A rental car agency owns a total of $5x$ cars and $2x$ trucks, where $x$ is a positive integer. If the agency purc

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

A rental car agency owns a total of $5x$ cars and $2x$ trucks, where $x$ is a positive integer. If the agency purc

by M7MBA » Thu Aug 27, 2020 1:28 am

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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) $x = 11$

Answer: A

Source: Manhattan GMAT

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Source: Beat The GMAT — Data Sufficiency | Thu Aug 27, 2020 1:28 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

Re: A rental car agency owns a total of $5x$ cars and $2x$ trucks, where $x$ is a positive integer. If the agency

by deloitte247 » Sun Aug 30, 2020 9:14 am

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Total no. of cars = 5x
Total no. of trucks = 2x
With C new cars, the total no. of cars = 5x + c
Target question: If the agency purchases C new cars, will the new ratio of cars to trucks be at least 3 to 1?
$$Is\ 5x+c\ :\ 2x\ge3:1$$
$$\frac{5x+c}{2x}\ge\frac{3}{1}$$
$$5x+c\ge6x$$
$$c\ge6x-5x$$
$$Is\ c\ge x$$
Statement 1 => c = x + 5
This means that c>x and x will need 5 to be equal to c.
$$Therefore,\ c>x\ and\ definitely\ \frac{5x+c}{2x}>\frac{3}{1}$$
Hence, statement 1 is SUFFICIENT

Statement 2=> x = 11
This statement does not provide us with any information regarding C. So, it is not enough to arrive at the conclusion on any relationship between C and x. Hence, statement 2 is NOT SUFFICIENT/.

Since only statement 1 is sufficient, the correct option is, therefore, option A.