BTGmoderatorDC wrote: ↑Wed Apr 15, 2020 5:24 pm
A rental car agency purchases fleet vehicles in two sizes: a full-size car costs $10,000, and a compact costs $9,000. How many compact cars does the agency own?
(1) The agency owns 7 total cars.
(2) The agency paid $66,000 for its cars.
OA
B
Source: Veritas Prep
Say the agency purchased x no. of full-size and y no. of compact cars.
Thus, it paid $(10,000x + 9,000y). We have to get the value of y.
(1) The agency owns 7 total cars.
x + y = 7. Can't get the unique value of y. Insufficient.
(2) The agency paid $66,000 for its cars.
10,000x + 9,000y = 66,000
10x + 9y = 66
y = (66 – 10x)/9 = 7 + (3 – 10x)/9
we know that x and y are positive integers. Thus, while keeping y a positive integer, we must try a few values of x.
The first positive integer value of x is 3 and the corresponding positive integer value of y is 5. We can certainly have other combinations, but then y would not remain a positive integer.
Thus, y = 5 compact cars. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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