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A rental car agency owns a total of 5x cars and 2x trucks, where x is 13 Mar 2020, 04:55
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67% (01:41) correct 33% (02:15) wrong based on 282 sessions

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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
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A rental car agency owns a total of 5x cars and 2x trucks, where x is 13 Mar 2020, 06:37
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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.
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A rental car agency owns a total of 5x cars and 2x trucks, where x is 15 Mar 2020, 08:25
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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

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
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A rental car agency owns a total of 5x cars and 2x trucks, where x is 15 Mar 2020, 20:12
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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

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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A rental car agency owns a total of 5x cars and 2x trucks, where x is 14 Nov 2022, 06:24
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