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A certain store sells chairs individually or in sets of 6

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A certain store sells chairs individually or in sets of 6  [#permalink]

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New post 18 Apr 2012, 19:52
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A
B
C
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77% (01:18) correct 23% (01:03) wrong based on 269 sessions

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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
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Re: A certain store sells chairs individually or in sets of 6  [#permalink]

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New post 19 Apr 2012, 00:56
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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?

Say the price of a set of 6 chairs is x and the price of an individual chair is y.

(1) The charge for purchasing a set of 6 chairs is 10 percent less than the charge for purchasing the 6 chairs individually --> x=0.9*6y --> two unknowns one equation. Not sufficient to calculate x.

(2) The charge for purchasing a set of 6 chairs is $20 more than the charge for purchasing the 5 chairs --> x=5y+20 --> two unknowns one equation. Not sufficient to calculate x.

(1)+(2) We have two distinct linear equations with two unknowns so we can solve for x and y. Sufficient.

Answer: C.
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Re: A certain store sells chairs individually or in sets of 6  [#permalink]

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New post 19 Apr 2012, 10:08
TomB wrote:
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


Charge for set of 6 < Charge for 6 individual chairs

Charge for purchasing set of 6 chairs?

Stmnt 1: It is insufficient because we need a number (the actual charge) but stmnt 1 only gives us data in percentages.
Stmnt 2: Again insufficient because we have no data regarding the charge of 5 chairs.

Using both together, we can derive the following equation where x = cost of one chair
5x + 20 = 90% of 6x
We can solve it to get the value of x and hence, the value of the set of 6. Hence, sufficient.

Answer (C)
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Re: A certain store sells chairs individually or in sets of 6  [#permalink]

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New post 28 Dec 2018, 09:31
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”.
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Re: A certain store sells chairs individually or in sets of 6 &nbs [#permalink] 28 Dec 2018, 09:31
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