Bunuel
A rental car agency owns a total of 5x cars and 2x trucks, where x is a positive integer. If the agency purchases c new cars, will the new ratio of cars to trucks be at least 3 to 1 ?
(1) c = x + 5
(2) x = 11
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.