A certain store sells chairs individually or in sets of 6. The store

Solution:
In this question we can directly give the answer as “C”, that is the beauty of the DS questions. Even without solving the question we can answer by reading the question and analyzing the statements properly.
In this question, if we analyze the statement 1 and 2 properly we get the relation between the cost of the set of 6 chairs and the cost of the individual chair. Hence we can find the answer to the question by combining the statements.

Let’s solve the question in detail

Let the cost of the set of 6 chairs be “a”, and the cost of the individual chair be “b”.

Analysis of statement 1: The charge for purchasing a set of 6 chairs is 10 percent less than the charge for purchasing the 6 chairs individually.
From this statement, we can find the relation between “a” and “b”
i.e. \(a=0.9 ×6b\)
We have two unknowns and only one equation, we cannot get the values of “a” and “b” here.
Hence statement 1 is not sufficient to answer. We can eliminate options A and D.

Analysis of statement 2: The charge for purchasing a set of 6 chairs is $20 more than the charge for purchasing the 5 chairs
From this statement we get; \(a=5b+20\)
We have two unknowns and only one equation, we cannot get the values of “a” and “b” here.
Hence statement 2 is not sufficient to answer. We can eliminate option B.

Combining the statements 1 and 2 we get;
From statement 1; \(a=0.9 ×6b\)
From statement 2; \(a=5b+20\)
Here we have two distinct linear equations we can find the unique values of “a” and “b”.
[Note: Do not waste time-solving the equations and finding the values of “a” and “b” ]
Hence combining the statements we get the answer.

The correct answer option is “C”.

A certain store sells chairs individually or in sets of 6. The store charges less for purchasing a set of 6 chairs than for purchasing 6 chairs individually. How much does the store charge for purchasing a set of 6 chairs?

(1) The charge for purchasing a set of 6 chairs is 10 percent less than the charge for purchasing the 6 chairs individually.

(2) The charge for purchasing a set of 6 chairs is $20 more than the charge for purchasing the 5 chairs

Say , the cost per chair = x$
the cost of 6 chairs bought dividually = 6x
We need to find the cost of the set of 6 chairs = p (say)
Statement 1 :- p = 90/100 * 6x = 5.4x
since we dont know x , hence cant find p

Statement 2 :- p = 20 + 5x ; Cant find p since both are unknown.

Together , p - 5x = 20
5.4x - 5x = 20

We can find the value of x and hence 6x.
Hence C is the answer as both the statements are required.
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