Problem Solving

karthikpandian19 wrote:A total of "n" trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of "n", are parked in the lot?

1. 1/6 n
2. 5/12 n
3. 1/2 n
4. 8/15 n
5. 11/12 n

Let trucks = t
cars = c
t + c = n
c = t/4 implies n = 5t/4 or t = 4n/5
2t/3 are pick ups in terms of n
No. of pick ups parked in the lot = (2/3) * (4n/5) = 8n/15

The correct answer is 4.

karthikpandian19 wrote:A total of "n" trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of "n", are parked in the lot?

A. 1/6 n
B. 5/12 n
C. 1/2 n
D. 8/15 n
E. 11/12 n

We can let the number of cars = c and number of trucks = t; thus:

c + t = n

and

c = (1/4)t

Thus:

(1/4)t + t = n

t + 4t = 4n

5t = 4n

t = 4n/5

Since 2/3 of the trucks are pickups, there are (2/3)(4n/5) = 8n/15 pickups in the parking lot.

Answer: D

Hi All,

We're told that a TOTAL of N trucks and cars are parked in a lot, the number of cars is 1/4 the number of trucks and 2/3 of the trucks are pickups. We're asked for the number PICKUPS, in terms of N, that are parked in the lot. This question can be solved by TESTing VALUES. While the obvious variable is N, there are actually 3 variables (including the number of cars and the number of trucks), so we won't necessarily start with choosing a value for N...

The two fractions in the question that refer to TRUCKS are 1/4 and 2/3. The common denominator of those two fractions is 12, so let's start by setting the number of trucks equal to 12 and then calculate the values of everything else...

IF.... there are 12 TRUCKS
Pickups = (2/3)(12) = 8
Cars = (1/4)(12) = 3
Total vehicles = N = 12+3 = 15

So we're looking for an answer that equals 8 when N=15. There's only one answer that matches...

Final Answer: D

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