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.

## Data sufficiency

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- GMATGuruNY
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Let T = the total number of cars and n = the total number of salespeople.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.

**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.

The correct answer is C.

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*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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Newaz111 wrote: ↑Fri May 22, 2015 11:06 pmA 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:

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.

**Answer: C**

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