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A certain dealership has a number of cars to be sold by its

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?

(1) If each of the salespeople sells 4 of the cars, 23 cars will remain unsold.
(2) If each of the salespeople sells 6 of the cars, 5 cars will remain unsold.

Data Sufficiency
Question: 7
Category: Algebra Simultaneous equations
Page: 153
Difficulty: 600


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New post 27 Dec 2013, 05:38
SOLUTION

A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?

(1) If each of the salespeople sells 4 of the cars, 23 cars will remain unsold --> \(# \ of \ cars=4s+23\) --> we need to know the number of salespeople (s) to answer the question. Not sufficient.

(2) If each of the salespeople sells 6 of the cars, 5 cars will remain unsold --> \(# \ of \ cars=6s+5\) --> we need to know the number of salespeople (s) to answer the question. Not sufficient.

(1)+(2) \(# \ of \ cars=4s+23=6s+5\) --> \(s=9\) --> \(# \ of \ cars=4s+23=4*9+23\). Sufficient.

Answer: C.
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A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?

(1) If each of the salespeople sells 4 of the cars, 23 cars will remain unsold.
(2) If each of the salespeople sells 6 of the cars, 5 cars will remain unsold.

Let s be the number of salespeople and cbe the number of cars sold.
To find: c

Statement 1:
\(c = 4s + 23\)
c has many values for different s.
Not sufficient.

Statement 2:
\(c = 6s + 5\)
c has many values for different s.
Not sufficient.

Combining Statements (1) and (2),
\(c = 4s +23\)
\(c= 6s + 5\)
Solving the above simultaneous equation, we get s = 9 and c = 59

Hence, answer is (C).

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A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?

(1) If each of the salespeople sells 4 of the cars, 23 cars will remain unsold.
(2) If each of the salespeople sells 6 of the cars, 5 cars will remain unsold.

Let there n be number of cars and K be the no. of sales people.

Using St 1, we can say that total no.of cars ie. n = 4K+23
We cannot find n using this information. Hence A and D ruled out

Using st2,we get that n =6K+5. Again using this equation, we cannot find n so B is ruled out

Combining both the statements, we get 4K+23= 6K+5 or 2K=18 or K =9 (No. of Sales people) and n =59.

Ans C
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New post 30 Dec 2013, 05:12
A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?

(1) If each of the salespeople sells 4 of the cars, 23 cars will remain unsold --> \(# \ of \ cars=4s+23\) --> we need to know the number of salespeople (s) to answer the question. Not sufficient.

(2) If each of the salespeople sells 6 of the cars, 5 cars will remain unsold --> \(# \ of \ cars=6s+5\) --> we need to know the number of salespeople (s) to answer the question. Not sufficient.

(1)+(2) \(# \ of \ cars=4s+23=6s+5\) --> \(s=9\) --> \(# \ of \ cars=4s+23=4*9+23\). Sufficient.

Answer: C.
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A certain dealership has a number of cars to be sold by its sale [#permalink]

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New post 10 Jan 2014, 11:09
TriColor wrote:
Q12:
A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?
(1) If each of the salespeople sales 4 of the cars, 23 cars will remain unsold.
(2) If each of the salespeople sales 6 of the cars, 5 cars will remain unsold.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


They don't really give you an equation in the stem, all we need to find is T, given that X(i)*S(j) = Cars to be sold, where i,j denote the observations: numbers of cars for observation (i) sold per seller (j). In other words, how many cars each person sells (we don't know that everyone sells equally many cars).

1) This gives us x(i) = 4 for all observations x(i). So we have 4*S = T - 23 <-- this many cars have been sold. Clearly insufficient, we have 2 variables.
2) This gives us x(i) = 6, for all x(i).. So we have 6*S = T - 5.. Also insufficient, for the same reason as 1.

1 + 2. First, note that the information in 1 and 2 is NOT the same, one is not a multiple of the other. So we have 2 equations, 2 unknowns, and thus we can solve for T.

Answer: C

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Just look at the remainder: 23 and 5 --> So the change is 23 - 5 = 18, and the change in the #of sold cars is 2 (from 4 to 6)
18/2 = 9 Salesperson just plugin this number and the answer is:
1) 9*4 + 23 = 59
2) 9*6 +5 = 59
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New post 05 Aug 2014, 09:25
Bunuel,

Are we supposed to take that the salespersons are same in both the statements?

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Bunuel,

Are we supposed to take that the salespersons are same in both the statements?


Yes.

A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?

(1) If each of the salespeople sells 4 of the cars, 23 cars will remain unsold

(2) If each of the salespeople sells 6 of the cars, 5 cars will remain unsold

"The" in both statements refer to the salespeople mentioned in the stem.
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New post 25 Oct 2015, 14:27
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Hello from the GMAT Club BumpBot!

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Hello Moderators,

This is a classical question of remainders in the DS word problem format. Do you think we should add the tag - "Remainders" to this as well?
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Re: A certain dealership has a number of cars to be sold by its   [#permalink] 06 Aug 2017, 00:43
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