each sofa".
Please assist in clarifying.

QUESTION:
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.

INTERPRETATION:
1. A small factory produces only chairs and sofas = (C= chairs; S= sofas)
2. Factory uses 1 cushion for each chair = (1 C= 1 cushion)
3. Factory uses 4 cushions for each sofa = (1 S = 4 cushion)
4. Total Cushions for furniture = 300
=> \(C*1 + 4*S = 300\)
or \(C+4S = 300\)

5. HOW MANY SOFAS?? (S=??)

STATEMENT 1: Last week the factory produced more chairs than sofas.
lets see what does this statement give us?
C > S
Max number of C= ??
(Always remember that Min of one function will give max of other; in case we have two function/variables)
LET S=1
So, 4S= 4
C= 300-4S= 296.
But then, C and S both can Vary

Per statement I, Min C= ?? such that C>S
How about we try C=S
in this case we get
S+4S =300
or S=C=60

Since, C>S
Therefore, S<60
SAY S=59, SO, C= 64

Note that, "C" CAN TAKE ANY VALUE FROM 64 TO 296
& "S" CAN TAKE ANY VALUE FROM 1 TO 59

Therefore, STATEMENT 1 is NOT SUFFICIENT



STATEMENT 2: Last week the factory produced a total of 150 chairs and sofas.
This implies

C+S=150

from question we have
C+4S=300

using 2 equation above we can get
S=50
C=100

Therefore, STATEMENT 2 is SUFFICIENT

Hence, B

DROP KUDOS, IF THIS HELPS!!!!

Chidinho

c is not the number of cushions.
c is the number of chairs. s is the number of sofas.

If we have c chairs, how many cushions do we have? c cushions (1 cushion per chair)
If we have s sofas, how many cushion do we have? 4s cushions (4 cushions per sofa)

So total number of cushions = c + 4s
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\(c + 4s = 300\)

(1) We can get different values; INSUFFICIENT.

(2) This statements tells us that c + s = 150 chairs and sofas

This means 300 cushions were used for 150 chairs and sofas.

\(s = 50\)

SUFFICIENT.

Answer is B.
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