Problem Solving

A Taxi Company purchases 5 cars each time and rents 3 cars each time. If purchasing 5 cars or renting 3 cars is one time, and the number of the total cars increased 14 in the past year, what is the total time of the purchasing and renting?
A 3
B 4
C 5
D 6
E 7

ketkoag wrote:A Taxi Company purchases 5 cars each time and rents 3 cars each time. If purchasing 5 cars or renting 3 cars is one time, and the number of the total cars increased 14 in the past year, what is the total time of the purchasing and renting?
A 3
B 4
C 5
D 6
E 7

5P +3R= 2T, where T is total Time.
Note that 5P+3R= Total Cars at any time. The only way this can be 14 is when P=1 and R =3. So this gives
14=2T
T=7
Choose E.

ketkoag wrote:A Taxi Company purchases 5 cars each time and rents 3 cars each time. If purchasing 5 cars or renting 3 cars is one time, and the number of the total cars increased 14 in the past year, what is the total time of the purchasing and renting?
A 3
B 4
C 5
D 6
E 7

What's the source of this question? It includes some pretty horrible wording.

I interpreted it completely differently from dtweah.

Under my interpretation, "one time" is buying 5 OR renting 3.

If the number of cars increased by 14, then we must have had one purchase and 3 rentals (since the only way to "make" 14 out of 3s and 5s is one 5 and three 3s).

Therefore, there are 4 "times"... choose B.

Again, the wording is atrocious in the question and I find it hard to believe that a real GMAT question would be so poorly written.

a friend of mine asked me this question and the question has the exact wordings that he provided to me.. i find it confusing too, but anyways got the concept..
thanks.....

IMO B as well. I didn't understand the 1st half of the second sentence, but the way I looked at it. 3*3 = 9 + 5 = 15

so in total three 3's and one 5 = 4

Stuart Kovinsky wrote:

ketkoag wrote:A Taxi Company purchases 5 cars each time and rents 3 cars each time. If purchasing 5 cars or renting 3 cars is one time, and the number of the total cars increased 14 in the past year, what is the total time of the purchasing and renting?
A 3
B 4
C 5
D 6
E 7

What's the source of this question? It includes some pretty horrible wording.

I interpreted it completely differently from dtweah.

Under my interpretation, "one time" is buying 5 OR renting 3.

If the number of cars increased by 14, then we must have had one purchase and 3 rentals (since the only way to "make" 14 out of 3s and 5s is one 5 and three 3s).

Therefore, there are 4 "times"... choose B.

Again, the wording is atrocious in the question and I find it hard to believe that a real GMAT question would be so poorly written.

I struggled between those two interpretations. Very confusing problem. Under my interpretation you get
4 when p=1 and R =3. So I really think
P+R should give total time, b/c 1 P means 5 cars and 3 Rs mean 3 cars.
But that interpretation conflicts with my set up. But nice take.