A rental car agency owns a total of 5x cars and 2x trucks, where x is

Step 1: Analyze Question Stem

• Total cars = 5x
• Total trucks = 2x.

o x is a positive integer.
• Current ratio of cars to trucks = 5: 2, which can be written as 2.5: 1 (by dividing both values by 2)
• New cars purchased = c

o Thus, total cars = 5x + c
• New ratio = (5x + c) : 2x, which can be written as \(\frac{{5x + c}}{2x}: 1\) (by dividing both values by 2x)


o We need to find out if \(\frac{{5x +c}}{2x} ≥ 3\) or not

 \(5x + c ≥ 6x\)
 c ≥ x or not.

Thus, if c ≥ x, then the ratio will be at least 3 to 1. Keeping this in mind, let’s analyze each statement.

Step 2: Analyze individual statements

Statement 1: c = x + 5

• If c = x + 5, then that means c ≥ x.

o Thus, the ratio will definitely be at least 3 to 1

.
Hence, statement 1 is sufficient and we can eliminate answer options B, C, and E.

Statement 2: x = 11.

• This statement doesn’t tell us, if c ≥ x or not.

Hence, statement 2 is not sufficient and the current answer is Option A.
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Total cars = \(5x + c\) & Total trucks = \(2x\)

Question: Is \(\frac{5x + c}{2x} > \frac{3}{1}\) ?
--> Is \(5x + c > 6x\) ?
--> Is \(c > x\) ?

(1) \(c = x + 5\)
--> \(c\) is definitely greater than \(x\) --> Sufficient

(2) \(x = 11\)
We do not know anything about the value of "\(c\)" --> Insufficient

Option A

Original ratio of Cars : Trucks = 5x : 2x. That means the company already have 2.5 times cars to trucks. If c is equal or more than 50% of 2x, i.e if c is more than x than the ratio of Cars to trucks will be at least 3 to 1.

1) c is 5 more than x. Sufficient.

2) It only tells us there were 55 cars and 22 trucks before adding the new cars. Not sufficient.

A is the answer.

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