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Three friends rented a car for a week and divided the cost

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Three friends rented a car for a week and divided the cost [#permalink] New post 22 Mar 2010, 07:01
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Three friends rented a car for a week and divided the cost equally. What was the total cost of renting the car?

(1) if the three friends had kept the car for a second week, they could have obtained the two-week rate, which was 1.5 times the cost of a one-week rental.

(2) If a fourth friend had joined the three friends and the cost had been divided equally among the four friends, the cost to each of the original three would have been reduced by $15.
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Re: Couldn't there be mulitple answers for statement 2? [#permalink] New post 22 Mar 2010, 07:06
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hartattack11 wrote:
Three friends rented a car for a week and divided the cost equally. What was the total cost of renting the car?

(1) if the three friends had kept the car for a second week, they could have obtained the two-week rate, which was 1.5 times the cost of a one-week rental.

(2) If a fourth friend had joined the three friends and the cost had been divided equally among the four friends, the cost to each of the original three would have been reduced by $15.



Stmt1: Let say cost of car is 3x and each person paid x.
in this case total cost will be 3x+(1.5)3x = 7.5x and each will pay 2.5 x in this case. But cannot determine cost so insufficient.

Stmt2: Let say cost of car is 12x. In case three would have paid then each has to pay 12x /3 = 4x.
In case four would have paid then each has to pay 12x /4 = 3x
Diff is 15$ => 4x - 3x = 15 => x = 15
and cost of car will be 12x = 12 * 15 = 180$, hence sufficient.

So, answer is b
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Re: Couldn't there be mulitple answers for statement 2? [#permalink] New post 22 Mar 2010, 09:24
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Let x be the car rental.
Statement1: First week the rental is x.
If it is two weeks then rental would be 1.5x. But we can not find x here. Insufficient.
Statement2: If fourth frined joined then each of three friends pay 15$ less. That means the fourth friend pays = 3*15 = 45.
So each one among 4 people will pay $45. Total rental will be 4*45 = 180.

Ans is B.
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Re: Three friends rented a car for a week and divided the cost [#permalink] New post 31 Aug 2013, 22:10
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1 st in insuff clearly cause we cant derive the first week rental rate.


as per second statement, suppose the rent for car is x.
then it implies x/3 - 15 =x/4.we can find x .so suff
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Re: Couldn't there be mulitple answers for statement 2? [#permalink] New post 22 Mar 2010, 07:25
Thanks sidhu4u, I appreciate the quick response. It looks as though you have a good way of approaching these types of problems. Could you expound on your approach and the method that you use? Sometimes I just can't wrap my brain around these problems and it's just gets frustrating. Thanks again.
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Re: Couldn't there be mulitple answers for statement 2? [#permalink] New post 22 Mar 2010, 10:13
hartattack11 wrote:
Thanks sidhu4u, I appreciate the quick response. It looks as though you have a good way of approaching these types of problems. Could you expound on your approach and the method that you use? Sometimes I just can't wrap my brain around these problems and it's just gets frustrating. Thanks again.


Hey thanks a lot. For these problems, in the second statement since I knew the rent of the car has to be divided into 3 and then 4 parts i kept it as 12x i.e. the LCM of 3 and 4 so that calculations can become easy. If there would be more persons for example 5 i would have kept it 60. This saves a lot of unnecessary time to do the fractions but you need to be careful in the end for what they are asking.
And I just tried to translate the statement into equations first so that we know what all values we have and what else we need. :-D
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Re: Couldn't there be mulitple answers for statement 2? [#permalink] New post 24 Mar 2010, 09:30
Im thinking D. We agree that statement 2 is good, but from statement 1, we know that 3(a/14) = 1.5(a/7). Here, 'a' is the total cost of renting the car, and we divide by 14 to get the per-day rate for each person over a 2 week period.
Re: Couldn't there be mulitple answers for statement 2?   [#permalink] 24 Mar 2010, 09:30
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