## Data sufficiency

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### Data sufficiency

by Newaz111 » Fri May 22, 2015 11:06 pm
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.

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by GMATGuruNY » Sat May 23, 2015 1:53 am
Newaz111 wrote: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 T = the total number of cars and n = the total number of salespeople.

Statement 1: If each of the salespeople sells 4 of the cars, 23 cars will remain unsold.
Here, the total number of cars sold by the n salespeople = 4n.
Since 23 cars remain unsold, we get:
T = 4n + 23.
If n=1, then T = (4*1) + 23 = 27.
If n=2, then T = (4*2) + 23 = 31.
Since T can be different values, INSUFFICIENT.

Statement 2: If each of the salespeople sells 6 of the cars, 5 cars will remain unsold.
Here, the total number of cars sold by the n salespeople = 6n.
Since 5 cars remain unsold, we get:
T = 6n + 5.
If n=1, then T = (6*1) + 5 = 11.
If n=2, then T = (6*2) + 5 = 17.
Since T can be different values, INSUFFICIENT.

Statements combined:
Since T = 4n + 23 and T = 6n + 5, we get:
4n + 23 = 6n + 5
18 = 2n
n = 9.
Thus, T = (4*9) + 23 = 59.
SUFFICIENT.

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by [email protected] » Tue May 26, 2015 1:16 pm
GMATGuruNY has the right solution, but on test-day you don't need the right solution to a problem like this--you can do it even faster by recognizing the n variables, n equations principle.

In order to solve for a system of equations with n different variables, you need n unique equations. As the Guru points our, the question stem gives us two distinct variables, and each statement gives us only a single equation. That means that we cannot solve for our variables with either statement alone, but the two together must be sufficient--simple as that, no solving necessary!

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### Re: Data sufficiency

by [email protected] » Wed Jun 16, 2021 4:05 am
Newaz111 wrote:
Fri May 22, 2015 11:06 pm
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.
Solution:

Question Stem Analysis:

We need to determine the number of cars to be sold by the salespeople in a car dealership. We can let the number of cars to be sold be c and the number of salespeople be s. We need to determine the value of c.

Statement One Alone:

We see that c = 4s + 23. However, we have one equation and two variables, and we can’t determine the value of c. Statement one alone is not sufficient.

Statement Two Alone:

We see that c = 6s + 5. However, we have one equation and two variables, so we can’t determine the value of c. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we have two linear equations and two variables. Note that neither equation is dependent on the other, which means that one equation is not a linear multiple of the other., Thus, we can determine the value of c (and also s). Both statements together are sufficient.