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

Question

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

Bunuel · Accepted Answer

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.

KarishmaB · Answer

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)

KrishnakumarKA1 · Answer

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”. Hence combining the statements we get the answer. The correct answer option is “C”.

sayan640 · Answer

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.
 GMATinsight

totaltestprepNick · Answer

C https://www.youtube.com/watch?v=yCsOXFkquIk Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

MartyMurray · Answer

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?

We can answer this DS question without much formal math by using logic in the following way.

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

This statement provides only the relative difference between the charge for 6 chairs purchased individually and the charge for purchasing a set of 6 chairs.

So, neither this statement nor the passage provides any absolute number that we can use to calculate the charge for a set of 6 chairs.

Insufficient.

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

This statement provides an absolute number difference between the cost of a set of 6 chairs and the cost of 5 chairs purchased individually.

However, that difference alone is not sufficient for calculating the cost of a set of 6 chairs because neither this statement nor the passage provides information indicating how that difference of $20 relates to the cost of a set of 6 chairs.

After all, the per chair prices of individually purchased chairs and chairs purchased in a set are different, and this statement does not indicate how those two different prices are related. So, the $20 difference is between two different prices such that we don't know their relationship.

Accordingly, the $20 difference alone is not sufficient for determining either price.

Insufficient.

Statements (1) and (2) combined

In combination, the statements may not appear sufficient because (1) relates the cost of a set of 6 to the cost of 6 purchased individually whereas (2) relates the cost of a set of 6 to the cost of 5 purchased individually. However, if we consider carefully the logic of what's presented, we can see the following.

Statement (1) provides the relative relationship between the per chair cost of a set of 6 and the per chair cost of chairs purchased individually. Given what (1) says, we know that the per-chair cost of a chair in a set is 10 percent less than the per-chair cost of chairs purchased individually. So, statement (1) effectively tells us the relationship between the different per chair prices.

Statement (2) provides the absolute difference between the cost of 6 chairs purchased as a set and the cost of 5 chairs purchased individually.

Thus, simply put, in combination, the two statements provide both a relationship between the prices and an absolute difference between two different multiples of the prices.

So, the information provided by the two statements locks in the prices because only certain specific prices that differ by 10 percent will produce a difference of 20 when multiplied by 5 and 6, and we could figure out what those prices are.

We could, though we don't have to, express the relationship mathematically as follows:

5P + 20 = 6(0.9P)

We can see that, using that equation, we could determine P and, thus, 6(0.9P) to answer the question.

Sufficient.

Correct answer:   C

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

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GMAT Data Sufficiency (DS) Questions

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

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